Test Bank for Essentials of Statistics for the Behavioral Sciences 10th Edition

Test Bank for Essentials of Statistics for the Behavioral Sciences 10th Edition

richard@qwconsultancy.com

1|Pa ge

Chapter 01 1. A researcher uses an anonymous survey to investigate the television-viewing habits of 100 American adolescents. The researcher plans to make an inference about the television-viewing habits of all American adolescents based on the results of the survey. The entire group of American adolescents is an example of a _____. a. sample

b. statistic c. population d. parameter ANSWER: c DIFFICULTY: Apply REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Apply 2. A researcher uses an anonymous survey to investigate the social media habits of American college students. Based on the set of 300 surveys that were completed and returned, the researcher finds that students spend an average of 2 hours each day using social media. The set of 300 students who returned surveys is an example of a _____. a. parameter

b. statistic c. population d. sample ANSWER: d DIFFICULTY: Apply REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Apply 3. In order for a researcher to obtain a random sample, they need to specifically do which of the following things? a. rule out confounding variables b. ensure that each person in the population has an equal chance of being selected for the sample c. make certain that results are valid d. make sure that each participant has an equal chance of being assigned to each experimental condition ANSWER: b DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 4. In contrast to a datum, which of the following descriptions is most consistent with the concept of data? a. the mean average of 15 participants’ individual scores on a problem-solving task b. the percentile that the score of 1 participant on a problem-solving task falls into c. the individual scores of 15 participants on a problem-solving task d. the individual score of 1 participant on a problem-solving task ANSWER: c DIFFICULTY: Analyze REFERENCES: 1.1 Statistics, Science, and Observations Copyright Cengage Learning. Powered by Cognero.

Page 1

KEYWORDS:

Bloom’s: Analyze

5. A researcher is curious about the average monthly car insurance bill for high school students in the state of Florida. If this average could be obtained, it would be an example of a _____. a. parameter

b. statistic c. population d. sample ANSWER: a DIFFICULTY: Apply REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Apply 6. Which statement below regarding populations is true? a. Populations typically are small in size. b. Populations cannot consist of non-human animal research subjects. c. The experimental research method should be used to examine populations. d. It usually is challenging to obtain data from every person in a population.

ANSWER: d DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 7. The relationship between a statistic and a sample is the same as the relationship between _____. a. a sample and a population b. a statistic and a parameter c. a parameter and a population d. descriptive and inferential statistics ANSWER: c DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 8. Organizing a set of scores in a table or computing an average to summarize a data set is an example of using ______. a. parameters b. random sampling c. descriptive statistics d. inferential statistics ANSWER: c DIFFICULTY: Remember REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Remember 9. A characteristic, usually a numerical value, which describes a sample is called a _____.

Copyright Cengage Learning. Powered by Cognero.

Page 2

a. parameter b. statistic c. variable d. constant ANSWER: b DIFFICULTY: Remember REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Remember 10. A researcher is interested in average first semester change in weight (gain or loss) for students at a local college. Thus, they record the individual change in weight for a small group of 25 freshman from this college during their first semester.

Then, the researcher calculates the average change in weight during the first semester among these 25 students. The average is an example of a ______. a. statistic

b. parameter c. variable d. constant ANSWER: a DIFFICULTY: Apply REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Apply 11. The average verbal SAT score for the entire class of incoming college freshmen in the United States is 530. However, if a sample of 20 incoming college freshmen is randomly selected from the United States, it is likely that this sample’s average verbal SAT score will not be exactly 530. This is consistent with the concept of _____. a. statistical error

b. inferential error c. sampling error d. descriptive error ANSWER: c DIFFICULTY: Apply REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Apply 12. Random assignment helps to strengthen causal inferences within an experiment by ruling out potential confounding variables otherwise introduced to an experiment due to individual differences in participants.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 13. A recent study reported that students who just finished playing a prosocial video game were more likely to help others than students who had just finishing playing a neutral or antisocial game. For this study, the kind of game given to the Copyright Cengage Learning. Powered by Cognero.

Page 3

students was the _____. a. control group

b. quasi-independent variable c. independent variable d. dependent variable ANSWER: c DIFFICULTY: Apply REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Apply 14. Which of the following statements is consistent with a research study conducted with the correlational method? a. One variable is measured, and two groups are compared. b. Two variables are measured, and two groups are compared. c. One variable is measured, and there is only one group of participants. d. Two variables are measured, and there is only one group of participants.

ANSWER: d DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 15. For a research study examining how participant gender influences support for equality in society, participant gender is an example of which kind of variable? a. quasi-independent variable

b. independent variable c. quasi-dependent variable d. dependent variable ANSWER: a DIFFICULTY: Apply REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Apply 16. For an experiment comparing the effectiveness of two different teaching methods for improving the social skills of autistic children, the dependent variable would be the _____. a. experimental methodology

b. autistic children c. teaching methods used to teach social skills d. levels of improvement in social skills among autistic children ANSWER: d DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 17. The number of absences for each student within a psychology class is an example of a _____ variable. a. nominal Copyright Cengage Learning. Powered by Cognero.

Page 4

b. discrete c. continuous d. dependent ANSWER: b DIFFICULTY: Apply REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Apply 18. The amount of time that it takes a person to solve a problem is an example of a(n) _____ variable. a. independent b. nominal c. continuous d. discrete ANSWER: c DIFFICULTY: Apply REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Apply 19. If it is impossible to divide the existing categories of a variable, then it is an example of a(n) _____ variable. a. interval b. ordinal c. discrete d. continuous ANSWER: c DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 20. Which kind of variable requires the use of real limits? a. ordinal b. interval c. discrete d. continuous ANSWER: d DIFFICULTY: Remember REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Remember 21. A doctor is measuring children’s heights to the nearest inch and obtains scores such as 40, 41, 42, and so on. What are the real limits for a score of X = 42? a. 41 and 43

b. 41.5 and 42.5 c. 41.75 and 42.25 Copyright Cengage Learning. Powered by Cognero.

Page 5

d. 41.25 and 42.75 ANSWER: b DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Analyze 22. Students in an introductory art class are classified as art majors and non-art majors. Which scale of measurement is being used to classify the students? a. nominal

b. ordinal c. interval d. ratio ANSWER: a DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 23. The participants in a research study self-report their sleep quality levels by choosing the response option that best characterizes their average sleep quality per night from the following response options: 1 = extremely low sleep quality, 2 = very low sleep quality, 3 = low sleep quality, 4 = extremely high sleep quality. Which measurement scale is being used to classify sleep quality? a. nominal

b. ordinal c. interval d. ratio ANSWER: b DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 24. Barbara is a psychologist who measures relationship satisfaction among couples by observing non-verbal behavior (e.g., smiling, mimicking partner actions). In this example, non-verbal behavior is an example of a(n) _____. a. discrete variable

b. operational definition c. construct d. real limits ANSWER: b DIFFICULTY: Apply REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Apply 25. Martha conducts a research study in which she measures how long participants spend trying to solve an impossible problem-solving task before giving up as a measure of perseverance. In this example, perseverance is an example of a(n) _____. a. operational definition Copyright Cengage Learning. Powered by Cognero.

Page 6

b. independent variable c. dependent variable d. construct ANSWER: d DIFFICULTY: Apply REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Apply 26. What additional information is obtained by measuring two individuals on an ordinal scale compared to a nominal scale?

a. whether the measurements are the same or different b. the direction of the difference c. the size of the difference d. whether the measurements are valid ANSWER: b DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 27. What additional information is obtained by measuring two individuals on an interval scale compared to an ordinal scale?

a. whether the measurements are the same or different b. the direction of the difference c. the size of the difference d. whether the measurements are reliable ANSWER: c DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 28. What scale of measurement is being used when a researcher measures the amount of car accidents that participants have been involved in during their lifetime? a. nominal

b. ordinal c. interval d. ratio ANSWER: d DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 29. After assessing two individuals’ intelligence levels using a questionnaire, a researcher can conclude that Tom’s intelligence score is 4 points higher than Bill’s. The observations that serve as the basis for this conclusion must come from a(n) _____.

Copyright Cengage Learning. Powered by Cognero.

Page 7

a. construct. b. discrete variable c. ordinal scale of measurement d. interval scale of measurement ANSWER: d DIFFICULTY: Apply REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Apply 30. Sam is a researcher measuring individuals’ attitudes toward police officers. Individuals respond to a survey question that asks them to choose the number (0-4) that best characterizes their attitudes toward police officers using the provided response options: 0 = Extremely negative attitude, 1 = Negative attitude, 2 = Neutral attitude, 3 = Positive attitude, 4 = Extremely positive attitude. In this example, attitudes toward police officers are being measured using a(n) _____ scale of measurement. a. ordinal

b. nominal c. interval d. ratio ANSWER: c DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 31. The main distinction between an interval and ratio scale of measurement is that _____. a. a score of 0 on a ratio scale does not represent the complete absence of that variable b. a ratio scale does not allow for comparisons between two scores regarding whether one score is higher or lower than the other c. a score of 0 on a ratio scale represents the complete absence of that variable

d. a ratio scale does not allow for comparisons between two scores regarding differences in size ANSWER: c DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 32. Consider the mathematical expressions of (ΣX)2 and ΣX2. A valid generalization is that _____. a. in both equations summing will be the last operation performed b. in both equations squaring will be the last operation performed c. the first equation typically will yield a higher computed value d. the first equation typically will yield a lower computed value ANSWER: c DIFFICULTY: Analyze REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Analyze Copyright Cengage Learning. Powered by Cognero.

Page 8

33. Keith conducts a research study to examine how mental fatigue influences frustration levels. He has one group of participants complete a mentally exhausting problem-solving task for ten minutes, and a second group of participants complete an easy crossword puzzle for ten minutes. Then, he observes participant reactions to being prevented from achieving a desired goal on a second unrelated task as a measure of frustration levels. In this research study, the experimental condition is _____. a. the group of participants who complete the easy crossword puzzle

b. the group of participants who complete the mentally exhausting problem-solving task c. frustration levels d. task type ANSWER: b DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 34. The mathematical expression of ΣX – 2 differs from the mathematical expression of Σ(X – 2) in each of the following ways except for which? a. The first step to solving each expression is different.

b. The final step to solving each expression is different. c. Original scores are added together in one expression but not the other. d. Squaring takes place in one equation but not the other.

ANSWER: d DIFFICULTY: Analyze REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Analyze 35. Consider the mathematical expressions of Σ(X + 2) and Σ(X + 2)2. A valid generalization is that _____. a. in both equations squaring will be the last operation performed b. in both equations squaring will be the first operation performed c. the first equation typically will yield a higher computed value d. the first equation typically will yield a lower computed value ANSWER: d DIFFICULTY: Analyze REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Analyze 36. The value of (ΣX)2 for the scores 1, 5, and 2 is 64. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 37. The value of ΣX2 for the scores 1, 0, 2, and 4 is 14.

Copyright Cengage Learning. Powered by Cognero.

Page 9

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 38. The value of ΣX + 1 for the scores 1, 0, 2, and 4 is 10. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 39. What is the value of Σ(X + 2) for the scores 1, 2, 1, and 3? a. 10 b. 8 c. 7 d. 15 ANSWER: d DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 40. What is the value of Σ(X + 1)2 for the scores 0, 1, 2, 4? a. 100 b. 39 c. 36 d. 49 ANSWER: b DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 41. Which of the following is a critical unique aspect of the experimental method when examining the relationship between two variables? a. manipulation of one variable

b. prediction of one variable c. manipulation of two variables d. prediction of two variables ANSWER: a DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 10

REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 42. Sarah is conducting a research study in which one group of participants consume one cup of coffee, whereas another group of participants consume two cups of coffee. Then, she assesses attention levels of these participants following coffee consumption. This is an example of a(n) _____ research study. a. descriptive

b. correlational c. quasi-experimental d. experimental ANSWER: d DIFFICULTY: Apply REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Apply 43. What is the value of ΣX2 for the scores 2, 4, and 5? a. 11 b. 45 c. 36 d. 33 ANSWER: b DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 44. What is the value of Σ(X + 1) for the scores 2, 3, 5? a. 6 b. 9 c. 11 d. 13 ANSWER: d DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 45. What is the value of Σ(X – 1)2 for the scores 1, 3, and 4? a. 49 b. 12 c. 13 d. 30 ANSWER: c DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation Copyright Cengage Learning. Powered by Cognero.

Page 11

KEYWORDS:

Bloom’s: Understand

46. You are instructed to subtract 2 points from each score, square each of these resulting values, and then find the sum of these squared values. How would this set of instructions be expressed in summation notation? a. Σ(X – 2)

b. Σ(X – 2)2 c. ΣX – 2 d. (X – 2)2 ANSWER: b DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 47. You are instructed to square each score and subtract four points from the sum of these squared scores. How would this set of instructions be expressed in summation notation?

a. Σ(X 2) – 4 b. (ΣX)2 – 4 c. (X – 4)2 d. ΣX 2 – 4 ANSWER: a DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 48. Of the following options, which of the following is done first in the order of operations? a. squaring b. division c. addition d. summation (Σ) ANSWER: a DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 49. Using the average score to describe a sample is an example of an inferential statistic. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 50. Using polling results from a sample of 100 registered voters in Iowa to predict the outcome of a statewide election set Copyright Cengage Learning. Powered by Cognero.

Page 12

to take place one week later is an example of using inferential statistics.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 51. A population is the set of all individuals of interest in a particular study. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Remember 52. A researcher interested in vocabulary development among toddlers obtains a sample of 2-year-old children to participate in a research study. The average vocabulary development score for the group of toddlers is an example of a parameter.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Apply 53. The goal for an experiment is to examine whether changes in one variable are responsible for causing changes in a second variable.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 54. An environmental psychologist conducts a correlational research study by assessing the energy consumption rates of students in college dorms over a one year period.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Apply 55. A recent study uncovered a correlation between gum disease and heart disease. This result indicates that gum disease Copyright Cengage Learning. Powered by Cognero.

Page 13

causes individuals to develop heart disease.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 56. A variable is a characteristic or condition that changes or has different values for different individuals. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 1.1 Statistics and Behavioral Sciences KEYWORDS: Bloom’s: Remember 57. A recent newspaper report describes that having more siblings causes increases in social skills. This is a valid statement to make given the nature of this research.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Apply 58. A research study uncovers that college graduates have higher lifetime work earnings than individuals who do not receive college degrees. This is an example of a nonequivalent groups study.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 59. A discrete variable must be measured on a nominal or an ordinal scale. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 60. Classifying people into groups based on college major is an example of measurement using an ordinal scale. a. True Copyright Cengage Learning. Powered by Cognero.

Page 14

b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 61. To determine the size of a difference between two individuals on a measured variable, a researcher must use either an interval or a ratio scale of measurement.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 62. If a researcher assesses two individuals using a measurement tool with a nominal scale, it is impossible to determine which individual has the larger score on the construct of interest.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 63. If a researcher measures two individuals on an ordinal scale, it is possible to determine how much difference exists between the two people.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 64. For statistical purposes, there usually is not much reason to differentiate between interval and ordinal scales of measurement.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 65. Participants reporting the number of cell phones they have owned in their lifetime would be an example of a discrete variable.

a. True Copyright Cengage Learning. Powered by Cognero.

Page 15

b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 66. A high school gym teacher records the weights of students prior to beginning a fitness regimen. This is an example of measuring a discrete variable.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 67. In an introductory theater class, the professor records each student’s favorite movie at the beginning of the semester.

The teacher is measuring a continuous variable.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.2 Variables and Measurement KEYWORDS: Bloom’s: Understand 68. A data set is described as consisting of N = 15 scores. Based on the notation being used, the data set is a sample and contains data from a subset of the population.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 69. To compute ΣX2, you first square the scores and then add together the squared scores. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 70. When conducting an experimental research study, it is important that researchers treat participants within experimental conditions in the same manner except for the experimental group that they are assigned to. This helps to reduce the impact of potential confounding variables otherwise introduced to an experiment due to individual differences in participants.

Copyright Cengage Learning. Powered by Cognero.

Page 16

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 71. Corey is an English teacher in high school. On the first day of class, he assesses his students’ vocabulary knowledge using a test he has created. Then, at the end of the course, he measures students’ vocabulary knowledge using the same test to examine whether vocabulary knowledge has increased for students following completion of his course. This is an example of a pre-post study.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 72. For the following scores, ΣX2 = (ΣX)2. Scores: 1, 2, 3, 4 a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 73. For the following scores, Σ(X + 1) = 18. Scores: 2, 3, 5, 6 a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 74. For the following scores, Σ(X + 1)2 = 74. Scores: 1, 2, 4, 5 a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 75. The term “margin of error” that is frequently utilized when reporting the results of political polls is consistent with the concept of parameters.

Copyright Cengage Learning. Powered by Cognero.

Page 17

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.1 Statistics and Behavioral Sciences KEYWORDS: Bloom’s: Understand 76. For the following scores, ΣX 2 = 64. Scores: 1, 2, 5 a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 77. Lauren is a psychologist interested in whether observing helpful actions while consuming media causes greater future helping behavior. She designs a research study in which one group of participants watch a pleasant television show depicting people helping others for 20 minutes, whereas a second group of participants watch a pleasant television show for 20 minutes where no helping behavior takes place. After watching the show assigned to them, participants in each group are then provided the opportunity to help another student who drops a folder of papers, and Lauren records whether each participant helps this other student or not. In this research study, the control condition is _____. a. the group of participants who watch the pleasant television show for 20 minutes where no helping behavior takes place b. the group of participants who watch the pleasant television show for 20 minutes where helping behavior takes place c. the participants that help the student who drops the folder of papers

d. the participants that do not help the student who drops the folder of papers ANSWER: a DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 78. A quasi-independent variable is most similar to and consistent with which of the following terms? a. pre-post research study b. non-equivalent groups research study c. control group d. manipulation ANSWER: b DIFFICULTY: Analyze REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Analyze 79. A datum is different from data as a term in that a datum refers to _____. a. a sample b. a population Copyright Cengage Learning. Powered by Cognero.

Page 18

c. one score d. a set of scores ANSWER: c DIFFICULTY: Understand REFERENCES: 1.1 Statistics and Behavioral Sciences KEYWORDS: Bloom’s: Understand 80. Inferential statistics allow researchers to _____. a. describe data sets b. make predictions and generalizations about populations c. operationally define a construct d. verify the validity of a research study ANSWER: b DIFFICULTY: Remember REFERENCES: 1.1 Statistics and Behavioral Sciences KEYWORDS: Bloom’s: Remember 81. A tenet of the scientific method is that _____ allow researchers to examine mental processes and behavior in an empirical, scientific manner. a. correlational research studies

b. experimental research studies c. operational definitions d. constructs ANSWER: c DIFFICULTY: Analyze REFERENCES: 1.2 Observations, Measurement, and Variables KEYWORDS: Bloom’s: Analyze 82. Statistical techniques are classified into two major categories: descriptive and inferential. Describe the general purpose of each category.

The purpose of descriptive statistics is to summarize and simplify the organization and presentation of ANSWER: data. The purpose of inferential statistics is to use the limited data from a sample as the basis for making general conclusions about the population.

DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 83. Describe the concept of “sampling error.” Note: your description should include the concepts of sample, population, statistic, parameter, and random sample.

A parameter is a value that is obtained from a population of scores and is used to describe the ANSWER: population. A statistic is a value obtained from a sample and used to describe the sample. Typically, it is impossible to obtain measurements for an entire population, so researchers must rely on information from samples. When sampling, obtaining a random sample from the population of interest such that every person in the population has an equal chance of being selected for the sample is ideal. Obtaining a random sample maximizes the likelihood that statistics computed from samples are consistent with unknown population parameters. However, samples provide only limited information about their Copyright Cengage Learning. Powered by Cognero.

Page 19

populations. Thus, sample statistics are usually not identical to their corresponding population parameters. The error or discrepancy between a statistic and the corresponding parameter is called sampling error.

DIFFICULTY: Understand REFERENCES: 1.1 Statistics, Science, and Observations KEYWORDS: Bloom’s: Understand 84. Describe the distinctions between descriptive study, correlational, and experimental research methods.

When using the descriptive study research method, a researcher measures one or more variables to ANSWER: better understand and describe each variable. In contrast, when using the correlational research method, a researcher measures two variables to examine the relationship between these two variables.

When using the experimental research method, a researcher manipulates an independent variable by assigning participants to different levels of that variable, and then subsequently measures their standing on a dependent variable. The descriptive study research method allows researchers to describe variables in isolation, correlational research methods allow researchers to understand relationships between variables, and experimental research methods allow researchers to determine whether one variable causes change in another.

DIFFICULTY: Understand REFERENCES: 1.3 Three Data Structures, Research Methods, and Statistics KEYWORDS: Bloom’s: Understand 85. Calculate each value requested for the following set of scores. Scores: 1, 3, 4 a. Σ(X – 1) b. ΣX2 c. (ΣX)2 d. Σ(X – 1)2 ANSWER:

a. 5 b. 26 c. (8)2 = 64 d. 13

DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand 86. Calculate each value requested for the following set of scores. a. b. c. d.

ANSWER:

ΣX ΣY ΣXΣY ΣXY

X Y 1 0 2 4 3 –1 5 –2 a. 11 b. 1 c. 11 d. –5

DIFFICULTY: Understand REFERENCES: 1.4 Statistical Notation KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 20

Copyright Cengage Learning. Powered by Cognero.

Page 21

Chapter 02 1. What is the total number of scores for the distribution shown in the following table?

X f 4 3 2 1

7 5 4 2 4 a.

b. 10 c. 18 d. 39 ANSWER: c DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 2. A sample of n = 12 scores ranges from a high of X = 7 to a low of X = 4. If these scores are placed in a frequency distribution table, how many X values will be listed in the first column? a. 4

b. 12 c. 3 d. 7 ANSWER: a DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 3. For the following data, N = _____.

X f 4 3 2 1

2 3 1 2 a. 8

b. 10 c. 20 d. 18 ANSWER: a DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 4. For the data in the following table, what is the value of ΣX? X f 4

1

Copyright Cengage Learning. Powered by Cognero.

Page 1

3 2 1

0 2 1 a. 4

b. 9 c. 10 d. 13 ANSWER: b DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 5. For the scores in the following table, what is the value of ΣX 2?

X f 3 2 1

1 2 4 a. 23

b. 15 c. 11 d. 21 ANSWER: d DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 6. For the following frequency distribution of quiz scores, how many individuals took the quiz?

X f 5 4 3 2 1

6 5 5 3 2 5 a.

b. 21 c. 15 d. 14 ANSWER: b DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 7. For the following distribution of quiz scores, if a score of X = 4 or lower is a failing grade, how many individuals failed the quiz?

X f 6

3

Copyright Cengage Learning. Powered by Cognero.

Page 2

5 4 3 2 1

6 5 5 3 2 a. 9

b. 14 c. 10 d. 15 ANSWER: d DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 8. For the following distribution of quiz scores, how many individuals had a score of X = 4?

X f 6 5 4 3 2 1

1 6 4 4 2 2 a. 4

b. 2 c. 5 d. 6 ANSWER: a DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 9. A researcher surveys a sample of n = 10 adults and asks them to indicate their favorite day of the week. If the data were organized in a frequency distribution table, what would be included in the first column? a. a list of adults

b. a list of days of the week c. a list of frequencies d. a list of averages ANSWER: b DIFFICULTY: Apply REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 10. A researcher surveys a sample of n = 20 college students and asks each person to identify their favorite movie. If the data were organized in a frequency distribution table, what would be included in the last column? a. a list of movies

b. a list of students Copyright Cengage Learning. Powered by Cognero.

Page 3

c. a list of frequencies d. a list of averages ANSWER: c DIFFICULTY: Apply REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 11. A set of scores ranges from a high of X = 63 to a low of X = 28. If these scores were put in a grouped frequency distribution table, what would be the best choice for the interval width? a. 2 points

b. 5 points c. 7 points d. 10 points ANSWER: b DIFFICULTY: Analyze REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Analyze 12. A set of scores ranges from a high of X = 18 to a low of X = 5. If these scores were put in a grouped frequency distribution table with an interval width of 2 points, which of the following would be the top interval in the table? a. 4-5

b. 5-6 c. 18-19 d. 17-18 ANSWER: c DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 13. Which of the following is not an appropriate interval width to use when constructing a grouped frequency distribution table?

a. 5 points b. 2 points c. 4 points d. 10 points ANSWER: c DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 14. Using the frequency distribution table below, what is the proportion of individuals that scored a 4?

X f 6 5 4

4 3 7

Copyright Cengage Learning. Powered by Cognero.

Page 4

3 2 1

2 2 2 a. 0.2

b. 0.7 c. 0.35 d. 0.1 ANSWER: c DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 15. Which statement below is correct regarding a grouped frequency distribution table? a. The ∑f cannot be determined. b. The ∑X cannot be determined. c. Interval widths should be restricted to either 10 or 20. d. The bottom score in each class interval should be divisible by 5.

ANSWER: b DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 16. For the following grouped frequency distribution table of exam scores, how many students had scores higher than X = 54?

X f 60-64 3 55-59 4 50-54 5 45-49 2 40-44 1 a. 7 b. 12 c. 8 d. 3 ANSWER: a DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 17. For the following grouped frequency distribution table of exam scores, what is the lowest score on the exam?

X f 90-99 3 80-89 1 70-79 2 Copyright Cengage Learning. Powered by Cognero.

Page 5

60-69 50-59

3 4

a. X = 70 b. X = 74 c. X = 90 d. Cannot be determined ANSWER: d DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 18. For the following grouped frequency distribution table of exam scores, how many students had scores lower than X = 75?

X f 95-99 6 90-94 3 85-89 4 80-84 5 75-79 2 70-74 1 a. 2 b. 3 c. 6 d. 1 ANSWER: d DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 19. In a grouped frequency distribution table, one interval is listed as 35-39. If the scores represent a continuous variable, what are the real limits for this interval? a. 34.5 and 39.5

b. 35.5 and 39.5 c. 34 and 40 d. 35.25 and 39.25 ANSWER: a DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 20. For the following grouped frequency distribution table, how many people had scores less than X = 14?

X f 30-34 3 Copyright Cengage Learning. Powered by Cognero.

Page 6

25-29 20-24 15-19 10-14 5-9

2 2 5 4 1

a. 5 b. 1 c. 12 d. Cannot be determined ANSWER: d DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 21. Percentile ranks are closely tied to which of the following terms? a. stem and leaf displays b. Σf c. cumulative percentages d. ΣX ANSWER: c DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 22. For the following grouped frequency distribution table, how many people have scores greater than X = 45?

X f 60-69 4 50-59 3 40-49 7 30-39 2 a. 2 b. 4 c. 7 d. cannot be determined ANSWER: d DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 23. For the following grouped frequency distribution table, what is the width of each class interval?

X f 20-29 2 30-39 5 Copyright Cengage Learning. Powered by Cognero.

Page 7

40-49 50-59

4 1

a. 9 b. 10 c. 5 d. 2 ANSWER: b DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 24. If the following grouped frequency distribution table pertaining to a continuous variable were shown in a histogram, the width of the bar above the 15-19 interval would reach from _____ to _____.

X 20-24 15-19 10-14 5-9

f 2 5 4 1

a. X = 14.5 to X = 19.5 b. X = 15.5 to X = 18.5 c. X = 15.5 to X = 19.5 d. X = 15.0 to X = 19.0 ANSWER: a DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 25. In a frequency distribution graph, frequencies are presented on the _____ and the scores (categories) are listed on the _____.

a. X axis; Y axis b. horizontal line; vertical line c. Y axis; X axis d. class interval; axis ANSWER: c DIFFICULTY: Remember REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Remember 26. Which type(s) of frequency distribution graph(s) should be used for data that come from an interval scale of measurement? a. histograms or bar graphs

b. bar graphs c. histograms or polygons Copyright Cengage Learning. Powered by Cognero.

Page 8

d. histograms, bar graphs, or polygons ANSWER: c DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 27. Which type(s) of frequency distribution graph(s) should be used for data that come from a nominal scale of measurement? a. histograms

b. bar graphs c. histograms or bar graphs d. bar graphs or polygons ANSWER: b DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 28. If a distribution of scores is shown in a bar graph, the scores were measured using a(n) _____ scale of measurement. a. nominal or ordinal b. ordinal or interval c. interval or ratio d. nominal or interval ANSWER: a DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 29. A researcher surveys a sample of n = 200 college students and asks each person to identify their favorite movie.

Which kind of graph should be used to present these results? a. histogram

b. polygon c. pie chart d. bar graph ANSWER: d DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 30. A researcher collects a sample of n = 20 Introductory Psychology textbooks and records the number of pages in each book. The results are then placed in a grouped frequency distribution table using intervals of 0-99 pages, 100-199 pages, 200-299 pages, and so on. If the results were converted into a frequency distribution graph, which kind of graph(s) would be appropriate? a. a bar graph

b. a histogram or bar graph Copyright Cengage Learning. Powered by Cognero.

Page 9

c. a histogram d. a histogram or polygon ANSWER: d DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 31. A biologist records the number and types of fish caught in a local lake during a 2- year period. The biologist reports that 7% of the fish caught during this period were trout, whereas 43% of the fish caught were bass. These reports of the number of trout and bass at this lake are examples of _____. a. cumulative frequencies

b. percentile ranks c. relative frequencies d. smooth curves ANSWER: c DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 32. After recording the final grade (A, B, C, D, F) for each individual in a class of N = 26 students, the professor would like to display the grade distribution in a frequency distribution graph. Which kind of graph should be used? a. bar graph

b. histogram c. polygon d. pie chart ANSWER: a DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 33. What is the percentile rank for a score of 4 in the frequency distribution table below?

Xf 64 55 41 33 26 11

a. 45th b. 60th c. 50th Copyright Cengage Learning. Powered by Cognero.

Page 10

d. 55th ANSWER: d DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 34. If a set of scores for a variable is displayed in a frequency distribution polygon, which scale of measurement was used to measure the variable? a. nominal or ordinal

b. ordinal or interval c. ratio or ordinal d. interval or ratio ANSWER: d DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 35. A frequency distribution graph represents frequencies associated with scores for a variable with vertical bars that have space between them. Which scale of measurement was used to measure this variable? a. nominal

b. ordinal c. interval d. ratio ANSWER: a DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 36. If a set of scores is displayed using a smooth curve, which scale of measurement was used to measure the scores? a. nominal b. interval c. nominal or ordinal d. interval or ratio ANSWER: d DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 37. For the scores shown in the following stem and leaf display, what is the highest score in the distribution?

Stem and Leaf Display 4 159 3 098 2 89103 Copyright Cengage Learning. Powered by Cognero.

Page 11

1

39

a. 43 b. 49 c. 13 d. 159 ANSWER: b DIFFICULTY: Understand REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Understand 38. How many individual scores are in the following distribution?

a. N = 5 b. N = 6 c. N = 10 d. N = 4 ANSWER: c DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 39. For the following distribution of quiz scores, what is ΣX?

Copyright Cengage Learning. Powered by Cognero.

Page 12

a. 28 b. 15 c. 23 d. 10 ANSWER: a DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 40. The normal distribution is an example of a _____. a. histogram showing data from a sample b. polygon showing data from a sample c. bar graph showing data from a population d. smooth curve showing data from a population ANSWER: d DIFFICULTY: Remember REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Remember 41. Consider the distribution of exam scores for the first exam within a college course. If the set of exam scores forms a symmetrical distribution, what can be concluded about the students’ scores? a. Most of the students had relatively high scores.

b. Most of the students had relatively low scores. c. About an equal number of students had relatively high and relatively low scores. d. A substantial number of students had very high scores and a substantial number of students had very low scores.

ANSWER: c DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs Copyright Cengage Learning. Powered by Cognero.

Page 13

KEYWORDS:

Bloom’s: Apply

42. If a set of exam scores forms a negatively skewed distribution, what can you likely conclude about the students’ scores? a. Most of the students had relatively high scores.

b. Most of the students had relatively low scores. c. About an equal number of students had relatively high and relatively low scores. d. It is not possible to draw any conclusions about students’ scores with this information.

ANSWER: a DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 43. Which term is used to describe the shape of a frequency distribution graph in which most scores pile up on the lefthand side of the graph and taper off to the right? a. symmetrical

b. positively skewed c. negatively skewed d. normal ANSWER: b DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 44. Which of the following statements pertaining to skewed and normal distributions is correct? a. A skewed distribution tends to have lower scores, and a normal distribution tends to have higher scores. b. A skewed distribution tends to have higher scores, and a normal distribution tends to have lower scores. c. A skewed distribution tends to have two tails, and a normal distribution tends to have one tail. d. A skewed distribution tends to have one tail, and a normal distribution tends to have two tails.

ANSWER: d DIFFICULTY: Remember REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Remember 45. The students in a psychology class seem to think that the midterm exam was very difficult. If they are correct, what is the most likely shape for the distribution of exam scores? a. symmetrical

b. positively skewed c. negatively skewed d. normal ANSWER: b DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 14

46. In a frequency distribution graph with negative skew, scores with the highest frequencies are _____ of the distribution. a. on the right side

b. on the left side c. in the middle d. represented at two distinct peaks ANSWER: a DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 47. What is the shape of the distribution for the following set of data? Scores: 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5 a. symmetrical b. positively skewed c. negatively skewed d. normal ANSWER: b DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 48. What is the shape of the frequency distribution for the following set of data?

Xf 55 44 32 22 11

a. symmetrical b. positively skewed c. negatively skewed d. normal ANSWER: c DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 49. What is the shape of the frequency distribution for the following set of data regarding students’ scores on a 10-item quiz?

Xf 91 Copyright Cengage Learning. Powered by Cognero.

Page 15

81 73 66 56

a. symmetrical b. positively skewed c. negatively skewed d. normal ANSWER: b DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 50. Compared to a grouped frequency distribution table, a stem and leaf plot offers the advantage of being able to identify every individual score from a data set.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Understand 51. A group of quiz scores ranges from 3 to 10, but no student had a score of X = 7. If the scores are put in a frequency distribution table, X = 7 would not be listed in the X column.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 52. It is customary to list the score categories in a frequency distribution table from the highest down to the lowest. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Remember 53. For the distribution shown in the table below, 60% of scores are less than X = 3.

Xf 52 Copyright Cengage Learning. Powered by Cognero.

Page 16

45 33 28 17

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 54. For the following frequency distribution of quiz scores, 10% of students have scores of X = 2.

Xf 54 44 36 24 12

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 55. For the following distribution of scores, 80% of individuals scored either a 2 or greater than 2.

Xf 54 43 36 23 14

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables Copyright Cengage Learning. Powered by Cognero.

Page 17

KEYWORDS:

Bloom’s: Understand

56. For the following distribution of scores that come from a continuous variable, the upper real limit for the interval that includes X = 2 is 2.

Xf 53 42 35 21 13

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 57. A grouped frequency distribution table lists one interval as 15-20. The width of this interval is 5 points. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 58. Consider the following scores: 15, 33, 41, 29, 18, 47, 21, 26. The stem and leaf display below accurately represents these scores.

Stem and Leaf Display 1 58 2 916 3 3 4 17 a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Apply 59. In a grouped frequency distribution table, scores range from X = 15 to X = 52 with class interval widths of 5. The bottom class interval should be 15-19..

a. True Copyright Cengage Learning. Powered by Cognero.

Page 18

b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 60. If a set of scores covers a range of 70 points, then the grouped frequency table for the scores should use an interval width of 7 points.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 61. A set of scores ranges from X = 13 to X = 73. If the scores were put in a grouped frequency distribution table with an interval width of 10 points, the top interval would be 73-82.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 62. In a grouped frequency distribution table, the bottom value in each class interval should be a multiple of the interval width.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 63. A set of quiz scores ranges from a low of X = 58 to a high of X = 93. If the scores are place in a grouped frequency distribution table with an interval width of 5 points, the bottom interval should be 55-60.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 64. Consider that a sample of individuals each report how many siblings they have, and this data is then put into a grouped frequency distribution table. This grouped frequency distribution table will not provide enough information to obtain a complete listing of the original responses of individuals.

Copyright Cengage Learning. Powered by Cognero.

Page 19

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 65. This grouped frequency distribution appropriately adheres to the guidelines pertaining to creating grouped frequency distribution tables.

X f 25-29 1 20-24 6 15-19 5 10-14 8 5-9 3 0-4 2 a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply 66. In general, more information is lost in a grouped frequency distribution table that has class intervals with a width of 10 than a grouped frequency distribution table that has class intervals with a width of 5.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 67. A professor records the number of students who are absent each day for the semester. Given the scale of measurement used when measuring this variable, a bar graph should be used to show the frequency distribution.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 68. Smooth curves and relative frequencies are more often used to describe population than sample data. a. True b. False ANSWER: True Copyright Cengage Learning. Powered by Cognero.

Page 20

DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 69. A sports historian records the number of times that the Minnesota Twins finished 1st, 2nd, 3rd, 4th, or 5th in their division for each of the last 20 years. If the results are presented in a frequency distribution graph, then a histogram should be used.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 70. No space is left between adjacent bars in a histogram. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Remember 71. A set of scores ranging from a high of 41 to a low of 5 is organized into a grouped frequency distribution table using an interval width of 5 points. If the distribution is shown in a graph, then a bar graph should be used.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 72. The classrooms in a Psychology department are numbered from 200 to 210. The department chair records the number of classes held in each room during the spring semester. If the results needed to be presented in a frequency distribution graph, the professor should use a bar graph.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 73. Consider the following scores pertaining to a data set: 12, 30, 40, 25. To complete a stem and leaf display, leaves of 2, 0, 0, and 5 should be created.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 21

ANSWER: True DIFFICULTY: Apply REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Apply 74. A bar graph is constructed so that adjacent bars touch. a. True b. False ANSWER: False DIFFICULTY: Remember REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Remember 75. A distribution of scores on a driver’s license test forms is normally shaped. This is an example of a symmetrical distribution.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 76. In August in Florida, the daily high temperatures are typically high with only a few relatively cool days. A frequency distribution graph showing daily average temperatures in Florida for August would probably form a negatively skewed distribution.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 77. Consider the following scores pertaining to a data set: 22, 31, 43, 19. To complete a stem and leaf display, stems of 2, 1, 3, and 9 should be created.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Apply 78. Consider the following scores: 10, 19, 21, 28, 26, 22, 30, 15, 18, 20. The stem and leaf display below accurately depicts this data.

Stem and leaf display Copyright Cengage Learning. Powered by Cognero.

Page 22

1 0958 2 08620 3 1 a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Apply 79. In a negatively skewed distribution, scores either pile up on the left side of the distribution or pile up on the right side of the distribution.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 80. For the scores shown in the following stem and leaf display, how many individuals had scores in the 20s?

Stem and Leaf Display 4 674 3 09817 2 891652 1 39 a. b. c. d.

ANSWER: b DIFFICULTY: Understand REFERENCES: 2.4 Stem and Leaf Displays KEYWORDS: Bloom’s: Understand 81. A set of scores ranges from a high of X = 45 to a low of X = 11. If these scores were placed in an appropriately designed grouped frequency distribution table, which of the following would be the bottom interval in the table? a. 40-45

b. 40-44 c. 10-15 d. 10-14 ANSWER: d DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 23

82. Find each value requested for the set of scores in the following frequency distribution table. a. N X f b. ΣX 5 3 c. ΣX2 4 4 3 2 2 1 1 3 a. N = 13 ANSWER: b. ΣX = 42 c. ΣX2 = 164

DIFFICULTY: Understand REFERENCES: 2.1 Frequency Distributions and Frequency Distribution Tables KEYWORDS: Bloom’s: Understand 83. Briefly explain the appropriate manners in which to graphically represent data measured using a nominal, ordinal, interval, or ratio scale of measurement.

Data measured using either a nominal or ordinal scale of measurement should be graphically ANSWER: represented using a bar graph. Data measured using either an interval or ratio scale of measurement should be graphically represented using either a histogram or polygon.

DIFFICULTY: Understand REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Understand 84. For the following scores: a. Construct a frequency distribution table. b. Sketch a histogram of the frequency distribution.

1, 2, 3, 1, 1, 4, 2 1, 5, 6, 2, 2, 1, 3 ANSWER: a.

X f 6 1 5 1 4 1 3 2 2 4 1 5 b.

Copyright Cengage Learning. Powered by Cognero.

Page 24

DIFFICULTY: Apply REFERENCES: 2.3 Frequency Distribution Graphs KEYWORDS: Bloom’s: Apply 85. For the following scores, construct a grouped frequency distribution table using an appropriate width. Based on the table, what is the shape of the distribution?

62, 73, 91, 92, 90, 94, 87, 81, 68, 80, 92, 85 63, 92, 94, 78, 84, 90, 80, 74, 82, 92, 93, 73

ANSWER:

X f Negatively skewed 60-64 2 65-69 1 70-74 3 75-79 1 80-84 5 85-89 2 90-94 10 DIFFICULTY: Apply REFERENCES: 2.2 Grouped Frequency Distribution Tables KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 25

Chapter 03 1. What is the mean for the following sample of scores? Scores: 2, 4, 5, 9 a. 20 b. 4.5 c. 4 d. 5 ANSWER: d DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 2. A person’s phone bills for the last three months were $20, $75, and $55, respectively. What was the mean average amount for the three phone bills? a. $60

b. $50 c. $55 d. $65 ANSWER: b DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 3. What is the mean average for the following set of quiz scores? Scores: 4, 5, 9, 2, 3, 7 a. 10 b. 4 c. 5 d. 6 ANSWER: c DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 4. A population of N = 6 scores has ΣX = 42. What is the population mean? a. µ = 8 b. µ = 4 c. µ = 6 d. µ = 7 ANSWER: d DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 5. What is the mean for the population of scores presented in the frequency distribution table below?

Copyright Cengage Learning. Powered by Cognero.

Page 1

X

f

8

3

7

3

6

0

5

2

4

1

3

2

2

2

1

3

a. µ = 3.50 b. µ = 4.50 c. µ = 5.00 d. µ = 4.25 ANSWER: b DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 6. What is the mode for the population of scores presented in the frequency distribution table below?

X

f

5

1

4

4

3

3

2

4

1

2

a. 3 b. 4 c. 2 d. 2 and 4 ANSWER: d DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 7. A population with a mean of µ = 9 has ΣX = 54. How many scores are in the population? a. N = 9 b. N = 7 c. N = 6 Copyright Cengage Learning. Powered by Cognero.

Page 2

d. N = 14 ANSWER: c DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 8. A sample of n = 10 scores has a mean of M = 3. What is ΣX for this sample? a. 30 b. 3.33 c. 0.3 d. 13 ANSWER: a DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 9. After 2 points are subtracted from every score in a sample of size n = 4, the new sample mean is found to be M = 18.

What was the mean for the original sample? a. M = 14

b. M = 22 c. M = 16 d. M = 20 ANSWER: d DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 10. After every score in a sample of n = 5 is multiplied by 2, the mean is calculated and found to be M = 8. What was the mean of the original sample? a. M = 10

b. M = 4 c. M = 16 d. M = 3 ANSWER: b DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 11. A population has a mean of µ = 15. If 6 points are added to each score, what is the mean for the new distribution of scores? a. µ = 9

b. µ = 15 c. µ = 21 d. µ = 11 Copyright Cengage Learning. Powered by Cognero.

Page 3

ANSWER: c DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 12. A sample of size n = 5 has a mean of M = 10. If each score in the sample is multiplied by 3, then what is the mean for the new distribution? a. M = 50

b. M = 30 c. M = 10 d. M = 3.33 ANSWER: b DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 13. One sample with n = 4 scores has a mean of M = 12, and a second sample with n = 6 scores has a mean of M = 8. If the two samples are combined, what is the mean for the combined set of scores? a. M = 4.8

b. M = 9.6 c. M = 48 d. M = 10 ANSWER: b DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 14. A sample of n = 5 scores has a mean of M = 7. After one score is removed from the sample, the mean for the remaining scores is found to be M = 6. What was the score that was removed? a. X = 6

b. X = 9 c. X = 11 d. Cannot be determined from the information provided.

ANSWER: c DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 15. A sample of n = 6 scores has a mean of M = 5. One person with a score of X = 19 is added to the distribution. What is the mean for the new set of scores? a. M = 5

b. M = 6 c. M = 7 d. M = 8 Copyright Cengage Learning. Powered by Cognero.

Page 4

ANSWER: c DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 16. In a sample of n = 6 scores the largest score is X = 10, and the mean is M = 6. If the largest score is changed from X = 10 to X = 22, then what is the value of the new mean? a. M = 6

b. M = 7 c. M = 8 d. M = 9 ANSWER: c DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 17. Which of the following actions will always change the value of the mean? a. changing the value of one score b. adding a new score to the distribution c. removing a score from the distribution d. adding the same amount to each score in a distribution ANSWER: a DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 18. A set of N = 4 scores has a mean of µ = 11. If 12 points are subtracted from one of the scores, what is the new value for the population mean? a. µ = 8

b. µ = 11 c. µ = 10 d. µ = 9 ANSWER: a DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 19. Which of the following phrases is not consistent with central tendency as a statistical measure? a. average score b. most typical score c. spread of scores d. middle score ANSWER: c Copyright Cengage Learning. Powered by Cognero.

Page 5

DIFFICULTY: Understand REFERENCES: 3.1 Overview KEYWORDS: Bloom’s: Understand 20. Which statement below is consistent with computing a weighted average of two individual samples? a. A computed weighted average will always be closer to the mean average of the larger sample than the mean average of the smaller sample. b. A computed weighted average will always be closer to the mean average of the smaller sample than the mean average of the larger sample. c. A weighted average will always equal the average of the two individual sample means.

d. This cannot be determined from the information provided.

ANSWER: a DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 21. A sample has a mean of M = 50. If one new person is added to this sample, what effect will this have on the sample mean?

a. The sample mean will increase. b. The sample mean will decrease. c. The sample mean will remain the same. d. This cannot be determined from the information provided.

ANSWER: d DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 22. A sample of n = 5 scores has a mean of M = 10. One new score is added to the sample, and the new mean is calculated to be M = 9. What is the value of the new score? a. X = 5

b. X = 5.5 c. X = 4.5 d. X = 4 ANSWER: d DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 23. The mode is the only measure of central tendency that is appropriate to utilize for a variable measured with which scale of measurement? a. ordinal

b. nominal c. interval d. ratio Copyright Cengage Learning. Powered by Cognero.

Page 6

ANSWER: b DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 24. Consider the two frequency distribution tables below that each pertain to distinct samples. What is the weighted average of these samples when combined?

Sample A Xf 62 50 41 32 24 11 Sample B Xf 52 45 31 20 15

a. M = 2 b. M = 3 c. M = 4 d. M = 5 ANSWER: b DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 25. What is the median for the data represented in the histogram below?

Copyright Cengage Learning. Powered by Cognero.

Page 7

a. 1.80 b. 3 c. 2 d. 1.50 ANSWER: c DIFFICULTY: Apply REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Apply 26. A population of N = 5 scores has a mean of µ = 8. If one score with a value of X = 4 is removed from the population, what is the value for the new mean? a. µ = 9

b. µ = 8 c. µ = 7 d. µ = 10 ANSWER: a DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 27. The mode is similar to the median as a measure of central tendency in that _____. a. its value must correspond to an actual score in the data set b. it balances the distance between scores above and below its value c. it represents the middle of a distribution d. there are no symbols used to differentiate between whether its value(s) pertains to populations or samples ANSWER: d DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 8

28. What is the value of the median for the following set of scores? Scores: 1, 4, 6, 7, 9, 15, 15, 16, 25, 30 a. 11 b. 8 c. 12 d. 15 ANSWER: c DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 29. What is the median for the following set of scores? Scores: 1, 5, 11, 12, 20 a. 5 b. 11.5 c. 11 d. 8 ANSWER: c DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 30. What is the median for the population of scores presented in the frequency distribution table below?

Xf 57 42 31 21 13

a. 4.5 b. 5 c. 3.5 d. 4 ANSWER: a DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 31. What is the median for the population of scores presented in the frequency distribution table below?

Xf 52 43 Copyright Cengage Learning. Powered by Cognero.

Page 9

32 21 11

a. 3 b. 4 c. 3.5 d. 4.5 ANSWER: b DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 32. Which statement below must be false regarding a distribution of scores? a. 75% of the scores are above the mean b. 75% of the scores are above the median c. 75% of the scores are above the mode d. 75% of the scores are the same value as the mode ANSWER: b DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 33. What is the mode for the following sample of n = 11 scores? Scores: 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7 a. 6 b. 3 c. 2 d. 2.5 ANSWER: c DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 34. What is the mode for the population of scores shown in the frequency distribution table?

Xf 53 44 33 23 12

a. 2 Copyright Cengage Learning. Powered by Cognero.

Page 10

b. 3 c. 3.5 d. 4 ANSWER: d DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 35. Which of the following statements must be false regarding a distribution of scores? a. No individual has a score exactly equal to the mean. b. No individual has a score exactly equal to the median. c. No individual has a score exactly equal to the mode. d. All of these statements are false.

ANSWER: c DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 36. Which statement below is true? a. It is possible for a distribution of scores to have two means. b. It is possible for a distribution of scores to have two means or two medians. c. It is possible for a distribution of scores to have two modes. d. It is possible for a distribution of scores to have two medians or two modes.

ANSWER: c DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 37. A researcher assesses eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements of eye color collected for this sample? a. Mean

b. Median c. Mode d. Any of the three measures of central tendency could be used ANSWER: c DIFFICULTY: Apply REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Apply 38. A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students.

However, one of the participants fails to solve the problems so the researcher has an undetermined score. What is the best measure of central tendency for these data? a. the mean

b. the median Copyright Cengage Learning. Powered by Cognero.

Page 11

c. either the mean or mode d. either the mean or median ANSWER: b DIFFICULTY: Apply REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Apply 39. One item on a questionnaire asks students how many times per day in a typical week they make a call on their cell phones. The responses for a sample of n = 12 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?

Xf 5+ 5 44 31 20 12 00

a. the mean b. the median c. the mean or median d. the mean or mode ANSWER: b DIFFICULTY: Apply REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Apply 40. Under which circumstance below is the median likely to be a better measure of central tendency than the mean? a. with a symmetrical distribution b. with an extremely skewed distribution c. when the data consist of nominal measurements d. when the data come from a continuous variable.

ANSWER: b DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 41. What is the preferred measure of central tendency for scores measured on an ordinal scale? a. the mean b. the median c. either the median or mean d. the mode Copyright Cengage Learning. Powered by Cognero.

Page 12

ANSWER: b DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 42. A sample of scores has a mean of M = 26, a median of 28, and a mode of 29. What is the most likely shape for the sample distribution? a. symmetrical

b. positively skewed c. negatively skewed d. cannot be determined from the information given ANSWER: c DIFFICULTY: Apply REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Apply 43. An introductory to psychology professor has students report their major on the first day of classes. Then, the professor decides to determine the major that is most representative of the students in their class. Which measure of central tendency should they utilize? a. the mean

b. the median c. the mode d. the weighted average ANSWER: c DIFFICULTY: Apply REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Apply 44. Consider a 100-point college exam for which there is a large number of students that perform extremely well, as well as a large number of students that perform extremely poorly. Which statement below is true? a. The distribution of scores is probably symmetrical.

b. The distribution of scores probably has a mean close to 75. c. The distribution of scores is probably bimodal. d. The distribution of scores probably has a median close to 75.

ANSWER: c DIFFICULTY: Apply REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Apply 45. The value of X = 9 in the distribution below is the _____.

Copyright Cengage Learning. Powered by Cognero.

Page 13

a. minor mode. b. major mode. c. median. d. mean.

ANSWER: a DIFFICULTY: Apply REFERENCES: 3.4 Mode KEYWORDS: Bloom’s: Apply 46. A distribution of scores has no mode and the same median and mean values. This indicates that the _____. a. same frequencies of individuals scored for every possible X value in the distribution b. distribution is negatively skewed c. distribution is positively skewed d. mean and median are large values within the possible range of the distribution ANSWER: a DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Understand 47. A distribution of scores is positively skewed. Which is the most probable order, from smallest to largest, for the three measures of central tendency? a. Mean, median, mode

b. Mode, median, mean c. Mean, mode, median d. Median, mean, mode ANSWER: b DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Understand 48. Which of the following statements is true regarding the mode as a measure of central tendency? a. The mode value has to be calculated, just as mean and median values have to be calculated.

Copyright Cengage Learning. Powered by Cognero.

Page 14

b. The mode value is often useful to report as supplementary information in conjunction with the mean or median value. c. The mode value may not necessarily be a score that is in a distribution of scores.

d. The mode value often is more valuable to report for interval and ratio data.

ANSWER: b DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 49. For a perfectly symmetrical distribution, which relationship is always true? a. mean = median b. mean = mode c. median = mode d. mean = median = mode ANSWER: a DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Understand 50. A student takes a 10-point quiz each week in statistics class. If the student’s quiz scores for the first three weeks are 10, 8, and 8, then the mean score is M = 9.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 51. A sample of n = 6 scores has ΣX = 48. This sample has a mean of M = 6. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 52. A sample of n = 8 scores has a mean of M = 16. For this sample, ΣX = 128. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

53. A sample with a mean of M = 20 has ΣX = 120. There are n = 5 scores in this sample. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 54. For the scores in the following frequency distribution table, the mean is M = 3.

Xf 53 41 33 23 12

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 55. The median is considered to be the “balance point” for a distribution because it is the score for which the total distance between scores below the median and the median is identical to the total distance between scores above the median and the median.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 56. In a sample of n = 5 scores, if four scores are each above the mean by 1 point, then the fifth score is above the mean by 4 points.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 57. A sample has a mean of M = 30. If a new score of X = 45 is added to the sample, then the sample mean would Copyright Cengage Learning. Powered by Cognero.

Page 16

increase.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 58. The median is the value in a distribution of scores that separates the lowest 50% of scores from the highest 50% of scores.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.2 The Median KEYWORDS: Bloom’s: Understand 59. The major mode in the distribution of scores below is X = 5.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Apply 60. In a symmetrical distribution, the right side of the graph is a mirror image of the left side of the graph. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of the Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 17

61. Regardless of whether a distribution of scores that is symmetrically shaped has one mode or two modes, the mean value tends to be similar to the median value.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of the Distribution KEYWORDS: Bloom’s: Understand 62. The median is the best measure of central tendency to use in order to describe the distribution of scores below pertaining to the average daily coffee consumption of a sample of individuals.

Daily Cups of Coffee Consumed (X) f 4 or more 2 3 2 2 1 1 3 0 3 a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Apply 63. A sample of n = 5 scores has a mean of M = 4. After one new score is added to the sample, the new mean is calculated to be M = 6. The new score was X = 12.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 64. A sample of n = 6 scores has a mean of M = 10. After one score is removed from the sample, the mean is calculated to be M = 8. The removed score must have a value less than 10.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 65. A sample of n = 20 scores has a mean of M = 30. A second sample of n = 10 scores has a mean of M = 50. If the two samples are combined, the weighted sample mean will be less than 40.

Copyright Cengage Learning. Powered by Cognero.

Page 18

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Apply 66. For a 100-point exam, a score of X = 75 is above the median. a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Apply 67. If a sample has an even number of scores, at least one individual will have a score exactly equal to the median. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 68. A sample has n = 6 scores: 1, 1, 3, 4, 6, and 8. The median for this sample is 3.5. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 69. For any distribution of sample scores, at least one individual will have a score exactly equal to the mode. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.4 The Mode KEYWORDS: Bloom’s: Understand 70. It is possible for a distribution to have more than one median. a. True b. False ANSWER: False Copyright Cengage Learning. Powered by Cognero.

Page 19

DIFFICULTY: Understand REFERENCES: 3.3 The Median KEYWORDS: Bloom’s: Understand 71. It is possible to have a distribution of scores where no individual has a score exactly equal to the mean. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.2 The Mean KEYWORDS: Bloom’s: Understand 72. A researcher records the list of finishes (e.g., 1st, 2nd, 3rd, 4th) for a track team throughout their season. The mean is the best measure of central tendency to report in this circumstance to describe the most typical finish for this track team.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Apply 73. Skewed distributions, open-ended distributions, or discrete variables are situations for which the mean cannot be calculated or for which the mean may not be the best measure of central tendency to utilize.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 74. For a severely skewed distribution, the mean often provides a better measure of central tendency than the median or the mode.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 75. For a distribution that measures a discrete variable with an even number of scores, the median is usually just as valid as the mode to use as a measure of central tendency.

a. True b. False ANSWER:

False

Copyright Cengage Learning. Powered by Cognero.

Page 20

DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 76. It is possible for the value of the median to be greater than the value of the mode. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Understand 77. A distribution of scores has a mean of 52, a median of 54, and a mode of 56. Based on this information, it appears that the distribution is symmetrical.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Apply 78. If a positively skewed distribution has a mean of 40, then the median and the mode are probably both greater than 40. a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Apply 79. For a negatively skewed distribution, the mode is usually larger than either the median or the mean a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 3.5 Central Tendency and the Shape of a Distribution KEYWORDS: Bloom’s: Understand 80. What is the purpose of determining a measure of central tendency?

The purpose of determining a measure of central tendency is to identify the center of the distribution ANSWER: and find the single score that best represents the entire distribution.

DIFFICULTY: Understand REFERENCES: 3.1 Overview KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 21

81. Explain why it is necessary to have several different procedures for determining and calculating central tendency.

No single method for determining central tendency will always produce a score that is representative of ANSWER: the center of the distribution in every situation. Although the mean works well in most situations, there are circumstances in which the mean is not representative or cannot be calculated. For instance, the median is often a better measure of central tendency to use in skewed or open-ended distributions, when data is measured using an ordinal or nominal scale of measurement, or when a variable is discrete in nature. The mode is often a better measure of central tendency to use for discrete variables or variables measured using a nominal scale of measurement.

DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand 82. Compute the mean, median, and mode for the set of scores presented in the following frequency distribution table.

Xf 71 64 53 41 31 22 13 The mean is 60/15 = 4, the median is 5, and the mode is 6.

ANSWER: DIFFICULTY: Understand REFERENCES: 3.4 The Mode

83. a. Determine the best measure of central tendency to use to represent the data in the histogram below, and justify your response. b. Calculate the measure of central tendency reported for part a.

ANSWER: a. The median is the best measure of central tendency to use given that the data depicted in this histogram is positively skewed. b. 2 Copyright Cengage Learning. Powered by Cognero.

Page 22

84. A line graph can be used to graphically represent mean or median values for a data set when the values of a variable are measured using either a(n) _____ scale of measurement. a. nominal or ratio

b. nominal or ordinal c. ordinal or interval d. interval or ratio ANSWER: d DIFFICULTY: Understand REFERENCES: 3.6 Selecting a Measure of Central Tendency KEYWORDS: Bloom’s: Understand

Copyright Cengage Learning. Powered by Cognero.

Page 23

Chapter 04 1. Which of the following is a consequence of increasing variability? a. The distance from one score to another tends to increase, and a single score tends to provide a more accurate representation of the entire distribution. b. The distance from one score to another tends to increase, and a single score tends to provide a less accurate representation of the entire distribution. c. The distance from one score to another tends to decrease, and a single score tends to provide a more accurate representation of the entire distribution. d. The distance from one score to another tends to decrease, and a single score tends to provide a less accurate representation of the entire distribution.

ANSWER: b DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 2. What is the range for the following set of scores obtained for a discrete variable for which 0 is not a possible score?

Scores: 5, 7, 9, 13 a. 4 points

b. 5 points c. 8 points d. 13 points ANSWER: c DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 3. For the following scores, which action will increase the range? Scores: 2, 6, 11, 15 a. subtract 1 point from the score X = 2 b. subtract 3 points from the score X = 6 c. subtract 4 points from the score X = 11 d. subtract 3 points from the score X = 15 ANSWER: a DIFFICULTY: Apply REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Apply 4. In a population of N = 10 scores obtained for a discrete variable for which 0 is not a possible score, the smallest score is X = 8 and the largest is X = 20. What is the range for this population? a. 8

b. 10 c. 12 d. 20 ANSWER: c DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 1

REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 5. A sample consists of n = 16 scores. How many of the scores are used to calculate the range? a. 2 scores b. 4 scores c. 8 scores d. 16 scores ANSWER: a DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 6. Which set of scores below has the smallest standard deviation? a. 11, 17, 31, 53 b. 5, 11, 42, 22 c. 145, 143, 145, 147 d. 27, 105, 10, 80 ANSWER: c DIFFICULTY: Apply REFERENCES: 4.2 Defining Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 7. One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.

Which set of sample statistics would present the clearest picture of a real difference between the two treatments?

a. M1 = 36, M2 = 40, and both variances = 43 b. M1 = 36, M2 = 40, and both variances = 6 c. M1 = 38, M2 = 40, and both variances = 43 d. M1 = 38, M2 = 40, and both variances = 6 ANSWER: b DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 8. A set of scores ranges from a low of X = 25 to a high of X = 33 and has a mean of 29. Which of the following is the most likely value for the standard deviation for these scores? a. 2 points

b. 5 points c. 10 points d. 34 points ANSWER: a DIFFICULTY: Apply REFERENCES: 4.2 Defining Variance and Standard Deviation Copyright Cengage Learning. Powered by Cognero.

Page 2

KEYWORDS:

Bloom’s: Apply

9. What is the value of SS (sum of squared deviations) for the following population? Population: 1, 1, 1, 5 a. 2 b. 7 c. 12 d. 6 ANSWER: c DIFFICULTY: Understand REFERENCES: 4.2 Defining Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 10. Compute the interquartile range for the following scores that represent a continuous variable: 1, 2, 2, 2, 4, 5, 10, 12 a. 2 b. 5.5 c. 4.5 d. 11 ANSWER: b DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 11. Which of the following is not a unique advantage of the interquartile range as measure of variability? a. The interquartile range is less influenced than the range by extreme scores. b. The interquartile range can be utilized in open-ended distributions. c. The interquartile range can be used for data measured with an ordinal scale of measurement. d. The interquartile range can be used for data measured with a ratio scale of measurement.

ANSWER: d DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 12. A population of N = 5 scores has a mean of µ = 20 and a standard deviation of σ = 4. Which of the following is the correct interpretation of the standard deviation? a. The average distance of scores from the mean of µ = 20 is 5 points.

b. The average distance of scores from the mean of µ = 20 is 1 point. c. The average distance of scores from the mean of µ = 20 is 4 points. d. The average squared distance of scores from the mean of µ = 20 is 4 points.

ANSWER: c DIFFICULTY: Understand REFERENCES: 4.2 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 13. Why do deviation scores have to be squared before calculating the standard deviation?

Copyright Cengage Learning. Powered by Cognero.

Page 3

a. Squaring is necessary when calculating inferential statistics. b. If deviation scores are not squared, then the average distance from the mean will always equal 0. c. Squaring deviation scores allows for degrees of freedom to be calculated. d. If deviation scores are not squared, then the interquartile ranges are incalculable.

ANSWER: b DIFFICULTY: Understand REFERENCES: 4.2 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 14. It is only appropriate and possible to calculate the variance and standard deviation as measures of variability for variables measured using a(n) _____ scale of measurement. a. ordinal

b. ratio c. interval or ratio d. ordinal or nominal ANSWER: c DIFFICULTY: Understand REFERENCES: 4.2 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 15. When calculating the standard deviation, it is customary to round to _____ decimal place(s). a. 3 b. 4 c. 1 d. 2 ANSWER: d DIFFICULTY: Understand REFERENCES: 4.2 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 16. A population has SS = 100 and σ2 = 5. How many scores are in the population? a. 25 b. 20 c. 200 d. 400 ANSWER: b DIFFICULTY: Apply REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Apply 17. Which of the following symbols identifies the population standard deviation? a. s b. N Copyright Cengage Learning. Powered by Cognero.

Page 4

c. σ d. σ2 ANSWER: c DIFFICULTY: Remember REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Remember 18. A population has SS = 100 and σ2 = 4. What is the value of Σ(X – µ) for the population? a. 0 b. 25 c. 100 d. 400 ANSWER: a DIFFICULTY: Apply REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Apply 19. A population of N = 10 scores has µ = 21 and σ = 3. What is the population variance? a. 7 b. 100 c. 2 d. 9 ANSWER: d DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 20. The sum of the squared deviation scores is SS = 50 for a population of N = 10 scores. What is the variance for this population? a. 500

b. 5 c. 4 d. 50 ANSWER: b DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 21. What is the variance for the following population of scores? Scores: 2, 5, 6, 3 a. 2.50 b. 3.33 c. 4 d. 5 Copyright Cengage Learning. Powered by Cognero.

Page 5

ANSWER: a DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 22. A population of N = 10 scores has a standard deviation of σ = 2. What is the value of SS, the sum of the squared deviations, for this population? a. 40

b. 20 c. 5 d. 12 ANSWER: a DIFFICULTY: Apply REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Apply 23. In which circumstance is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a population? a. when the population mean is a whole number

b. when the population mean is not a whole number c. when the population variance is a whole number d. when the population variance is not a whole number ANSWER: b DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 24. What is the value of SS (sum of squared deviations) for the following sample? Scores: 2, 4, 5, 9 a. 26 b. 5 c. 10 d. 16 ANSWER: a DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 25. Which response option below is the standard deviation of the sample of n = 11 scores depicted below?

Copyright Cengage Learning. Powered by Cognero.

Page 6

a. s = 1.91 b. s = 2.61 c. s = 2.49 d. s = 4 ANSWER: b DIFFICULTY: Apply REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Apply 26. A sample of n = 4 scores, has ΣX = 4, and ΣX2 = 32. What is the value of SS for this sample? a. 8 b. 14 c. 24 d. 28 ANSWER: d DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 27. Which response option below is consistent with the standard deviation for the population of N = 10 scores depicted below?

Copyright Cengage Learning. Powered by Cognero.

Page 7

a. 2.53 b. 3.00 c. 2.67 d. 3.16 ANSWER: a DIFFICULTY: Apply REFERENCES: 4.2 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Apply 28. A sample of n = 6 scores has SS = 40. If these same scores were a population, then the SS for the population would be _____.

a. 40 b. greater than 40 c. less than 40 d. This is impossible to determine without additional information ANSWER: a DIFFICULTY: Apply REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Apply 29. What the variance for the following sample of n = 3 scores? Scores: 1, 4, 7 a. 6 b. 9 c. 3 d. 15 ANSWER: b DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 30. What are the values for SS and variance for the following sample of n = 4 scores? Scores: 1, 3, 0, 4 a. SS = 10 and variance = 2.5 b. SS = 10 and variance = 3.33 c. SS = 12 and variance = 2.5 d. SS = 12 and variance = 3.33 ANSWER: b DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 31. Which symbol below identifies the sample variance? a. s b. s2 Copyright Cengage Learning. Powered by Cognero.

Page 8

c. σ d. σ 2 ANSWER: b DIFFICULTY: Remember REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Remember 32. A sample of n = 15 scores has M = 20 and s2 = 9. What is the sample standard deviation? a. 3 b. 4.5 c. 9 d. 81 ANSWER: a DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 33. A set of 5 scores has SS = 20. If the scores are from a sample, the sample variance is ____. If the scores comprise a population, the population variance is ____.

a. s2 = 5; σ2 = 4 b. s2 = 4; σ2 = 5 c. s2 = 5; σ2 = 5 d. s2 = 5; σ2 = 5 ANSWER: a DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 34. The sum of the squared deviation scores is SS = 20 for a sample of n = 6 scores. What is the variance for this sample? a. s2 = 4 b. s2 = 5 c. s2 = 80 d. s2 = 100 ANSWER: a DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 35. A population of N = 5 scores has a variance of σ2 = 24. If the scores were from a sample, what value would be obtained for the sample variance?

a. s2 = 14 b. s2 = 16 Copyright Cengage Learning. Powered by Cognero.

Page 9

c. s2 = 20 d. s2 = 30 ANSWER: d DIFFICULTY: Apply REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Apply 36. A sample of n = 5 scores has a standard deviation of s = 5. What is the value of SS, the sum of the squared deviations for this sample? a. 100

b. 25 c. 125 d. 20 ANSWER: a DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 37. Which of the following statements is correct regarding a biased statistic? a. A biased statistic occurs when the average value of a statistic overestimates the corresponding population parameter. b. A biased statistic occurs when the average value of a statistic underestimates the corresponding population parameter. c. A biased statistic occurs when the average value of a statistic is equal to the corresponding population parameter. d. A biased statistic occurs when the average value of a statistic either underestimates or overestimates the corresponding population parameter.

ANSWER: d DIFFICULTY: Understand REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Understand 38. If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently _____ the population variance. a. underestimate

b. overestimate c. equal d. Impossible to determine ANSWER: a DIFFICULTY: Understand REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Understand 39. Because sample variances are computed by dividing SS by n – 1, the average value of the sample variances from all possible random samples consistently _____ the population variance.

Copyright Cengage Learning. Powered by Cognero.

Page 10

a. underestimate b. overestimate c. equal d. Impossible to determine ANSWER: c DIFFICULTY: Understand REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Understand 40. All the possible samples of n = 4 scores are selected from a population with µ = 20. If the average for all of the sample means is calculated, which value will be obtained? a. 20

b. 4 c. 5 d. Impossible to determine ANSWER: a DIFFICULTY: Understand REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Understand 41. A population has µ = 30 and σ = 10. If 5 points are added to every score in the population, what are the new values for the mean and standard deviation? a. µ = 40 and σ = 10

b. µ = 35 and σ = 15 c. µ = 35 and σ = 10 d. µ = 40 and σ = 15 ANSWER: c DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 42. A population of scores has µ = 10 and σ = 2. If every score in the population is multiplied by 4, then what are the new values for the mean and standard deviation? a. µ = 40 and σ = 8

b. µ = 40 and σ = 2 c. µ = 10 and σ = 8 d. µ = 10 and σ = 2 ANSWER: a DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 43. A researcher conducts a research study to examine how a new treatment for anxiety compares in efficacy to a standard therapy. This researcher assigns clinically anxious participants to either a new treatment or standard treatment for six Copyright Cengage Learning. Powered by Cognero.

Page 11

months, and then observes anxiety levels following. The researcher finds that the new treatment group has an average anxiety score of M = 50 with a standard deviation of s = 5 following treatment, whereas the standard treatment group has an average anxiety score of M = 60 with a standard deviation of s = 6. Which statement below is consistent with how these results would be reported in an APA style journal article? a. Clinically anxious individuals who received a new treatment displayed greater anxiety levels (M = 60.00, SD = 6.00) than clinically anxious individuals who received a standard treatment (M = 50.00, SD = 5.00). b. Clinically anxious individuals who received a new treatment displayed less anxiety levels (M = 60.00, SD = 6.00) than clinically anxious individuals who received a standard treatment (M = 50.00, SD = 5.00). c. Clinically anxious individuals who received a new treatment displayed less anxiety levels (M = 50.00, SD = 5.00) than clinically anxious individuals who received a standard treatment (M = 60.00, SD = 6.00). d. Clinically anxious individuals who received a new treatment displayed greater anxiety levels (M = 50.00, SD = 5.00) than clinically anxious individuals who received a standard treatment (M = 60.00, SD = 6.00).

ANSWER: c DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 44. Which of the following is true for most distributions? a. Around 30% of the scores will be located within one standard deviation of the mean. b. Around 50% of the scores will be located within one standard deviation of the mean. c. Around 70% of the scores will be located within one standard deviation of the mean. d. Around 90% of the scores will be located within one standard deviation of the mean.

ANSWER: c DIFFICULTY: Understand REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 45. Which of the following values for the population standard deviation would cause a score located above the mean average to have the most extreme position in the distribution? a. σ = 1

b. σ = 2 c. σ = 3 d. σ = 4 ANSWER: a DIFFICULTY: Understand REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 46. On an exam with a mean of µ = 80, a person scores X = 90. Which of the following values for the standard deviation would position this person highest within the class? a. σ = 2

b. σ = 5 c. σ = 10 d. σ = 15 ANSWER:

a

Copyright Cengage Learning. Powered by Cognero.

Page 12

DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 47. On an exam with a mean of µ = 70, a person scores X = 60. Which of the following values for the standard deviation would position this person highest within the class? a. σ = 2

b. σ = 5 c. σ = 10 d. σ = 15 ANSWER: d DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 48. In order to determine if 10 points below the mean on an exam is an extreme negative score, the _____ needs to be known. a. mode

b. standard deviation c. range d. median ANSWER: b DIFFICULTY: Understand REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 49. The box plot below depicts the median number of hours a population of N = 12 students reported studying for their first exam within a class. Which statement below is not true based on the box plot?

a. The median is 5. b. The highest score in the distribution is 7. c. The lowest score in the distribution is 1. d. The interquartile range is 5.

ANSWER: d Copyright Cengage Learning. Powered by Cognero.

Page 13

DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 50. Which of the following characteristics tends to increase the likelihood that a clear difference between two sample means is detected statistically? a. a small difference between sample means

b. large variances within each sample c. small variances within each sample d. small sample sizes ANSWER: c DIFFICULTY: Understand REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 51. The range and the variance are both measures of distance. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 4.2 Defining Variance and Standard Deviation KEYWORDS: Bloom’s: Remember 52. A sample that was obtained from a continuous variable consists of the following scores: 2, 5, 8, and 9. The range of these scores is 7.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 53. The range is considered to be a relatively crude measure of variability. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Understand 54. For a population of scores, the sum of the deviation scores is equal to 0. a. True b. False ANSWER: True Copyright Cengage Learning. Powered by Cognero.

Page 14

DIFFICULTY: Understand REFERENCES: 4.2 Defining Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 55. For a population, a deviation score is computed as X – σ. a. True b. False ANSWER: False DIFFICULTY: Remember REFERENCES: 4.2 Defining Variance and Standard Deviation KEYWORDS: Bloom’s: Remember 56. The value for SS can be less than zero. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 57. A positive deviation score indicates that a score in a distribution is less than the mean. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 4.2 Defining Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 58. Data sets can be divided into four quartiles. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 4.1 Introduction to Variability KEYWORDS: Bloom’s: Remember 59. The sample variance and sample standard deviation is also referred to as the estimated population variance and estimated population standard deviation, respectively.

a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Remember Copyright Cengage Learning. Powered by Cognero.

Page 15

60. In a sample with a mean of M = 4 made up of four scores, two scores are free to vary and the third and fourth scores are fixed.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 61. If the population variance is 6, then the population standard deviation is σ = 36. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 62. The sample mean is unbiased because the average of all possible sample means derived for samples of a specific size is equal to the population mean.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Understand 63. The symbol for sample variance is s. a. True b. False ANSWER: False DIFFICULTY: Remember REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Remember 64. A sample of n = 5 scores has SS = 60 and s2= 15. If the 5 scores were a population, the value of SS would still be 60, but the variance would be σ2 = 10.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 16

65. A sample with a variance of s2 = 36 has a standard deviation equal to s = 6. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 66. A sample of n = 9 scores has SS = 72. The variance for this sample is s2 = 9. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 67. If a sample of n = 5 scores has ΣX = 10 and ΣX2 = 100, then SS = 80. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 68. A sample with SS = 30 and a variance of s2 = 10 has n = 4 scores. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 69. To calculate the variance for a sample, SS is divided by the appropriate degrees of freedom. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 70. The sample standard deviation and sample mean are examples of biased statistics. a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 17

ANSWER: False DIFFICULTY: Remember REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Remember 71. After a researcher adds 6 points to every score in a sample, the standard deviation is found to be s = 12. The original sample had a standard deviation of s = 6.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 72. After a researcher multiplies every score in a sample by 3, the standard deviation is found to be s = 3. The original sample had a standard deviation of s = 9.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 73. Multiplying every score in a sample by a constant value will change the value of the standard deviation. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Understand 74. In a population with a mean of µ = 30 and a standard deviation of σ = 5, a score of X = 18 would be an extreme value, far out in the tail of the distribution.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 75. If a person scores X = 66 on an exam with µ = 70, they scored worse relative to others in the class if σ = 10 than if σ = 5.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 18

ANSWER: False DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 76. If a person scores X = 80 on an exam with m = 75, they scored worse relative to others in the class if σ = 8 than if σ = 4.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 77. For a sample with M = 10 and s = 2, a score of X = 13 would be considered an extreme score, far out in the tail of the distribution.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 78. For a sample with M = 40 and s = 4, about 70% of the individuals will have scores between X = 32 and X = 48. a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 79. For a population with µ = 75 and σ = 15, about 95% of the individuals will have scores between X = 45 and X = 105. a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply 80. In the context of inferential statistics, the sample variance is classified as error variance. a. True b. False ANSWER: True DIFFICULTY: Remember Copyright Cengage Learning. Powered by Cognero.

Page 19

REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Remember 81. Compute the SS, variance and standard deviation for the following population. Scores: 1, 4, 5, 2, 5, 7 ANSWER: SS = 24, σ2 = 4 and σ = 2 DIFFICULTY: Understand REFERENCES: 4.3 Measuring Variance and Standard Deviation for a Population KEYWORDS: Bloom’s: Understand 82. For the following sample of scores that represent a continuous variable, calculate the range and interquartile range.

Then, compute the SS, variance, and standard deviation. Scores: 7, 9, 1, 3 Range = 9, Interquartile Range = 6, SS = 40, s2 = 13.33, and s = 3.65 ANSWER:

DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 83. Calculate the variance and the standard deviation for the following sample data. Scores: 1, 0, 3, 1, 2, 4, 0, 5 ANSWER: s2 = 3.43 and s = 1.85 DIFFICULTY: Understand REFERENCES: 4.4 Measuring Variance and Standard Deviation for a Sample KEYWORDS: Bloom’s: Understand 84. Without some correction, sample variability is said to be “biased.” Define the term biased, and explain how this bias is corrected in the formula for sample variance.

Without some correction, the variability computed for a random sample from the population tends to be ANSWER: smaller than the population variability. Whenever a statistic consistently underestimates (or overestimates) the corresponding population parameter, the statistic is said to be biased. The bias in sample variability is corrected by dividing the sum of squared deviations (SS) by n – 1 (instead of n) in the formula for sample variance.

DIFFICULTY: Understand REFERENCES: 4.5 Sample Variance as an Unbiased Statistic KEYWORDS: Bloom’s: Understand 85. Use the histogram below that depicts population data to complete each of the following:

a. Compute the mean and standard deviation. b. Classify the score of X = 10 as being an extreme or typical score in the distribution. Justify your response. c. Classify the score of X = 2 as being an extreme or typical score in the distribution. Justify your response.

ANSWER: a. µ = 7.00 and σ = 2.31 b. Typical; This score is within two standard deviations of µ = 7.00 Copyright Cengage Learning. Powered by Cognero.

Page 20

c. Extreme; This score is not within two standard deviations of µ = 7.00.

DIFFICULTY: Apply REFERENCES: 4.6 More about Variance and Standard Deviation KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 21

Chapter 05 1. Which position in a distribution corresponds to a z-score of z = –1.00? a. below the mean by 1 point b. below the mean by 1 standard deviation c. above the mean by 1 point d. above the mean by 1 standard deviation ANSWER: b DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 2. Which z-score corresponds to a score that is above the mean by 2 standard deviations? a. +2 b. +10 c. –2 d. This is impossible to determine without knowing the value of the standard deviation.

ANSWER: a DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 3. Which z-score value represents the location farthest from the mean? a. z = +0.50 b. z = –0.50 c. z = –1.00 d. z = –2.00 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 4. For a population with µ = 84 and σ = 4, what is the z-score corresponding to X = 80? a. –1.00 b. +1.00 c. +1.25 d. –1.50 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 5. For a population with a standard deviation of σ = 5, what is the z-score corresponding to a score that is 9 points above the mean?

Copyright Cengage Learning. Powered by Cognero.

Page 1

a. z = +0.50 b. z = –1.80 c. z = +1.80 d. This is impossible to determine based on the provided information.

ANSWER: c DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 6. Consider a population that has a score of X = 15 associated with a z-score of +1.50. What does this z-score indicate about the location of X = 15? a. A score of X = 15 is 1.5 mean units below the standard deviation.

b. A score of X = 15 is 1.5 mean units above the standard deviation. c. A score of X = 15 is 1.5 standard deviations above the mean. d. A score of X = 15 is 1.5 standard deviations below the mean.

ANSWER: c DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 7. Transforming a set of scores into a standardized distribution of z-scores consists of graphically _____ the scores. a. relabeling b. redistributing c. manipulating d. analyzing ANSWER: a DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 8. For a population with µ = 40 and σ = 8, what is the z-score corresponding to X = 34? a. z = –0.50 b. z = –0.75 c. z = –1.00 d. z = –1.50 ANSWER: b DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 9. For a population with µ = 100 and σ = 20, what is the X value corresponding to z = –0.25? a. X = 85 b. X = 95 Copyright Cengage Learning. Powered by Cognero.

Page 2

c. X = 105 d. X = 115 ANSWER: b DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 10. Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether _____. a. an individual is different from a sample

b. a sample is noticeably different from a population c. a distribution of scores is standardized d. a distribution of scores is symmetrically shaped ANSWER: b DIFFICULTY: Understand REFERENCES: 5.6 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Understand 11. For a population with µ = 65 and σ = 4, what is the X value corresponding to z = –2.25? a. X = 56 b. X = 60 c. X = 74 d. X = 71 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 12. A population distribution has σ = 6. What position in this distribution is identified by a z-score of z = +2.33? a. 12 points above the mean b. 8.33 points above the mean c. 8.33 points below the mean d. 14 points above the mean ANSWER: d DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 13. On an exam with µ = 52, a person has a score of X = 44. Which value for the standard deviation would give this person the highest position in the class distribution? a. σ = 2

b. σ = 4 c. σ = 8 Copyright Cengage Learning. Powered by Cognero.

Page 3

d. This is impossible to determine based on the information provided.

ANSWER: c DIFFICULTY: Apply REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Apply 14. On an exam with µ = 52, a person scores X = 56. Which value for the standard deviation would give this person the highest position in the class distribution? a. σ = 2

b. σ = 4 c. σ = 8 d. This is impossible to determine based on the information provided.

ANSWER: a DIFFICULTY: Apply REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Apply 15. A population has µ = 50. Which value of σ would make X = 55 a central, representative score in the population distribution? a. σ = 1

b. σ = 6 c. σ = 2 d. This is impossible to determine based on the information provided.

ANSWER: b DIFFICULTY: Apply REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Apply 16. A population has µ = 50. Which value of σ would make X = 55 an extreme value out in the tail of the population distribution? a. σ = 1

b. σ = 6 c. σ = 10 d. This is impossible to determine based on the information provided.

ANSWER: a DIFFICULTY: Apply REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Apply 17. A person scores X = 65 on an exam. Which set of parameters would give this person the worst grade on the exam relative to others? a. µ = 60 and σ = 10

b. µ = 60 and σ = 5 c. µ = 70 and σ = 10 Copyright Cengage Learning. Powered by Cognero.

Page 4

d. µ = 70 and σ = 5 ANSWER: d DIFFICULTY: Apply REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Apply 18. A population of scores has µ = 44. In this population, a score of X = 40 corresponds to z = –1.00. What is the population standard deviation? a. 2

b. 4 c. 8 d. 6 ANSWER: b DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 19. A researcher is interested in examining whether self-affirming oneself leads to decreased anxiety in response to threatening information. The researcher conducts a research study in which an individual is self-affirmed prior to receiving threatening information. Researchers know that, on average, individuals tend to have anxiety levels of µ = 10 with a standard deviation of σ = 2 when presented with this threatening information. If a self-affirmed individual has an anxiety level of X = 5 following the threatening message, it is reasonable to conclude that self-affirmation ______. a. increases anxiety levels following threatening information

b. does not have an influence on anxiety levels following threatening information c. does have an influence on anxiety levels following threatening information d. This is impossible to determine based on the information provided ANSWER: c DIFFICULTY: Apply REFERENCES: 5.6 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 20. In a population with σ = 5, a score of X = 46 corresponds to a z-score of z = +0.40. What is the population mean? a. µ = 41 b. µ = 40 c. µ = 48 d. µ = 44 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 21. Mark is provided a score of X = 57 that corresponds with a z-score of z = 1.60 to describe his performance on a graduate entrance exam. The graduate entrance exam has a standard deviation of σ = 10. What is the mean average for this graduate entrance exam? a. µ = 73 Copyright Cengage Learning. Powered by Cognero.

Page 5

b. µ = 41 c. µ = 39 d. µ = 68 ANSWER: b DIFFICULTY: Apply REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Apply 22. In a population of scores, X = 83 corresponds to z = –0.50 and X = 93 corresponds to z = +2.00. What are the values for the population mean and standard deviation? a. µ = 85 and σ = 4

b. µ = 85 and σ = 2 c. µ = 81 and σ = 4 d. µ = 81 and σ = 2 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 23. Tom scores an X = 43 on an exam with a mean of µ = 52. Tom’s score is associated with a z-score of –1.80. What is the value for the exam standard deviation? a. σ = 9

b. σ = 5 c. σ = 3 d. σ = 6 ANSWER: b DIFFICULTY: Apply REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Apply 24. In N = 25 games last season, the college basketball team averaged µ = 83 points with a standard deviation of σ = 8. In their final game of the season, the team scored 78 points. Based on this information, the number of points scored in the final game was _____. a. a little above average

b. far below average c. a little below average d. There is not enough information provided to know ANSWER: c DIFFICULTY: Apply REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Apply 25. Under which circumstance is a score that is 15 points above the mean an extreme score relatively far from the mean? a. when the population mean is much larger than 15 Copyright Cengage Learning. Powered by Cognero.

Page 6

b. when the population standard deviation is much larger than 15 c. when the population mean is much smaller than 15 d. when the population standard deviation is much smaller than 15 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 26. Under which circumstance is a score that is located 5 points above the mean a central value that is relatively close to the mean? a. when the population mean is much less than 5

b. when the population mean is much greater than 5 c. when the population standard deviation is much less than 5 d. when the population standard deviation is much greater than 5 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 27. If an entire population with µ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of _____ and a standard deviation of _____. a. µ = 0; σ = 1

b. µ = 60; σ = 1 c. µ = 0; σ = 8 d. µ = 60; σ = 8 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 28. The distribution of z-scores corresponding with a population of scores always has a variance of _____. a. σ2 = 1 b. σ2 = 2 c. σ2 = 0 d. This cannot be determined based on the information provided ANSWER: a DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 29. For any distribution, what is the z-score corresponding to the mean? a. 0 b. 1 Copyright Cengage Learning. Powered by Cognero.

Page 7

c. N d. This is impossible to determine based on the information provided.

ANSWER: a DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 30. For any distribution, what is the z-score corresponding to the median? a. 0 b. 1 c. N d. This is impossible to determine based on the information provided.

ANSWER: d DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 31. Last week, Sarah had exams in her math and Spanish classes. On the math exam, the mean was µ = 30 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 8, and Sarah had a score of X = 68. For which class should Sarah expect the better grade relative to her peers in each class? a. math

b. Spanish c. The grades should be the same because the two exam scores are in the same location. d. There is not enough information provided to determine which is the better grade.

ANSWER: a DIFFICULTY: Apply REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Apply 32. Last week Sarah had exams in her math and Spanish classes. On the math exam, the mean was µ = 40 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 8, and Sarah had a score of X = 68. For which class should Sarah expect the better grade relative to her peers in each class? a. math

b. Spanish c. The grades should be the same because the two exam scores are in the same location. d. There is not enough information provided to determine which is the better grade.

ANSWER: c DIFFICULTY: Apply REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Apply 33. Last week Tim obtained a score of X = 54 on a math exam with µ = 60 and σ = 8. He also scored X = 49 on an English exam with µ = 55 and σ = 3, and he scored X = 31 on a psychology exam with µ = 37 and σ = 4. For which class should Tim expect the worst grade relative to his peers?

Copyright Cengage Learning. Powered by Cognero.

Page 8

a. math b. English c. psychology d. All 3 grades should be the same.

ANSWER: b DIFFICULTY: Apply REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Apply 34. Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution? a. X = 40

b. X = 42 c. X = 43 d. This cannot be determined from the information provided.

ANSWER: a DIFFICULTY: Apply REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Apply 35. A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. When the distribution is standardized, which value will be obtained for a score of X = 58 from the original distribution? a. X = 53

b. X = 55 c. X = 58 d. X = 61 ANSWER: b DIFFICULTY: Understand REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Understand 36. Corey scores X = 70 on his first exam, for which the entire class scored a mean of µ = 78 and standard deviation of σ = 6. The instructor wants to standardize the distribution of exam scores to have µ = 100 and σ = 15. What will Corey’s grade on the exam be in the new distribution? a. X =118

b. X = 82 c. X = 80 d. X = 120 ANSWER: c DIFFICULTY: Apply REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 9

37. For a sample with M = 50 and s = 12, what is the X value corresponding to z = –0.25? a. X = 47 b. X = 53 c. X = 46 d. X = 52 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 38. For a sample, a score that is 12 points above the mean has a z-score of z = 1.20. What is the sample standard deviation? a. s = 4

b. s = 6 c. s = 8 d. s = 10 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 39. A sample of n = 20 scores has a mean of M = 32 and a standard deviation of s = 6. In this sample, what is the z-score corresponding to X = 28? a. z = +1.50

b. z = –1.00 c. z = –0.67 d. z = –1.50 ANSWER: c DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 40. A sample has M = 71 and s = 3. In this sample, what is the X value corresponding to z = +1.33? a. X = 75 b. X = 77 c. X = 67 d. X = 60 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 41. Which statement below is not true regarding standardized distributions? a. Standardized distributions consist of scores that have been transformed to create predetermined values for the Copyright Cengage Learning. Powered by Cognero.

Page 10

mean and standard deviation. b. Standardized distributions are used to make otherwise dissimilar distributions comparable.

c. The values for the mean and standard deviation for a standardized distribution match those values obtained in the original distribution. d. The z-score distribution is an example of a standardized distribution.

ANSWER: c DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 42. For a sample with M = 66, a score of X = 55.5 corresponds to z = –1.50. What is the sample standard deviation? a. 3 b. 4 c. 6 d. 7 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 43. For a sample with s = 9, a score of X = 67 corresponds to z = +1.00. What is the sample mean? a. M = 58 b. M = 76 c. M = 56 d. M = 78 ANSWER: a DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 44. A score that is 3 points lower than the sample mean has a z-score of z = –0.25, and a score of X = 44 has a z-score of – 0.75. What is the sample mean? a. M = 48

b. M = 51 c. M = 53 d. M = 56 ANSWER: c DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 45. For a sample of n = 20 scores, X = 25 corresponds to z = –1.20 and X = 40 corresponds to z = +1.80. What are the values for the sample mean and standard deviation? a. M = 33 and s = 6 Copyright Cengage Learning. Powered by Cognero.

Page 11

b. M = 30 and s = 6 c. M = 35 and s = 5 d. M = 31 and s = 5 ANSWER: d DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 46. Barbara scores X = 120 on a social work licensure exam for the state of Minnesota that has a mean of µ = 113 and a standard deviation of σ = 4. She moves to Wisconsin, and the state of Wisconsin is trying to determine which score she should receive on their licensure exam that has a mean of µ = 100 and standard deviation of σ = 8. Which score should Barbara receive on the Wisconsin licensure exam? a. X = 114

b. X = 112 c. X = 86 d. X = 106 ANSWER: a DIFFICULTY: Apply REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Apply 47. For an exam with a mean of M = 74 and a standard deviation of s = 8, Mary has a score of X = 80, Bob’s score corresponds to z = +1.50, and Sue’s score is located above the mean by 10 points. If the students are placed in order from smallest score to largest exam score, what is the correct order? a. Bob, Mary, Sue

b. Sue, Bob, Mary c. Mary, Bob, Sue d. Mary, Sue, Bob ANSWER: d DIFFICULTY: Apply REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Apply 48. A researcher may decide to transform original scores into a distribution with a pre-determined mean and standard deviation other than the z-score distribution because the z-score distribution _____. a. often has a standard deviation and mean that is too small

b. does not allow for comparisons between otherwise different distributions c. often contains decimals and negative values d. is not standardized ANSWER: c DIFFICULTY: Understand REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 12

49. A researcher is interested in whether a new reading technique influences the reading ability of elementary school children. The researcher knows that average reading ability among a population of third graders is µ = 3 with a standard deviation of σ = 1. If the researcher administers the new reading technique to a third grader who subsequently scores X = 4, it can be concluded that the new reading technique _____. a. decreases reading ability

b. does not have an influence on reading ability c. does have an influence on reading ability d. This cannot be determined based on the provided information ANSWER: b DIFFICULTY: Apply REFERENCES: 5.6 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 50. A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores? a. M = 85 and s = 12

b. M = 0 and s = 12 c. M = 0 and s = 1 d. Impossible to determine based on the provided information.

ANSWER: c DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 51. A positive z-score always corresponds to a score that is greater than the mean in a distribution. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 52. A z-score of z = –1.00 always indicates that a score is located exactly 1 standard deviation below the mean in a distribution.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 53. If two individuals in different populations have identical X scores, they also must have identical z-scores. a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 13

ANSWER: False DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 54. One purpose of a z-score is to provide an understanding of the exact location of a score in a distribution. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.1 Overview KEYWORDS: Bloom’s: Understand 55. A score that is 6 points above the mean corresponds to a z-score of z = +0.50. For this population, the standard deviation is σ = 12.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Apply 56. For a population with a mean of µ = 60 and a standard deviation of σ = 4, a score of X = 56 corresponds to a z-score of z = –0.50.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 57. For a distribution of scores, the location identified by z = +1.00 and the location identified by z = –1.00 are the same distance from the mean.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 58. In a distribution with σ = 20, a score that has a z-score of z = +0.50 is below the mean by 10 points. a. True b. False ANSWER: False Copyright Cengage Learning. Powered by Cognero.

Page 14

DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 59. For a population with µ = 50 and σ = 10, a score of X = 55 corresponds to z = +0.50. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 60. One purpose of a z-score is to standardize a score so that it can readily be compared with scores from other distributions that also have been transformed into z-scores.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.1 Overview KEYWORDS: Bloom’s: Understand 61. For a population with µ = 34, a score of X = 31 corresponds to z = –1.00. The standard deviation for the population is σ = 4.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 62. In a population with σ = 4, a score of X = 48 corresponds to z = 1.50. The mean for this population is µ = 40. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 63. On an exam, Tom scores 12 points above the mean and has a z-score of z = +2.00. The standard deviation for the set of exam scores must be either σ = 6 or σ = –6.

a. True b. False ANSWER: False DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 15

REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Apply 64. On an exam with a standard deviation of σ = 6, Tom’s score of X = 54 corresponds to a z-score of z = –1.00. The mean for the exam must be µ = 48.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Apply 65. Individuals that score typically to others in a population following a treatment will tend to have extreme z-scores. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.6 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Understand 66. For a population of exam scores, a score of X = 80 corresponds to z = –0.75 and a score of X = 72 corresponds to z = – 1.75. The population mean is µ = 85.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 67. Individuals noticeably different from the population following a treatment will tend to have extreme z-scores. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.6 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Understand 68. If a population of N = 20 scores is transformed into z-scores, the set of 20 z-scores will have ΣX = 0. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

69. Transforming an entire distribution of scores into z-scores changes an originally positively skewed distribution to a negatively skewed z-score distribution.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 70. Using z-scores, a population with µ = 40 and σ = 6 is standardized to create a new distribution with µ =53 and σ = 5.

In this transformation, an individual with a score of X = 34 from the original distribution will receive a transformed score of X = 47.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Apply 71. A population with µ = 50 and σ = 8 is standardized to create a new distribution with µ = 75 and σ = 4. After the transformation, an individual receives a new score of X = 76. The original score for this individual was X = 58.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Apply 72. A professor standardizes exam scores so that all exams have µ = 100 and σ = 15. If the original scores from the exam have µ = 56 and σ = 5, then a student with an original exam score of X = 50 would receive a standardized score of X = 82.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Apply 73. For a sample with a mean of M = 63 and a standard deviation of s = 5, a z-score of z = +1.40 corresponds to X = 72. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 17

74. A z-score indicates the distance in standard deviations a score (X) falls above or below the mean of a distribution. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 75. For a sample with a standard deviation of s = 10, a score of 5 will have a z-score of z = 0.50. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 76. For a sample with a standard deviation of s = 3, a z-score of z = +0.5 corresponds to a location that is 1.5 points above the sample mean.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 77. In a sample, a score of X = 31 corresponds to z = –1.00 and X = 39 corresponds to z = +0.60. The sample mean is M = 36.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Apply 78. For a sample with a mean of M = 73, a score of X = 71 corresponds to z = –0.25. The sample standard deviation is s = 8.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 18

79. For a sample with a standard deviation of s = 5, a score of X = 41 corresponds to z = +0.60. The mean for the sample is M = 38.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 80. A set of scores that is transformed into z-scores will result in standardized distribution of z-scores with the exact same mean of 0 and standard deviation of 1, regardless of whether the original scores are derived from a sample or population.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 5.4 Using z-Scores to Standardize a Distribution KEYWORDS: Bloom’s: Understand 81. Explain what is measured by the sign of a z-score and what is measured by its numerical value.

The sign indicates whether the score is located above (+) or below (–) the mean, and the number ANSWER: indicates the score’s distance from the mean in standard deviation units.

DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 82. For a population with µ = 40 and σ = 5, compute the z-score corresponding to each of the following X values: 41, 47, 33, 28

ANSWER:

X = 41 z = +0.20 X = 47 z = +1.40 X = 33 z = –1.40 X = 28 z = –2.40 DIFFICULTY: Understand REFERENCES: 5.2 z-Scores and Locations in a Distribution KEYWORDS: Bloom’s: Understand 83. For a sample distribution of scores, X = 36 corresponds to a z-score of z = –1.25, and X = 42 corresponds to a z-score of z = –0.75. What are the values for the mean and standard deviation for the distribution? (Hint: sketch a distribution and locate each of the z-score positions.)

M = 51 and s = 12 ANSWER:

DIFFICULTY: Understand REFERENCES: 5.3 Other Relationships between z, X, the Mean, and the Standard Deviation KEYWORDS: Bloom’s: Understand 84. A population of scores with µ = 46 and σ = 4 is standardized to create a new distribution with µ = 100 and σ = 8.

Copyright Cengage Learning. Powered by Cognero.

Page 19

a. What is the new value for each of the following scores from the original population? Scores: 43, 47, 55, 34 ANSWER: X= 43 new X = 94 X = 47 new X = 102 X = 55 new X = 118 X = 34 new X = 76 DIFFICULTY: Understand REFERENCES: 5.5 Other Standardized Distributions Based on z-Scores KEYWORDS: Bloom’s: Understand

Copyright Cengage Learning. Powered by Cognero.

Page 20

Chapter 06 1. Which of the following is a requirement for a random sample? a. Every individual has an equal chance of being selected. b. The probabilities cannot change during a series of selections. c. There must be sampling with replacement. d. Each of the other 3 choices are correct.

ANSWER: d DIFFICULTY: Understand REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom's: Understand 2. A class consists of 10 male students and 30 female students. If one student is randomly selected from the class, what is the probability of selecting a male student? a. p = 10/30

b. p = 10/40 c. p = 1/10 d. p = 1/40 ANSWER: b DIFFICULTY: Apply REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Apply 3. A class consists of 10 male and 30 female students. A random sample of n = 3 students is selected with replacement. If the first two students are both females, what is the probability that the third student is a male? a. p = 10/37

b. p = 10/38 c. p = 10/40 d. p = 8/38 ANSWER: c DIFFICULTY: Apply REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Apply 4. Which statement accurately describes the proportions in the tails of a normal distribution? a. Proportions in both the left-hand and right-hand tails tend to be relatively small. b. Proportions in both the left-hand and right-hand tails tend to be relatively large. c. The proportion in the left-hand tail is larger than the proportion in the right-hand tail. d. The proportion in the right-hand tail is larger than the proportion in the left-hand tail.

ANSWER: a DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 1

5. Which statement accurately describes the proportions in the tails of a normal distribution? a. The proportion in the left-hand tail is smaller than the proportion in the right-hand tail. b. Proportions in both the left-hand and right-hand tails tend to be relatively large. c. Proportions in both tails are the same. d. Proportions in both tails are negative.

ANSWER: c DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 6. Which statement accurately describes the proportions in the body of a normal distribution? a. Body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50. b. Body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50. c. Body proportions are always ≥ 0.50. d. Body proportions are always ≤ 0.50.

ANSWER: c DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 7. What proportion of a normal distribution is located in the tail above z = +1.50? a. 0.9332 b. 0.0668 c. 0.4332 d. 0.4501 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 8. What proportion of a normal distribution is located in the tail below z = –1.00? a. 0.8413 b. 0.1587 c. –0.3413 d. –0.1587 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 9. What proportion of a normal distribution is located between the mean and z = +1.40? a. 0.9192 b. 0.0808 Copyright Cengage Learning. Powered by Cognero.

Page 2

c. 0.4192 d. 0.8045 ANSWER: c DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 10. In order to facilitate independent random sampling, ____ must be utilized. a. random assignment b. manipulation c. sampling with replacement d. sampling without replacement ANSWER: c DIFFICULTY: Understand REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Understand 11. A vertical line drawn through a normal distribution at z = –0.60 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body? a. 0.7257

b. 0.2743 c. 0.2257 d. 0.3987 ANSWER: a DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 12. A vertical line drawn through a normal distribution at z = +2.11 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail? a. 0.6915

b. 0.4826 c. 0.9826 d. 0.0174 ANSWER: d DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 13. What is the probability of selecting an individual with a score greater than X = 7 based on the histogram below?

Copyright Cengage Learning. Powered by Cognero.

Page 3

a. p = 5/10 b. p = 4/10 c. p = 4/9 d. p = 5/9 ANSWER: b DIFFICULTY: Apply REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Apply 14. A vertical line drawn through a normal distribution at z = –0.75 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail? a. 0.7734

b. 0.2266 c. 0.7564 d. 0.2734 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 15. A vertical line is drawn through a normal distribution at z = +0.80. What proportion of the distribution is on the righthand side of the line? a. 0.7881

b. 0.2119 Copyright Cengage Learning. Powered by Cognero.

Page 4

c. 0.2881 d. 0.5753 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 16. A vertical line is drawn through a normal distribution at z = –1.20. What proportion of the distribution is on the righthand side of the line? a. 0.8849

b. 0.1151 c. 0.3849 d. 0.7698 ANSWER: a DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 17. What proportion of a normal distribution is located between z = –1.75 and z = +1.75? a. 0.4599 b. 0.9599 c. 0.0802 d. 0.9198 ANSWER: d DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 18. A population is normally distributed with µ = 145 and σ = 20. Which is the percentile rank for X = 171? a. 40.32% b. 9.68% c. 90.32% d. 92.15% ANSWER: c DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 19. What proportion of a normal distribution is located between z = 0 and z = +1.50? a. 0.9332 b. 0.0668 c. 0.4332 d. 0.4787 Copyright Cengage Learning. Powered by Cognero.

Page 5

ANSWER: c DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 20. What is the probability of randomly selecting a z-score greater than z = +1.25 from a normal distribution? a. p = 0.8944 b. p = 0.2266 c. p = 0.3944 d. p = 0.1056 ANSWER: d DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 21. What is the probability of randomly selecting a z-score less than z = –1.55 from a normal distribution? a. p = 0.3433 b. p = 0.0606 c. p = 0.4394 d. p = 0.9394 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 22. What is the probability of randomly selecting a z-score greater than z = –0.75 from a normal distribution? a. p = 0.4878 b. p = 0.2734 c. p = 0.7734 d. p = 0.2266 ANSWER: c DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 23. What is the probability of randomly selecting a z-score less than z = +2.25 from a normal distribution? a. p = 0.0122 b. p = 0.9878 c. p = 0.4878 d. p = 0.2112 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution Copyright Cengage Learning. Powered by Cognero.

Page 6

KEYWORDS:

Bloom’s: Understand

24. Marty is a principal who needs to contact the highest performing 15% of students in his school’s current graduating class about an opportunity to join the school’s academic honor society. At his school, students’ grade point averages is a normally distributed variable. Marty should contact students who have a grade point average that correspond with a zscore greater than or equal to _____. a. z = +1.04

b. z = +0.25 c. z = –1.04 d. z = –0.25 ANSWER: a DIFFICULTY: Apply REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Apply 25. Tiffany is a manager who needs to fire the worst performing 3% of employees. At her organization, employee performance is a normally distributed variable. Tiffany should fire employees who have a performance score that correspond with a z-score less than or equal to _____. a. z = +1.88

b. z = +0.08 c. z = –1.88 d. z = –0.08 ANSWER: c DIFFICULTY: Apply REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Apply 26. At an organization, scoring in the middle 80% of employees regarding job performance is designated as satisfactory.

Job performance is a normally distributed variable. Individuals designated as having satisfactory job performance would have job performance scores that correspond with z-scores equal to or between _____. a. z = –1.49 and z = +1.49

b. z = –0.39 and z = +0.39 c. z = –0.85 and z = +0.85 d. z = –1.28 and z = +1.28 ANSWER: d DIFFICULTY: Apply REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Apply 27. A normal distribution has a mean of µ = 30 with σ = 5. If a vertical line is drawn through the distribution at X = 39, which proportion of the scores are on the left side of the line? a. 0.5679

b. 0.0359 c. 0.4641 d. 0.9641 Copyright Cengage Learning. Powered by Cognero.

Page 7

ANSWER: d DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 28. A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 34, which proportion of the scores are on the left side of the line? a. 0.7257

b. 0.2743 c. 0.0668 d. 0.1976 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 29. A normal distribution has µ = 20 and σ = 4. Which is the probability of randomly selecting a score greater than X = 25 from this distribution? a. p = 0.3944

b. p = 0.1056 c. p = 0.8944 d. p = 0.7888 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 30. A population is normally distributed with a mean of µ = 145 and σ = 20. Which is the percentile rank for X = 136? a. 67.36% b. 35.64% c. 17.36% d. 32.64% ANSWER: d DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 31. A normal distribution has a mean of µ = 50 with σ = 6. If one score is randomly selected from this distribution, which is the probability that the score will be greater than X = 46? a. p = 0.7486

b. p = 0.2514 c. p = 0.2486 d. p = 0.7641 ANSWER: a Copyright Cengage Learning. Powered by Cognero.

Page 8

DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 32. A population is normally distributed with µ = 90 and σ = 8. For this population, which is the 29th percentile? a. X = 84.56 b. X = 85.60 c. X = 87.63 d. X = 94.60 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 33. A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, which is the probability that the score will be less than X = 78? a. p = 0.3643

b. p = 0.1765 c. p = 0.8643 d. p = 0.1357 ANSWER: d DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 34. A population is normally distributed with µ = 86 and σ = 12. For this population, what is the 78th percentile? a. X = 95.24 b. X = 97.89 c. X = 90.45 d. X = 80.63 ANSWER: a DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 35. Betsy is currently completing a school teaching placement in order to become an elementary school teacher. One component of the placement includes evaluations from teachers at the school. Evaluations of student teachers are normally distributed with µ = 100 and σ = 12. Betsy is informed that she must score within the interquartile range of this distribution on her evaluations in order to be certified as an elementary school teacher. Which scores encompass the range that Betsy may score to successfully become certified as an elementary school teacher? a. X = 84 and X = 100

b. X = 92 and X = 100 c. X = 92 and X = 108 d. X = 100 and X = 108 Copyright Cengage Learning. Powered by Cognero.

Page 9

ANSWER: c DIFFICULTY: Apply REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Apply 36. A normal distribution has a mean of µ = 40 with σ = 8. If one score is randomly selected from this distribution, which is the probability that the score will be less than X = 34? a. p = 0.7734

b. p = 0.2266 c. p = 0.2745 d. p = 0.4532 ANSWER: b DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 37. A normal distribution has a mean of µ = 60 with σ = 8. For this population, which is the X value that corresponds to the third quartile? a. X = 65.36

b. X = 54.64 c. X = 67.14 d. X = 62.45 ANSWER: a DIFFICULTY: Understand REFERENCES: 6.4 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 38. Cassie is a gym teacher who develops a training regimen to promote physical health among elementary school students. She knows that scores on a measure of physical health are normally distributed with µ = 75 and σ = 10. She randomly selects one student in her class to complete the training regimen, and this students scores X = 82 on the measure of physical health afterwards. Based on this score, Cassie can conclude that the training regimen _____. a. does have an effect on physical health because this score or larger would be expected 75.80% of the time even if the training regimen does not have an effect b. does have an effect on physical health because this score or larger would be expected 24.20% of the time even if the training regimen does not have an effect c. does not have an effect on physical health because this score or larger would be expected 24.20% of the time even if the training regimen does not have an effect d. does not have an effect on physical health because this score or larger would be expected 75.80% of the time even if the training regimen does not have an effect

ANSWER: c DIFFICULTY: Apply REFERENCES: 6.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 39. A normal distribution has a mean of µ = 90 with σ = 8. If one score is randomly selected from this distribution, which is the probability that the score will have a value between X = 80 and X = 102?

Copyright Cengage Learning. Powered by Cognero.

Page 10

a. p = 0.8914 b. p = 0.5689 c. p = 0.1086 d. p = 0.3974 ANSWER: a DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 40. Maddie teaches a class in which grades on an exam are normally distributed with a mean of µ = 100 and σ = 10. For retention purposes, Maddie is required to report the probability that a randomly selected score will have a value between X = 85 and X = 90. Which probability should Maddie include on her report? a. p = 0.2156

b. p = 0.3085 c. p = 0.2255 d. p = 0.0919 ANSWER: d DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 41. A researcher tests their new treatment for sleep disorder among an individual that has a sleep disorder. The researcher knows that individuals diagnosed with sleep disorder tend to have sleep quality scores that form a normal distribution with µ = 40 and σ = 6. The researcher finds that this individual has a sleep quality score of X = 53 following treatment. Which is the probability that a score this large or larger would be obtained if the new treatment had no effect? a. p = 0.0365

b. p = 0.9850 c. p = 0.0150 d. p = 0.4850 ANSWER: c DIFFICULTY: Apply REFERENCES: 6.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 42. Mitchell is getting ready to take a baseball rules exam in order to become certified as a baseball umpire in his local community. Past scores on the rules exam form a normal distribution with µ = 80 and σ = 6. Mitchell must score in the highest 25% of the distribution in order to become a certified umpire. Which minimum score does Mitchell need to obtain on the rules exam to become a certified umpire? a. X = 76

b. X = 84 c. X = 86 d. X = 81 ANSWER: b DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 11

REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 43. Delores must grade a driver’s test completed by a group of training students. She knows that driver’s test scores are normally distributed with µ = 50 and σ = 6. Students are required to score in the top 75% of students on the test in order to pass the test and continue on with the training course. Which score do students need to obtain at a minimum in order to pass the test and continue with the course? a. X = 40

b. X = 46 c. X = 54 d. X = 60 ANSWER: b DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 44. To avoid having her hours cut back at work, Bridgett must avoid performing in the lowest 40% of the distribution of workers at her job. Specifically, typical amount of items manufactured at her job form a normal distribution with µ = 100 and σ = 4. Bridgett needs to manufacture more than _____ items in order to avoid having her hours cut back at work. a. X = 99

b. X = 101 c. X = 103 d. X = 97 ANSWER: a DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 45. A highly selective university requires that applying students complete an entrance exam with µ = 60 and σ = 16.

Applying students must avoid scoring in the bottom 89.5% of scores on the exam in order to be accepted into the university. Applicants must score more than _____ in order to be accepted to the university. a. X = 80

b. X = 40 c. X = 76 d. X = 70 ANSWER: a DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 46. Scores on the SAT form a normal distribution with a mean of µ = 500 and standard deviation of σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted? a. X = 475

b. X = 525 c. X = 440 Copyright Cengage Learning. Powered by Cognero.

Page 12

d. X = 560 ANSWER: a DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 47. John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, which is the probability that John’s drive to work will take less than 35 minutes? a. 0.6554

b. 0.3446 c. 0.7257 d. 0.2743 ANSWER: d DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 48. Mary drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, which is the probability that Mary’s drive to work will take between 39 and 43 minutes? a. 0.0793

b. 0.2380 c. 0.4206 d. 0.2620 ANSWER: d DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 49. Intelligent quotient (IQ) scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQ scores above 140 are classified in the genius category. Which proportion of the population consists of geniuses? a. 0.9962

b. 0.5038 c. 0.4962 d. 0.0038 ANSWER: d DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 50. Intelligent quotient (IQ) scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQ scores between 90 and 110 are classified as average. Which proportion of the population is average? a. 0.7486 Copyright Cengage Learning. Powered by Cognero.

Page 13

b. 0.5028 c. 0.4972 d. 0.2486 ANSWER: c DIFFICULTY: Apply REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Apply 51. All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Understand 52. The probability of randomly selecting a red marble from a jar that contains 10 red marbles and 30 blue marbles is p = 1/40.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Understand 53. A jar contains 10 red marbles and 20 blue marbles. If you take a random sample of two marbles from this jar with replacement, and the first marble is blue, then the probability that the second marble is blue is p = 19/29.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Apply 54. Equal chance and constant probability are essential aspects of random sampling that is conducive to using probability. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Understand 55. The proportion in the tail of a normal distribution cannot be more than 0.50. a. True Copyright Cengage Learning. Powered by Cognero.

Page 14

b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 56. The symbol p refers to percentage. a. True b. False ANSWER: False DIFFICULTY: Remember REFERENCES: 6.1 Introduction to Probability KEYWORDS: Bloom’s: Remember 57. When the z-score value in a normal distribution is negative, the body is on the left-hand side of the distribution. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 58. The tail is on the right side of a normal distribution for any z-score value greater than zero. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 59. A vertical line drawn through a normal distribution at z = +1.40 divides the distribution into two sections. The proportion in the smaller section is 0.0808.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 60. A vertical line drawn through a normal distribution at z = –0.72 separates the distribution into two sections. The proportion in the smaller section is 0.2358.

a. True b. False ANSWER:

True

Copyright Cengage Learning. Powered by Cognero.

Page 15

DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 61. A vertical line drawn through a normal distribution at z = –0.50 separates the distribution into two sections. The proportion in the larger section is 0.6325.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 62. When finding percentile ranks for a percentile, the focus is always on identifying the percentile rank on the left side of a percentile.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 63. For a normal distribution, the term quartile is similar to the term percentile in interpretation. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 64. For a normal distribution, exactly 89.97% of the z-score values are less than z = +1.50. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 65. For a normal distribution, the first quartile corresponds with the 25th percentile. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks Copyright Cengage Learning. Powered by Cognero.

Page 16

KEYWORDS:

Bloom’s: Understand

66. For a normal distribution, the proportion of scores located between z = –0.70 and z = +0.70 is 0.5160. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 67. For a normal distribution, the interquartile range for a population of scores with σ = 18 is 24.12. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand 68. A vertical line is drawn through a normal distribution so that the proportion in the tail is 0.0455. The line was drawn at z = +0.12 or at z = –0.12.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 69. A vertical line is drawn through a normal distribution so that 17.36% of the distribution is located between the line and the mean. The line is drawn at z = +0.45 or at z = –0.45.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 70. For a normal distribution, the z-score boundary that separates the lowest 33% of the scores from the rest of the scores is z = –0.44.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 17

71. If one score is randomly selected from a normal distribution with µ = 90 and σ = 20, the probability of obtaining a score less than X = 100 is p = 0.0228.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 72. For a population with a mean of µ = 65 and σ = 10, 3.59% of the scores are greater than X = 83. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 73. For a normal distribution with µ = 100 and σ = 10, the score that separates the top 60% of the distribution from the rest of the distribution is X = 105.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 74. The middle 20% of a normal distribution is located between z = –0.25 and z = +0.25. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 75. For a normal distribution with µ = 50 and σ = 12, the score that separates the highest 25% of the scores from the rest of the distribution is located at X = 54.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 18

76. For a normal distribution with µ = 64 and σ = 9, the score that separates the bottom 1% of the distribution from the rest of the distribution is X = 43.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 77. If one score is randomly selected from a normal distribution with µ = 80 and σ = 10, the probability of obtaining a score less than X = 75 is p = 0.3085.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 78. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score greater than X = 73 is p = 0.4115.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 79. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 90 and X = 97 is p = 0.1319.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 80. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 80 and X = 120 is p = 0.6826.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 19

81. For a normal distribution: a. Which z-score separates the highest 25% of the distribution from the rest of the scores? b. Which z-score separates the highest 60% of the distribution from the rest of the scores? c. Which z-score separates the lowest 30% of the distribution from the rest of the scores? d. Which z-score separates the lowest 80% of the distribution from the rest of the scores? a. z = +0.67 ANSWER: b. z = –0.25 c. z = –0.52 d. z = +0.84

DIFFICULTY: Understand REFERENCES: 6.2 Probability and the Normal Distribution KEYWORDS: Bloom’s: Understand 82. For a normal distribution with a mean of µ = 100 and a standard deviation of σ = 20, find each of the following proportions:

a. Proportion of scores greater than X = 107 b. Proportion of scores less than X = 69 c. Proportion of scores less than X = 117 d. Proportion of scores between X = 91 and X = 102 a. 0.3632 ANSWER: b. 0.0606 c. 0.8023 d. 0.2134

DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 83. For a normal distribution with µ = 500 and σ = 100, find each of the following values: a. What X value separates the highest 9% of the distribution from the rest of the scores? b. What X values form the boundaries for the middle 40% of the distribution? c. What is the probability of randomly selecting a score greater than X = 425? a. X = 634 ANSWER: b. X = 448 and X = 552 c. p = 0.7734

DIFFICULTY: Understand REFERENCES: 6.3 Probabilities and Proportions for Scores from a Normal Distribution KEYWORDS: Bloom’s: Understand 84. For a normal distribution with µ = 80 and σ = 12, find the following values: a. What is the percentile rank for X = 75? b. What is the percentile rank for X = 100? c. What is the 11th percentile? d. What is the 98th percentile? e. What scores comprise Q1 and Q3, and what is the interquartile range? a. 33.72% ANSWER: b. 95.25% c. X = 65.24 d. X = 104.60 e. X for Q1 = 71.96 and X for Q3 = 88.04; Interquartile range = 16.08 Copyright Cengage Learning. Powered by Cognero.

Page 20

DIFFICULTY: Understand REFERENCES: 6.4 Percentiles and Percentile Ranks KEYWORDS: Bloom’s: Understand

Copyright Cengage Learning. Powered by Cognero.

Page 21

Chapter 07 1. Which is the expected value of M? a. the sample mean b. the population standard deviation c. the mean of the distribution of sample means d. the standard deviation of the distribution of sample means ANSWER: c DIFFICULTY: Remember REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Remember 2. Which is the standard error of M? a. the sample mean b. the sample standard deviation c. the mean of the distribution of sample means d. the standard deviation of the distribution of sample means ANSWER: d DIFFICULTY: Remember REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Remember 3. For a normal population with µ = 60 and σ = 50, the distribution of sample means based on n = 25 will have an expected value of ____ and a standard error of ____.

a. µM = 12; σM = 10 b. µM = 60; σM = 10 c. µM = 12; σM = 2 d. µM = 60; σM = 2 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 4. Samples of n = 36 scores are selected from a population. If the distribution of sample means has an expected value of µM = 30 and a standard error of σM = 4, what is the mean and the standard deviation for the population? a. µ = 30 and σ = 24

b. µ = 30 and σ = 8 c. µ = 40 and σ = 4 d. µ = 150 and σ = 18 ANSWER: a DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 1

5. A sample of n = 49 scores with M = 43 is selected from a population with µ = 40 and with σ = 21. What is the standard error for the sample mean?

a. σM = 8 b. σM = 6 c. σM = 3 d. σM = 2 ANSWER: c DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 6. A sample of n = 4 scores with M = 43 is selected from a normal population with µ = 40 and with σ = 8. What is the expected value for the sample mean? a. µM = 40

b. µM = 43 c. µM = 5 d. µM = 2 ANSWER: a DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 7. A sample of n = 64 scores is selected from a population with µ = 80 and with σ = 24. On average, how much error is expected between the sample mean and the population mean? a. 2.5 points

b. 1 point c. 2 points d. 3 points ANSWER: d DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 8. For the distribution of sample means for all random samples of a certain size from a population depicted below, what is the probability that a randomly selected sample will have a sample mean less than X = 6?

Copyright Cengage Learning. Powered by Cognero.

Page 2

a. p = 2/13 b. p = 1/13 c. p = 11/13 d. p = 4/13 ANSWER: a DIFFICULTY: Apply REFERENCES: 7.1 Samples, Populations, and the Distribution of Sample Means KEYWORDS: Bloom’s: Apply 9. Which symbol is used to identify the standard error of M? a. σM b. µ c. M d. MM ANSWER: a DIFFICULTY: Remember REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Remember 10. Under which circumstance will the distribution of sample means be normal? a. it is always normal b. only if the population distribution is normal c. only if the sample size is greater than 30 d. if the population is normal or if the sample size is greater than 30 Copyright Cengage Learning. Powered by Cognero.

Page 3

ANSWER: d DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 11. Which statement below is not consistent with the distribution of sample means? a. The distribution of sample means tends to pile up around the population mean. b. The distribution of sample means tends to be approximately normal. c. The distribution of sample means depicts the means of all the random samples of a particular sample size. d. The distribution of sample means tends to pile up around the population standard deviation.

ANSWER: d DIFFICULTY: Understand REFERENCES: 7.1 Samples, Distributions, and the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 12. All random samples of size n = 9 are selected from a normal population with µ = 55 and σ = 10, and the mean is computed for each sample. Then, all the possible samples of size n = 36 are selected from the same population, and the mean is computed for each sample. Which statement below is true? a. The distribution of sample means for samples of n = 9 is less variable than the distribution of sample means for n = 36. b. The distribution of sample means for n = 9 has a smaller mean than the distribution of sample means for n = 36. c. The distribution of sample means for n = 36 has a smaller mean than the distribution of sample means for n = 9. d. The distribution of sample means for samples of n = 36 is less variable than the distribution of sample means for n = 9.

ANSWER: d DIFFICULTY: Understand REFERENCES: 7.1 Samples, Distributions, and the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 13. Samples of size n = 9 are selected from a normal population with µ = 80 and with σ = 18. What is the expected value for the mean of the distribution of sample means? a. µM = 6

b. µM = 18 c. µM = 80/3 d. µM = 80 ANSWER: d DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 14. Samples of size n = 9 are selected from a normal population with µ = 80 and with σ = 18. What is the standard error for the distribution of sample means?

a. σM = 5 Copyright Cengage Learning. Powered by Cognero.

Page 4

b. σM = 18 c. σM = 6 d. σM = 2 ANSWER: c DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 15. An educational specialist develops a new teaching technique for a nutrition course. The educational specialist knows that typically scores on a well-validated measure of nutrition knowledge are normally distributed with µ = 20 and σ = 8.

The educational specialist administers their new teaching technique to a sample of n = 25 students who subsequently score M = 22.5 on the measure of nutrition knowledge. Which conclusion can the educational specialist make based on the results of this research study? a. The new teaching technique has an effect on nutrition knowledge because the computed z-score does not reach the z = ±1.96 threshold. b. The new teaching technique does not have an effect on nutrition knowledge because the computed z-score does not reach the z = ±1.96 threshold. c. The new teaching technique has an effect on nutrition knowledge because the computed z-score reaches the z = ±1.96 threshold. d. The new teaching technique does not have an effect on nutrition knowledge because the computed z-score reaches the z = ±1.96 threshold.

ANSWER: b DIFFICULTY: Apply REFERENCES: 7.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 16. A researcher develops a new exercise regimen for influencing muscle strength. The researcher knows that scores on a well-validated measure of muscle strength are normally distributed with µ = 15 and σ = 4. The researcher administers their new exercise regimen to a sample of n = 64 adults who subsequently score M = 16.5 on the measure of muscle strength.

Which conclusion can the researcher make based on the results of this research study? a. The new exercise regimen has an effect on muscle strength because the computed z-score does not reach the z = ±1.96 threshold. b. The new exercise regimen does not have an effect on muscle strength because the computed z-score does not reach the z = ±1.96 threshold. c. The new exercise regimen has an effect on muscle strength because the computed z-score reaches the z = ±1.96 threshold. d. The new exercise regimen does not have an effect on muscle strength because the computed z-score reaches the z = ±1.96 threshold.

ANSWER: c DIFFICULTY: Apply REFERENCES: 7.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 17. If all the possible random samples with n = 81 scores are selected from a normal population with µ = 80 and σ = 9, and the mean is calculated for each sample, what is the average of all the sample means? a. 81

b. 1 Copyright Cengage Learning. Powered by Cognero.

Page 5

c. 80 d. This cannot be determined with the provided information.

ANSWER: c DIFFICULTY: Apply REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Apply 18. If random samples, each with n = 16 scores, are selected from a normal population with µ = 100 and σ = 20, how much difference, on average, should there be between a sample mean and the population mean? a. 16 points

b. 3 points c. 4 points d. 5 points ANSWER: d DIFFICULTY: Apply REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Apply 19. For a normal population, a sample of n = 9 scores has a standard error of 10. For the same population, a sample of n = 25 scores would have a standard error of _____.

a. σM = 10 b. σM = 6 c. σM = 9 d. σM = 5 ANSWER: b DIFFICULTY: Apply REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Apply 20. Consider a normal population with µ = 50 and σ = 6. A sample size of at least which size needs to be obtained in order to achieve a standard error of σM = 2 or less? a. n = 16

b. n = 9 c. n = 3 d. n = 4 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Understand 21. A sample of n = 16 scores has a standard error of σM = 4. What is the standard deviation of the normally distributed population from which the sample was obtained? a. σ = 64 Copyright Cengage Learning. Powered by Cognero.

Page 6

b. σ = 16 c. σ = 4 d. σ = 32 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 22. A sample obtained from a population with σ = 48 has a standard error of σM = 6. How many scores are in the sample? a. n = 36 b. n = 64 c. n = 8 d. n = 12 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 23. Consider a normal population with µ = 75 and σ = 10. A sample of at least which size needs to be obtained in order to achieve a standard error of σM = 2.00 or less? a. n = 36

b. n = 16 c. n = 25 d. n = 4 ANSWER: c DIFFICULTY: Understand REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Understand 24. A random sample of n = 16 scores is obtained from a normal population with a mean of µ = 100 and a standard deviation of σ = 12. If the sample mean is M = 104, what is the z-score for the sample mean? a. z = –1.00

b. z = +3.20 c. z = +1.00 d. z = +1.33 ANSWER: d DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 25. A sample of n = 64 scores is selected from a population with µ = 60 and σ = 10. If the sample mean is M = 57, what is the z-score for this sample mean? a. z = –2.40 Copyright Cengage Learning. Powered by Cognero.

Page 7

b. z = +1.00 c. z = –2.00 d. z = +4.00 ANSWER: a DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 26. A sample is selected from a normal population with µ = 40 σ = 10. If the sample mean of M = 46 produces a z-score of z = +3.00, then how many scores are in the sample? a. n = 25

b. n = 4 c. n = 9 d. n = 36 ANSWER: a DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 27. A sample of n = 16 scores is selected from a normal population with σ = 32. If the sample mean of M = 81 produces a z-score of z = –1.75, then what is the population mean? a. µ = 89

b. µ = 95 c. µ = 67 d. µ = 92 ANSWER: b DIFFICULTY: Understand KEYWORDS: Bloom’s: Understand 28. For a normally distributed population with a mean of µ = 70 and a standard deviation of σ = 10, what is the probability of obtaining a sample mean greater than M = 67 for a sample of n = 64 scores? a. p = 0.0082

b. p = 0.9918 c. p = 0.9675 d. p = 0.4918 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 29. Which bit of information below is not obtainable from a z-score? a. whether a sample mean is above or below a population mean b. the distance of a sample mean from the population mean c. the population mean Copyright Cengage Learning. Powered by Cognero.

Page 8

d. the amount of standard errors a sample mean is from a population mean ANSWER: c DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 30. Researchers know that excessively low or high exposure to stress during early childhood can become problematic when individuals are exposed to stress as adults. The measurement of exposure to stress during childhood using a wellvalidated questionnaire forms a normal distribution with µ= 70 and σ = 6. Researchers know that individuals that score in the middle 65% of exposure to stress during childhood tend to respond the best to exposure to stress as adults. Based on this information, for a sample size of n = 16, which range of sample mean values on the stress questionnaire would be expected 65% of the time? a. M = 65.500 to M = 74.500

b. M = 68.000 to M = 72.000 c. M = 68.605 to M = 71.395 d. M = 67.564 to M = 72.436 ANSWER: c DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 31. If a sample of n = 4 scores is obtained from a normal population with µ = 70 and σ = 12, what is the z-score corresponding to a sample mean of M = 69? a. z = –0.17

b. z = +0.17 c. z = +1.25 d. z = –1.25 ANSWER: a DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 32. A sample of n = 81 scores is obtained from a population with µ = 80 and σ = 27. If the sample mean corresponds to a z-score of +2.33, what is the value of the sample mean? a. M = 77

b. M = 73 c. M = 87 d. M = 83 ANSWER: c DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 33. A sample from a normal population with µ = 50 and σ = 6 has a mean of M = 48.20. If the sample mean corresponds to a z = –1.50, then how many scores are in the sample?

Copyright Cengage Learning. Powered by Cognero.

Page 9

a. n = 36 b. n = 25 c. n = 16 d. n = 9 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 34. A random sample of n = 49 scores is obtained from a population with σ = 14. If the sample mean is 4.50 points greater than the population mean, what is the z-score for the sample mean? a. z = +2.25

b. z = +2.00 c. z = +1.50 d. This cannot be determined with the provided information.

ANSWER: a DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 35. For a normal population with µ = 40 and σ = 10, which of the following samples is least likely to be obtained? a. M is less than 38 for a sample of n = 4 b. M is less than 36 for a sample of n = 4 c. M is less than 38 for a sample of n = 100 d. M is less than 36 for a sample of n = 100 ANSWER: d DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 36. For a normal population with µ = 40 and σ = 10, which of the following samples has the highest probability of being obtained? a. M is less than 38 for a sample of n = 4

b. M is less than 36 for a sample of n = 4 c. M is less than 38 for a sample of n = 100 d. M is less than 36 for a sample of n = 100 ANSWER: a DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 37. A random sample of n = 4 scores is obtained from a normal population with µ = 30 and σ = 8. What is the probability that the sample mean will be less than than M = 22? a. p = 0.00003 Copyright Cengage Learning. Powered by Cognero.

Page 10

b. p = 0.0228 c. p = 0.1587 d. p = 0.3085 ANSWER: b DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 38. A random sample of n = 64 scores is obtained from a normal population with µ = 30 and σ = 10. What is the probability that the sample mean will be greater than M = 31? a. p = 0.3944

b. p = 0.1056 c. p = 0.2119 d. p = 0.2881 ANSWER: c DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 39. A random sample of n = 25 scores is obtained from a normal population with µ = 30 and σ = 6. What is the probability that the sample mean will be within 2 points of the population mean? a. p = 0.9050

b. p = 0.9840 c. p = 0.4525 d. p = 0.4920 ANSWER: a DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 40. A sample is obtained from a normal population with µ = 100 and σ = 20. Which of the following samples would produce the most extreme z-score? a. a sample of n = 25 scores with M = 102

b. a sample of n = 100 scores with M = 102 c. a sample of n = 25 scores with M = 104 d. a sample of n = 100 scores with M = 104 ANSWER: d DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 41. When a sample size from a population is n = 1, then the standard error will always equal the _____. a. population standard deviation b. population mean Copyright Cengage Learning. Powered by Cognero.

Page 11

c. sample mean d. Impossible to determine based on the provided information ANSWER: a DIFFICULTY: Understand REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Understand 42. A sample of n = 4 scores is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean less than M = 52? a. p = 0.6915

b. p = 0.3085 c. p = 0.5793 d. p = 0.5602 ANSWER: c DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 43. A clinical psychologist is writing a grant proposal. As part of this process, they are required to provide the probability that a random sample of n = 9 scores selected from a normal distribution of anxiety scores with µ = 80 and σ = 12 has a mean between M = 76 and M = 84. Which probability should they provide? a. p = 0.9974

b. p = 0.6826 c. p = 0.3830 d. p = 0.2586 ANSWER: b DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 44. A random sample of n = 16 scores is selected from a normal distribution with µ = 500 and σ = 200. For this sample, which of the following statements is true? a. p(402 < M < 598) = 0.95

b. p(425 < M < 575) = 0.95 c. p(450 < M < 550) = 0.95 d. p(490 < M < 510) = 0.95 ANSWER: a DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 45. A researcher chooses to collect data from a large sample that represents a population instead of a smaller sample.

Which of the following is not a likely consequence of choosing to collect data from a large sample relative to a smaller sample?

Copyright Cengage Learning. Powered by Cognero.

Page 12

a. The expected difference between M and µ will decrease. b. The expected value of M will decrease. c. The standard error will decrease. d. The distribution of sample means will become more normally distributed.

ANSWER: b DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 46. A researcher is forced to collect data from a smaller sample of individuals to test their research hypotheses than originally anticipated. This will have the effect of ______. a. reducing the expected distance between M and µ

b. increasing the expected distance between M and µ c. increasing the expected value of M d. reducing the expected value of M ANSWER: b DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 47. Consider that a researcher is attempting to reduce the expected distance between M and µ as much as possible when conducting a research study. One thing they can do is _____. a. increase the sample size

b. decrease the sample size c. increase the population mean d. decrease the population mean ANSWER: a DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 48. A sample is selected from a normal population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean a typical, representative value for the population? a. a small sample and a small population standard deviation

b. a small sample and a large population standard deviation c. a large sample and a small population standard deviation d. a large sample and a large population standard deviation ANSWER: b DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 49. A sample is selected from a normal population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean an extreme, unrepresentative value for the population?

Copyright Cengage Learning. Powered by Cognero.

Page 13

a. a small sample and a small population standard deviation b. a small sample and a large population standard deviation c. a large sample and a small population standard deviation d. a large sample and a large population standard deviation ANSWER: c DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 50. A sample is selected from a normal population with µ = 54 and σ = 8. Which of the following samples would be considered extreme and unrepresentative for this population? a. M = 53 and n = 81

b. M = 52 and n = 36 c. M = 53 and n = 36 d. M = 52 and n = 81 ANSWER: d DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 51. Two random samples will likely have different means even if they are both the same size and both selected from the same population.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.1 Samples, Populations, and the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 52. The distribution of sample means consists of all sample means derived from all the possible random samples of a particular size (n) that can be obtained from a population.

a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 7.1 Samples, Populations, and the Distribution of Sample Means KEYWORDS: Bloom’s: Remember 53. For the distribution of sample means to be normally shaped, it must be derived from samples of at least n = 30 scores. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means Copyright Cengage Learning. Powered by Cognero.

Page 14

KEYWORDS:

Bloom’s: Understand

54. A sample of n = 25 scores is selected from a normal population with a mean of µ = 80. However, the calculated mean for this sample of scores is M = 81, not the population mean of µ = 80. This is consistent with the concept of sampling error.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.1 Samples, Populations, and the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 55. The distribution of sample means is an example of a sampling distribution. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.1 Samples, Distributions, and the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 56. If sample size is n = 30 or greater, the distribution of sample means will also be normally shaped, regardless of the shape of the original distribution of scores.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 57. According to the central limit theorem, the standard error for the distribution of sample means becomes smaller as the sample size decreases.

a. True b. False ANSWER: False DIFFICULTY: Remember REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Remember 58. Samples of n = 9 scores are selected from a normal population. If the distribution of sample means has an expected value of µM = 40, then the population has a mean of µ = 40.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means Copyright Cengage Learning. Powered by Cognero.

Page 15

KEYWORDS:

Bloom’s: Understand

59. The central limit theorem informs the numerator of the z-score for sample means equation. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 60. If the sample size is equal to the population variance (n = σ2), then the standard error is equal to σM = 1. a. True b. False ANSWER: True DIFFICULTY: Analyze REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Analyze 61. The mean of all the sample means obtained from all random samples of a certain sample size in a sampling distribution is an example of a biased statistic.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 62. A sample of n = 9 scores drawn from a normal population has a standard error of 2 points. This indicates that on average for random samples of size n = 9, sample means will differ by 2 points from µ.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 63. As the population standard deviation increases, the standard error will also increase. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

64. On average, a sample of n = 36 scores from a normal population with σ = 10 will provide a better estimate of the population mean than a researcher would get with a sample of n = 9 scores from a normal population with σ = 10.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 65. A sample is obtained from a normal population with σ = 20. If the sample mean has a standard error of 10 points, then the sample size is n = 4.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 66. Standard error allows sampling error to be defined and measured. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.4 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 67. A sample is selected from a normal population with µ = 40 and σ = 12. If the sample mean of M = 36 corresponds to z = –2.00, then the sample size is n = 64.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 68. The standard error equation can be rewritten to √(σ2/n). a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 69. A sample of n = 49 scores is selected from a normal population with a mean of µ = 60 and a standard deviation of σ = Copyright Cengage Learning. Powered by Cognero.

Page 17

12. The probability that the sample mean will be greater than M = 63 is equal to the probability of obtaining a z-score greater than z = +1.75

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 70. A sample of n = 9 scores is randomly selected from a normal population with µ = 80 and σ = 9. If the sample mean is M = 83, then the corresponding z-score will indicate that a sample mean of M = 83 is above µ = 80 by 3 standard error units.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 71. A sample of n = 16 scores is selected from a normal population with µ = 30 and σ = 9. The probability of obtaining a sample mean greater than 26 is equal to the probability of obtaining a z-score greater than z = –1.60.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 72. A sample of n = 100 scores is selected from a normal population with µ = 75 and σ = 11. The probability of obtaining a sample mean greater than M = 78 is p = 0.0032.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand 73. A sample of n = 36 scores is selected from a normal population with µ = 75 and σ = 7. The probability of obtaining a sample mean greater than M = 73 is p = 0.9056.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 18

74. A sample of n = 100 scores is selected from a normal population with µ = 60 and σ = 20. It is very unlikely that the sample mean will be greater than M = 66.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 7.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 75. A sample of n = 4 scores is selected from a normal population with µ = 80 and σ = 10. It is very unlikely that the sample mean will be less than 74.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 7.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 76. If the sample size is doubled, the standard error is cut in half. a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Apply 77. If the sample size is increased, then the standard error for sample means also increases. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Understand 78. On average, a sample of n = 36 scores will provide a better estimate of the population mean than a sample of n = 49 scores from the same population.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.4 More about Standard Error KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 19

79. A population has µ = 50 and σ = 22. For a sample of n = 81 scores from this population, a sample mean of M = 54 would be considered an extreme value.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 7.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply 80. The original population of scores for a variable has the same standard deviation (standard error) as the distribution of sample means for a specific sample size obtained from that population.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Understand 81. For a normal population with µ = 50 and σ = 6, describe the shape, the mean, and the standard deviation for the distribution of sample means in each of the following situations:

a. Samples of n = 4. b. Samples of n = 36.

ANSWER: a. Unknown shape with µM = 50 and σM = 3. b. Normal shape with µM = 50 and σM = 1.

DIFFICULTY: Apply REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Apply 82. A normal population has a mean of µ = 80 with σ = 20. a. If a single score is randomly selected from this population, how much distance, on average, will be found between the score and the population mean? b. If a sample of n = 25 scores is randomly selected from this population, how much distance, on average, will be found between the sample mean and the population mean? c. If a sample of n = 100 scores is randomly selected from this population, how much distance, on average, will be found between the sample mean and the population mean? a. σ = 20 points ANSWER: b. σM = 4 points c. σM = 2 points

DIFFICULTY: Apply REFERENCES: 7.2 Shape, Central Tendency, and Variability for the Distribution of Sample Means KEYWORDS: Bloom’s: Apply 83. A sample of n = 16 scores is selected from a normal population with µ = 60 and σ = 20. a. What is the probability that the sample mean will be greater than 52? b. What is the probability that the sample mean will be less than 54?

Copyright Cengage Learning. Powered by Cognero.

Page 20

c. What is the probability that the sample mean will be within 4 points of the population mean?

ANSWER:

a. z = –1.60, p = 0.9452 b. z = –1.20, p = 0.1151 c. z = ≥ –0.80 to ≤ +0.80, p = 0.5762

DIFFICULTY: Apply REFERENCES: 7.3 z-Scores and Probability for Sample Means KEYWORDS: Bloom’s: Apply 84. A researcher has a new treatment for anxiety. The researcher knows that anxiety scores are normally distributed with µ= 65 and σ = 12. The researcher administers their new treatment to a sample of individuals and subsequently measures anxiety levels. a. If the sample size was n = 25 and M = 61 after treatment, can the researcher conclude the new treatment has an effect?

Justify your response. b. If the sample size was n = 100 and M = 62 after treatment, can the researcher conclude the new treatment has an effect?

Justify your response.

ANSWER:

a. No, the researcher cannot conclude the new treatment has an effect. The z-score for the sample mean of M = 61 is z = –1.67. This z-score does not reach the z = ±1.96 threshold necessary to conclude that the sample mean would be that extreme simply by chance 5% of the time or less. b. Yes, the researcher can conclude the new treatment has an effect. The z-score for the sample mean of M = 62 is z = –2.50. This z-score is beyond the z = ±1.96 threshold necessary to conclude that the sample mean would be that extreme simply by chance 5% of the time or less. This sample mean is very extreme and unlikely to naturally occur without the aid of the new treatment.

DIFFICULTY: Apply REFERENCES: 7.5 Looking Ahead to Inferential Statistics KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 21

Chapter 08 1. Which of the following accurately describes a hypothesis test? a. a descriptive technique that allows researchers to describe a sample b. a descriptive technique that allows researchers to describe a population c. a statistical technique that uses the data from a sample to evaluate a hypothesis about a population d. a statistical technique that uses information about a population to evaluate a hypothesis about a sample ANSWER: c DIFFICULTY: Remember REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Remember 2. A hypothesis test involves a comparison of which two elements? a. research results from a sample and a hypothesis about a population b. research results from a population and a hypothesis about a sample c. research results from a population and a hypothesis about the population d. research results from a sample and a hypothesis about the sample ANSWER: a DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 3. What is measured by the numerator of the z-score test statistic? a. the likely distance between M and µ that would be expected if H0 was false b. the distance between the sample mean and hypothesized population mean c. the position of the sample mean relative to the critical region d. the boundaries for the critical region(s) ANSWER: b DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 4. What is measured by the denominator of the z-score test statistic? a. the amount of error expected between the sample mean and hypothesized population mean b. the distance between the sample mean and hypothesized population mean c. the position of the sample mean relative to the critical region d. the boundaries for the critical region(s) ANSWER: a DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 5. A researcher is interested in whether a new teaching method influences the public speaking skills of students in an introductory to communications class. The researcher knows that public speaking skills in the class are normally Copyright Cengage Learning. Powered by Cognero.

Page 1

distributed with µ = 10 and σ = 2. Which is the null hypothesis for this research study?

a. µteaching method = 10 b. µteaching method = 2 c. µteaching method ≠ 10 d. µteaching method ≠ 2 ANSWER: a DIFFICULTY: Apply REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Apply 6. Which of the following is directly communicated within the null hypothesis? a. the population mean before treatment b. the population mean after treatment c. the sample mean before treatment d. the sample mean after treatment ANSWER: b DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 7. A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (H0) put forth about the treatment? a. The treatment has an effect on anxiety.

b. The treatment divides each anxiety score by a constant. c. The treatment multiplies each anxiety score by a constant. d. The treatment has no effect on anxiety.

ANSWER: d DIFFICULTY: Apply REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Apply 8. A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) put forth about the treatment? a. The treatment has no effect on anxiety.

b. The treatment adds a constant to each anxiety score. c. The treatment multiplies each anxiety score by a constant. d. The treatment has an effect on anxiety.

ANSWER: d DIFFICULTY: Apply REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Apply 9. Which of the following accurately describes the critical region?

Copyright Cengage Learning. Powered by Cognero.

Page 2

a. sample means that are very unlikely to be obtained if the null hypothesis is true b. sample means that are very likely to be obtained if the null hypothesis is true c. sample means that are very unlikely to be obtained whether or not the null hypothesis is true d. sample means that are very likely to be obtained whether or not the null hypothesis is true ANSWER: a DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 10. If α = 0.05 for a two-tailed hypothesis test, how are the boundaries for the critical region determined? a. Boundaries are drawn so there is 2.5% (0.025) in each tail of the distribution. b. Boundaries are drawn so there is 5% (0.05) in each tail of the distribution. c. Boundaries are drawn so there is 10% (0.10) in each tail of the distribution. d. Boundaries are drawn so there is 5% (0.05) in the center of the distribution.

ANSWER: a DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 11. If a hypothesis test produces a z-score in the critical region, which decision should be made? a. reject the alternative hypothesis b. fail to reject the alternative hypothesis c. reject the null hypothesis d. fail to reject the null hypothesis ANSWER: c DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing 12. A sample of n = 25 individuals is selected from a population with µ = 80, and a treatment is administered to the sample. Which outcome is expected if the treatment has no effect? a. The sample mean after the treatment should be very different from 80, leading a researcher to reject the null hypothesis. b. The sample mean after the treatment should be very different from 80, leading a researcher to fail to reject the null hypothesis. c. The sample mean after the treatment should be close to 80, leading a researcher to reject the null hypothesis.

d. The sample mean after the treatment should be close to 80, leading a researcher to fail to reject the null hypothesis.

ANSWER: d DIFFICULTY: Apply REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Apply 13. Which of the following is an accurate definition of a Type I error? a. rejecting a false null hypothesis Copyright Cengage Learning. Powered by Cognero.

Page 3

b. rejecting a true null hypothesis c. failing to reject a false null hypothesis d. failing to reject a true null hypothesis ANSWER: b DIFFICULTY: Remember REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Remember 14. Which of the following is an accurate definition of a Type II error? a. rejecting a false null hypothesis b. rejecting a true null hypothesis c. failing to reject a false null hypothesis d. failing to reject a true null hypothesis ANSWER: c DIFFICULTY: Remember REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Remember 15. Which statement below is consistent with making a Type I error? a. concluding that a treatment has an effect when it really does b. concluding that a treatment has no effect when it really has no effect c. concluding that a treatment has no effect when it really does d. concluding that a treatment has an effect when it really has no effect ANSWER: d DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 16. What statement below is consistent with making a Type II error? a. concluding that a treatment has an effect when it really does b. concluding that a treatment has no effect when it really has no effect c. concluding that a treatment has no effect when it really does d. concluding that a treatment has an effect when it really has no effect ANSWER: c DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 17. When is a researcher at risk of making a Type I error? a. whenever H0 is rejected b. whenever H1 is rejected c. whenever H0 fails to be rejected Copyright Cengage Learning. Powered by Cognero.

Page 4

d. The risk of a Type I error is independent of the decision from a hypothesis test.

ANSWER: a DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 18. When is a researcher at risk of making a Type II error? a. whenever H0 is rejected b. whenever H1 is rejected c. whenever H0 fails to be rejected d. The risk of a Type II error is independent of the decision from a hypothesis test.

ANSWER: c DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 19. An instructor is interested in whether frequent feedback in their course to a small sample of students influences student performance. The instructor knows that final class scores are normally distributed with µ = 85 and σ = 6. Which is the alternative hypothesis for this research study?

a. µfrequent feedback = 85 b. µfrequent feedback = 6 c. µfrequent feedback ≠ 85 d. µfrequent feedback ≠ 6 ANSWER: c DIFFICULTY: Apply REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Apply 20. A researcher completes a hypothesis test using a = .05. Based on the evidence from the sample, the researcher decides to reject the null hypothesis. Which statement below is true? a. The researcher might have made a Type I error, but the probability is less than 10%.

b. The researcher might have made a Type II error. c. The researcher might have made a Type I error, but the probability is less than 5%. d. The researcher has made the correct decision.

ANSWER: c DIFFICULTY: Apply REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Apply 21. Which of the following statements is true regarding the influence of a small alpha level in the context of hypothesis testing? a. A small alpha level increases the likelihood of detecting statistical significance.

b. A small alpha level reduces the likelihood of a Type I error.

Copyright Cengage Learning. Powered by Cognero.

Page 5

c. A small alpha level reduces the effect size. d. A small alpha level increases statistical power.

ANSWER: b DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 22. Which of the following statements about the comparison between effect size and power is correct? a. Effect size and power always are the same. b. As effect size increases, power decreases. c. As effect size increases, power also increases. d. This is impossible to determine based on the information provided.

ANSWER: c DIFFICULTY: Understand REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Understand 23. Consider that a population is normally distributed with µ= 100 and σ = 6. What is the power of a α = 0.05, two-tailed hypothesis test with an expected treatment of 2 points and sample size of n = 64? a. 0.0038

b. 0.9962 c. 0.2206 d. 0.7611 ANSWER: d DIFFICULTY: Understand REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Understand 24. Which statement below accurately describes the relationship between the alpha level, the size of the critical region, and the risk of a Type I error? a. As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.

b. As the alpha level increases, the size of the critical region increases, and the risk of a Type II error increases. c. As the alpha level increases, the size of the critical region decreases, and the risk of a Type I error increases. d. As the alpha level increases, the size of the critical region decreases, and the risk of a Type II error increases.

ANSWER: a DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 25. Even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from the population mean. Which outcome is likely if this happens?

a. reject H0 and make a Type I error b. correctly reject H0 Copyright Cengage Learning. Powered by Cognero.

Page 6

c. fail to reject H0 and make a Type II error d. correctly fail to reject H0 ANSWER: a DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 26. Even if a treatment has an effect, it is still possible to obtain a sample mean after the treatment that is very similar to the original population mean. Which outcome is likely if this happens?

a. reject H0 and make a Type I error b. correctly reject H0 c. fail to reject H0 and make a Type II error d. correctly fail to reject H0 ANSWER: c DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 27. Which of the following statements correctly describes the effect of increasing the alpha level (for example, from a = 0.01 to a = 0.05)?

a. This action increases the likelihood of rejecting H0 and increases the risk of a Type I error. b. This action decreases the likelihood of rejecting H0 and increases the risk of a Type I error. c. This action increases the likelihood of rejecting H0 and increases the risk of a Type II error. d. This action decreases the likelihood of rejecting H0 and increases the risk of a Type II error.

ANSWER: a DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 28. By selecting a smaller alpha level, it _____. a. decreases the likelihood that H0 is rejected b. becomes easier to detect a treatment effect c. increases the risk of a Type I error d. decreases the likelihood that H0 fails to be rejected ANSWER: a DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 29. What is the effect of decreasing the alpha level (for example, from α = 0.05 to α = 0.01)? a. This action increases the likelihood of rejecting H0 and increases the risk of a Type II error.

Copyright Cengage Learning. Powered by Cognero.

Page 7

b. This action decreases the likelihood of rejecting H0 and increases the risk of a Type I error. c. This action decreases the likelihood of failing to reject H0 and decreases the risk of a Type I error. d. This action increases the likelihood of failing to reject H0 and increases the risk of a Type II error.

ANSWER: d DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 30. Which of the following is not an underlying assumption of hypothesis testing in the context of a research study? a. The distribution of sample means is normally distributed. b. The values obtained in the sample must be independent. c. The sample size must be greater than n = 30. d. Participants must be randomly selected from the population.

ANSWER: c DIFFICULTY: Understand REFERENCES: 8.3 More About Hypothesis Tests KEYWORDS: Bloom’s: Understand 31. Consider a researcher who is conducting final clinical trials to validate that a new treatment for anxiety is effective.

This researcher is extremely focused on avoiding mistakes in concluding that this new treatment is effective when it really is not when conducting their research. What should this researcher do? a. set a low sample mean

b. set a high sample mean c. set a low alpha level d. set a high alpha level ANSWER: c DIFFICULTY: Apply REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Apply 32. A two-tailed hypothesis test is being used to evaluate a treatment effect with α = 0.05. If the sample data produce a zscore of z = –2.24, which is the correct decision? a. reject the null hypothesis and conclude that the treatment has no effect

b. reject the null hypothesis and conclude that the treatment has an effect c. fail to reject the null hypothesis and conclude that the treatment has no effect d. fail to reject the null hypothesis and conclude that the treatment has an effect ANSWER: b DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 33. The critical boundaries for a hypothesis test are z = +1.96 and z = –1.96. If the z-score for the sample data is z = –1.90, which is the correct statistical decision?

Copyright Cengage Learning. Powered by Cognero.

Page 8

a. fail to reject H1 b. fail to reject H0 c. reject H1 d. reject H0 ANSWER: b DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 34. A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = +2.37. If the researcher is using a two-tailed test, which decision should be made? a. The researcher should reject the null hypothesis with α = .05 but not with α = .01.

b. The researcher should reject the null hypothesis with either α = .05 or α = .01. c. The researcher should fail to reject H0 with either α = .05 or α = .01. d. The researcher should fail to reject the null hypothesis with α = .01 but not with α = .05.

ANSWER: a DIFFICULTY: Apply REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Apply 35. A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? a. a sample mean near 80 for a small sample

b. a sample mean near 80 for a large sample c. a sample mean much different than 80 for a small sample d. a sample mean much different than 80 for a large sample ANSWER: d DIFFICULTY: Apply REFERENCES: 8.3 More about Hypothesis Tests KEYWORDS: Bloom’s: Apply 36. A researcher administers a treatment to a sample of participants selected from a population with µ = 90. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? a. a sample mean near 80 with α = 0.05

b. a sample mean near 80 with α = 0.01 c. a sample mean much different than 80 with α = 0.05 d. a sample mean much different than 80 with α = 0.01 ANSWER: c DIFFICULTY: Apply REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 9

37. A researcher administers a new treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis? a. σ = 5 and α = 0.01

b. σ = 5 and α = 0.05 c. σ = 10 and α = 0.01 d. σ = 10 and α = 0.05 ANSWER: b DIFFICULTY: Apply REFERENCES: 8.3 More about Hypothesis Tests KEYWORDS: Bloom’s: Apply 38. Which of the following statements is consistent with hypothesis testing? a. The edges of the distribution of sample means are consistent with the alternative hypothesis. b. A low alpha level increases the size of the critical region(s). c. All else equal, a one-tailed hypothesis test requires a more extreme treatment effect to detect statistical significance than a two-tailed hypothesis test. d. If conducted correctly, hypothesis testing eliminates the risk of error.

ANSWER: a DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 39. A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population that is known to have a mean of µ = 80. The results will be examined using a one-tailed hypothesis test.

Which of the following is the correct statement for the null hypothesis? a. µ > 80

b. µ > 80 c. µ < 80 d. µ < 80 ANSWER: d DIFFICULTY: Apply REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 40. A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z = +2.27. If the researcher is using a one-tailed test, which is the correct statistical decision? a. reject the null hypothesis with α = 0.05 but not with α = 0.01

b. reject the null hypothesis with either α = 0.05 or α = 0.01 c. fail to reject the null hypothesis with either α = 0.05 or α = 0.01 d. fail to reject the null hypothesis with α = 0.05 but not with α = 0.01 ANSWER: a DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 10

REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 41. A researcher expects a treatment to increase the scores for individuals in a population. The treatment is evaluated using a one-tailed hypothesis test, and the test produces z = +2.40. Based on this result, which is the correct statistical decision? a. reject the null hypothesis with α = 0.05 but not with α = 0.01

b. reject the null hypothesis with either α = 0.05 or α = 0.01 c. fail to reject H0 with either α = 0.05 or α = 0.01 d. fail to reject the null hypothesis with α = 0.05 but not with α = 0.01 ANSWER: b DIFFICULTY: Apply REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 42. A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population. If the researcher uses a one-tailed test with a = 0.01, which of the following correctly identifies the critical region? a. z > 2.33

b. z > 2.58 c. z < 2.33 d. z < 2.58 ANSWER: a DIFFICULTY: Apply REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 43. Which of the following statements comparing one-tailed with two-tailed hypothesis tests is correct? a. All else equal, a more extreme z-score is needed to obtain statistical significance for a one-tailed than twotailed hypothesis test. b. All else equal, a calculated z-score will be smaller for a one-tailed than two-tailed hypothesis test.

c. All else equal, a calculated z-score will be larger for a one-tailed than two-tailed hypothesis test. d. All else equal, a less extreme z-score is needed to obtain statistical significance for a one-tailed than two-tailed hypothesis test.

ANSWER: d DIFFICULTY: Understand REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Understand 44. Consider a researcher who is exploring new potential treatments for specific forms of cancer. This researcher is extremely focused on avoiding mistakes in concluding that treatments that may very well be effective are ineffective when conducting their research. What should this researcher do? a. set a lower sample mean

b. set a higher sample mean c. set a higher alpha level Copyright Cengage Learning. Powered by Cognero.

Page 11

d. set a lower alpha level ANSWER: c DIFFICULTY: Apply REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Apply 45. Under which circumstance can a very small treatment effect still be statistically significant? a. if the sample size (n) is very large b. if the sample standard deviation (σ) is very large c. if the standard error of M (σ M) is very large d. if the population mean (µ) is very large ANSWER: a DIFFICULTY: Understand REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Understand 46. A sample of n = 9 individuals is selected from a population with µ = 60 and σ = 6, and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen’s d for this sample? a. 0.33

b. 0.50 c. 1.00 d. 2.00 ANSWER: b DIFFICULTY: Understand REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Understand 47. A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of µ = 80 and a standard deviation of σ = 12. After treatment, the effect size is measured by computing Cohen’s d, and a value of d = 0.50 is obtained. Based on this information, what is the mean for the treated sample? a. M = 6

b. M = 82 c. M = 86 d. M = 91 ANSWER: c DIFFICULTY: Apply REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Apply 48. If a hypothesis test is found to have power = 0.80, which is the probability that the test will result in a Type II error? a. p = 0.20 b. p = 0.80 c. p = 0.60 d. This cannot be determined with the provided information.

Copyright Cengage Learning. Powered by Cognero.

Page 12

ANSWER: a DIFFICULTY: Understand REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Understand 49. Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. Which of the following should he do? a. decrease the sample size

b. use an alpha (α) of 0.01 instead of 0.05 c. decrease the population standard deviation d. use an alpha (α) of 0.05 instead of 0.01 ANSWER: d DIFFICULTY: Apply REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Apply 50. A researcher is interested in having as much ability as possible to identify a treatment effect if one really exists.

Which of the following strategies should they employ? a. change α from 0.05 to 0.01

b. change from a one-tailed test to a two-tailed test c. change the sample size from n = 25 to n = 100 d. change the population standard deviation from σ = 4 to σ = 8.

ANSWER: c DIFFICULTY: Apply REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Apply 51. The alpha level is a probability value that defines the sample means that will be classified as very unlikely in a hypothesis test.

a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Remember 52. In general, the null hypothesis states that a treatment has no effect on the population mean. a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Remember Copyright Cengage Learning. Powered by Cognero.

Page 13

53. The effect size is a measure of the magnitude of a treatment effect in standard error units. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 8.5 Concerns About Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Understand 54. The probability of a Type II error is represented by the symbol β (beta). a. True b. False ANSWER: True DIFFICULTY: Remember REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Remember 55. The critical region(s) for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 56. If a researcher rejects the null hypothesis when conducting a hypothesis test, it means that the sample data failed to provide sufficient evidence to conclude that the treatment had an effect.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 8.1 The Logic of Hypothesis Testing KEYWORDS: Bloom’s: Understand 57. In a hypothesis test, if the sample data is determined to be in the critical region with α = 0.05, then the same sample data would still be in the critical region if α were changed to 0.01.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 58. In a hypothesis test, if the sample data is determined to be in the critical region with α = 0.01, then the same sample Copyright Cengage Learning. Powered by Cognero.

Page 14

data would still be in the critical region if α were changed to 0.05.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 59. A Type I error occurs when a treatment has an effect but the decision is to fail to reject the null hypothesis. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 60. A Type II error occurs when a researcher concludes that a treatment has no effect when it actually does have an effect. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 61. In hypothesis testing, the magnitude of the difference between the sample and population mean influences whether statistical significance emerges, as well as the effect size.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.3 More About Hypothesis Tests KEYWORDS: Bloom’s: Understand 62. The alpha level determines the risk of a Type II error. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 63. A researcher can reduce the risk of a Type II error by using a larger sample size. a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 15

ANSWER: True DIFFICULTY: Analyze REFERENCES: 8.3 More About Hypothesis Tests KEYWORDS: Bloom’s: Analyze 64. It is always possible that the decision reached in a hypothesis test is incorrect. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.2 Uncertainty and Errors in Hypothesis Testing KEYWORDS: Bloom’s: Understand 65. If a researcher decides to reject the null hypothesis using an alpha level of α = 0.05 at the conclusion of a hypothesis test, then they would include the statement of “p < 0.05” when writing their research report.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 8.3 More about Hypothesis Tests KEYWORDS: Bloom’s: Apply 66. If a researcher does not uncover sufficient evidence for a treatment effect in a hypothesis test, then they would include the statement of “p < 0.05” when writing their research report.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 8.3 More about Hypothesis Tests KEYWORDS: Bloom’s: Apply 67. A researcher conveys that they have uncovered a statistically significant result in their research at a conference. This means that the null hypothesis in their hypothesis test was rejected.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 8.3 More about Hypothesis Tests KEYWORDS: Bloom’s: Apply 68. If other factors are held constant, then increasing the sample size increases the likelihood of rejecting the null hypothesis.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 16

ANSWER: True DIFFICULTY: Understand REFERENCES: 8.3 More about Hypothesis Tests KEYWORDS: Bloom’s: Understand 69. If a researcher expects that a treatment will decrease scores, then the critical region for the directional test will be in the left-hand tail of the distribution of sample means.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 70. A researcher administers a treatment to a sample from a population with a mean of µ = 60. If the treatment is expected to decrease scores, then the null hypothesis would state that µ ≥ 60.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 71. A researcher is evaluating a treatment that is expected to decrease scores. If a = 0.05 is used, then the critical region consists of z-scores less than z = –1.65.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 8.4 Directional (One-Tailed) Hypothesis Tests KEYWORDS: Bloom’s: Apply 72. A sample of n = 64 individuals is selected from a population with µ = 50 and σ = 12, and a treatment is administered to the sample. After treatment, the sample mean is M = 52. After calculating Cohen’s d as a measure of effect size, this treatment would be classified as having a large effect.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Apply 73. In a hypothesis test, the standard error for the distribution of sample means influences whether statistical significance is detected.

a. True Copyright Cengage Learning. Powered by Cognero.

Page 17

b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.3 More About Hypothesis Tests KEYWORDS: Bloom’s: Understand 74. In the context of a hypothesis test, the value obtained for Cohen’s d differs from the value obtained for a z-score in that it is independent of the sample size.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Understand 75. It is possible for a very small treatment effect to be statistically significant. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Understand 76. It is possible for a large treatment effect to not be statistically significant. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 8.5 Concerns about Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Understand 77. The power of a hypothesis test is the probability that the sample mean will be in the critical region even if the treatment actually has no effect.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Understand 78. If the power for a hypothesis test is calculated to be 0.80, then the probability of a Type I error is 0.20. a. True b. False ANSWER: False Copyright Cengage Learning. Powered by Cognero.

Page 18

DIFFICULTY: Understand REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Understand 79. A researcher deciding to increase the desired sample size from n = 25 to n = 100 prior to collecting data for a research study will increase the power of the statistical test.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Apply 80. A researcher decides to lower the alpha level that determines the critical region(s) prior to conducting a hypothesis test. This will increase the power of the hypothesis test.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Apply 81. The term error is used in two different ways in hypothesis testing: A Type I (or Type II) error and the standard error. a. What is standard error? What can a researcher do to reduce standard error in the context of hypothesis testing? b. What is the difference between a Type I and Type II error? What can a researcher do to influence the probability of a Type I error? a. The standard error is the expected difference between a sample mean and hypothesized population ANSWER: mean. The standard error can be reduced by increasing the sample size. b. A Type I error occurs when a researcher rejects the null hypothesis and concludes that a treatment has an effect when it really does not. A Type II error occurs when a researcher fails to reject the null hypothesis and concludes that a treatment has no effect when it really does. A researcher can choose a higher alpha level or increase sample size in order to reduce the likelihood of a Type I error.

DIFFICULTY: Apply REFERENCES: 8.3 More About Hypothesis Tests KEYWORDS: Bloom’s: Apply 82. Some researchers claim that herbal supplements such as ginseng or ginkgo biloba enhance human memory. To test this claim, a researcher selects a sample of n = 25 college students. Each student is given a ginkgo biloba supplement daily for six weeks and then all the participants are given a standardized memory test. For the population, scores on the test are normally distributed with µ = 70 and σ = 15. The sample of n = 25 students had a mean score of M = 75. a. Are the data sufficient to conclude that the herb has a significant effect on memory? Use a two-tailed test with α = 0.05. b. Compute Cohen’s d for this study.

ANSWER:

a.H0: µ = 70 (Students who take the herb are no different in memory.) With α = 0.05, the critical regions consist of z-scores beyond ±1.96. The standard error is σM= 3 and z = 1.67. The decision is to fail to reject H0 and conclude that the herb has no significant effect on memory.

Copyright Cengage Learning. Powered by Cognero.

Page 19

b. Cohen’s d = 5/15 = 0.33.

DIFFICULTY: Apply REFERENCES: 8.5 Concerns About Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Apply 83. A researcher examines whether an over-the-counter cold medication has an effect on mental alertness. A sample of n = 16 participants is obtained, and each person is given a standard dose of the medication one hour before being tested on a driving simulation task. For the general population, scores on the simulation task are normally distributed with µ = 60 and σ = 8. The individuals in the sample had an average score of M = 56. a. Can the researcher conclude that scores on the driving simulation task are significantly different after taking the medication? Use a two-tailed test with α = 0.05. b. Can the researcher conclude that scores on the driving simulation task are significantly lower after taking the medication? Use a one-tailed test with α = 0.01. c. Compute Cohen’s d to measure the size of the effect.

ANSWER:

a. H0: µ = 60 (The cold medication has no effect on mental alertness); H1: µ ≠ 60 (The cold medication has an effect on mental alertness). With α = .05, the critical regions consist of z-scores beyond ±1.96.

The standard error is σM = 2 and z = –2.00. The decision is to reject H0 and conclude that the cold medication has a significant effect on mental alertness. b. H0: µ ≥ 60 (The cold medication does not reduce mental alertness); H1: µ < 60 (The cold medication reduces mental alertness). With α = 0.01, the critical region consists of z-scores beyond z = -2.33. The standard error is σM = 2 and z = –2.00. The decision is to fail to reject H0 and conclude that the cold medication did not significantly reduce mental alertness. c. Cohen’s d = 4/8 = 0.50.

DIFFICULTY: Apply REFERENCES: 8.5 Concerns About Hypothesis Testing: Measuring Effect Size KEYWORDS: Bloom’s: Apply 84. A researcher selects a sample of n = 16 from a normal population with µ = 100 and σ = 20. If the treatment is expected to increase scores by 5 points, what is the power of a two-tailed hypothesis test using α = 0.05?

The critical region boundary of z = +1.96 corresponds to a sample mean of M = 109.8. If the treatment ANSWER: has a 5-point effect, then the distribution of sample means will be centered at µ = 105 and the boundary of M = 109.8 will have a z-score of z = 0.96. Power = p(z > 0.96) = 0.1685

DIFFICULTY: Apply REFERENCES: 8.6 Statistical Power KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 20

Chapter 09 1. Which of the following is a fundamental difference between a t statistic and a z-score? a. The t statistic uses the sample mean in place of the population mean. b. The t statistic uses the sample variance in place of the population variance. c. The t statistic computes the standard error by dividing the standard deviation by n – 1 instead of dividing by n. d. None of these are differences between t and z.

ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 2. Which of the following is not needed to compute a t statistic? a. the size of the sample b. the value of the population variance or standard deviation c. the value of the sample mean d. the value of the sample variance or standard deviation ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 3. Why are t statistics more variable than z-scores? a. The extra variability is caused by variations in the sample mean. b. The extra variability is caused by variations in the sample variance. c. The extra variability is caused by variations in the population mean. d. The extra variability is caused by variations in experimental control.

ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 4. If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic? a. The researcher must know the population median.

b. The researcher must know the population variance or standard deviation. c. The researcher must know the population size. d. The researcher does not need to know any information about the population.

ANSWER: d DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 5. If two samples are selected from the same population, under which circumstances will the two samples have exactly the Copyright Cengage Learning. Powered by Cognero.

Page 1

same t statistic? a. The samples are the same size and have the same variance.

b. The samples are the same size and have the same mean. c. The samples have the same mean and the same variance. d. The samples are the same size, have the same mean, and have the same variance.

ANSWER: d DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 6. A sample of n = 4 scores has SS = 60. Which is the variance for this sample? a. s2 = 30 b. s2 = 20 c. s2 = 60 d. s2 = 15 ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 7. On average, which value is expected for the t statistic when the null hypothesis is true? a. t = 0.00 b. t = 1.00 c. t = 1.96 d. t > 1.96 ANSWER: a DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 8. What is the sample variance and estimated standard error for a sample of n = 9 scores with SS = 72? a. s2 = 9 and sM = 3 b. s2 = 9 and sM = 1 c. s2 = 8 and sM = 3 d. s2 = 8 and sM = 1 ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 9. A sample of n = 4 scores has a variance of s2 = 64. What is the estimated standard error for the sample mean? a. sM = 1 Copyright Cengage Learning. Powered by Cognero.

Page 2

b. sM = 2 c. sM = 4 d. sM = 16 ANSWER: c DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 10. A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10. What is the estimated standard error for the sample mean?

a. sM = 4 b. sM = 2 c. sM = 2.5 d. sM = 1 ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 11. A sample with a mean of M = 40 and a variance of s2 = 12 has an estimated standard error of 2 points. How many scores are in the sample? a. n = 3

b. n = 6 c. n = 12 d. n = 10 ANSWER: a DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 12. A sample of n = 7 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance?

a. s2 = 24 b. s2 = 36 c. s2 = 28 d. s2 = 14 ANSWER: c DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 13. Which set of characteristics will produce the smallest value for the estimated standard error?

Copyright Cengage Learning. Powered by Cognero.

Page 3

a. a large sample size and a small sample variance b. a large sample size and a large sample variance c. a small sample size and a small sample variance d. a small sample size and a large sample variance ANSWER: a DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 14. Which of the following samples will have the smallest value for the estimated standard error? a. n = 4 with s2 = 16 b. n = 4 with s2 = 64 c. n = 16 with s2 = 16 d. n = 16 with s2 = 64 ANSWER: c DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 15. A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t statistic and M = 46 and s2 = 10, how many individuals were in the sample? a. n = 29

b. n = 11 c. n = 31 d. n = 9 ANSWER: c DIFFICULTY: Apply REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Apply 16. A researcher conducts a hypothesis test using a sample of n = 20 with M = 34 and s2 = 36 from an unknown population. What is the df value for the t statistic? a. df = 19

b. df = 35 c. df = 21 d. df = 37 ANSWER: a DIFFICULTY: Apply REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Apply 17. When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution? a. It is almost perfectly symmetrical like the normal distribution.

Copyright Cengage Learning. Powered by Cognero.

Page 4

b. It is flatter and more spread out than the normal distribution. c. It is taller and narrower than the normal distribution. d. There is no consistent relationship between the t distribution and the normal distribution.

ANSWER: b DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 18. With α = .05, the two-tailed critical region for a t test using a sample of n = 20 participants would have boundaries of _____.

a. t = ±2.136 b. t = ±2.080 c. t = ±2.093 d. t = ±2.086 ANSWER: c DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 19. Assuming all other factors are held constant, if the df value for a two-tailed t test with α = 0.05 were increased from df = 6 to df = 20, what would happen to the critical values for t? a. The critical values would further from t = 0.

b. The critical values would move closer to t = 0. c. The critical values would not change. d. This is impossible to determine without more information.

ANSWER: b DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests With the t Statistic KEYWORDS: Bloom’s: Apply 20. A researcher is using a two-tailed hypothesis test with α = 0.05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample? a. n = 22

b. n = 21 c. n = 20 d. n = 23 ANSWER: a DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests With the t Statistic KEYWORDS: Bloom’s: Apply 21. A sample has a mean of M = 39.50, a standard deviation of s = 4.30, and produces a t statistic of t = +2.14. For a twotailed hypothesis test, which of the following is the correct statistical decision for this sample? a. The researcher should reject the null hypothesis with α = 0.05 but not with α = .01.

Copyright Cengage Learning. Powered by Cognero.

Page 5

b. The researcher should reject the null hypothesis with either α = 0.05 or α = 0.01. c. The researcher should reject the null hypothesis with α = 0.01 but not with α = 0.05. d. This is impossible to determine based on the provided information.

ANSWER: d DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 22. A sample of n = 25 scores produces a t statistic of t = +2.052. If the researcher is conducting a two-tailed hypothesis test, which of the following is the correct statistical decision? a. The researcher should reject the null hypothesis with α = 0.05 but not with α = 0.01.

b. The researcher should reject the null hypothesis with either α = 0.05 or α = 0.01. c. The researcher should fail to reject the null hypothesis with either α = 0.05 or α = 0.01. d. This is impossible to determine based on the provided information.

ANSWER: c DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 23. A hypothesis test produces a t statistic of t = +2.19. If the researcher is conducting a two-tailed hypothesis test with α = 0.05, how large does the sample have to be in order to reject the null hypothesis? a. at least n = 11

b. at least n = 12 c. at least n = 13 d. at least n = 14 ANSWER: c DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 24. Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values? a. The two t statistics will be identical.

b. The sample with the larger variance will produce the larger t statistic. c. The sample with the smaller variance will produce the larger t statistic. d. There is no way to predict the relationship between the two t statistics.

ANSWER: c DIFFICULTY: Understand REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Understand 25. If other factors are held constant, which set of sample characteristics is most likely to produce a statistically significant t statistic?

a. n = 25 with s2 = 100 Copyright Cengage Learning. Powered by Cognero.

Page 6

b. n = 25 with s2 = 400 c. n = 100 with s2 = 100 d. n = 100 with s2 = 400 ANSWER: c DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 26. If n = 63 for a two-tailed hypothesis test in which a t-test should be utilized, which df value should be referenced when using the abridged t distribution table in the textbook in order to set the critical t values for the hypothesis test? a. df = 64

b. df = 60 c. df = 62 d. df = 80 ANSWER: b DIFFICULTY: Apply REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Apply 27. Which situtaion below violates an assumption for conducting hypothesis tests using the t statistic? a. Two observations in a sample are independent from one another. b. The population from which a small sample (n < 30) is obtained for a hypothesis test is normally distributed. c. The population from which a large sample (n > 30) is obtained for a hypothesis test is not normally distributed. d. None of these situations violates an assumption for conducting hypothesis tests using the t statistic.

ANSWER: d DIFFICULTY: Understand REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Understand 28. If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80?

a. M = 85 and s2 = 9 b. M = 85 and s2 = 18 c. M = 90 and s2 = 9 d. M = 90 and s2 = 18 ANSWER: c DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 29. If a treatment produces a sample mean of M = 25 with s = 18 among a sample of n = 36, which t-statistic should be obtained and which decision should be made if conducting a two-tailed hypothesis test with α = 0.05 and an expected Copyright Cengage Learning. Powered by Cognero.

Page 7

mean of µ= 30?

a. t = −1.67 and reject H0 b. t = −1.39 and reject H0 c. t = −1.67 and fail to reject H0 d. t = −1.39 and fail to reject H0 ANSWER: c DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 30. If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80? a. M = 85 for a sample of n = 25

b. M = 85 for a sample of n = 100 c. M = 90 for a sample of n = 25 d. M = 90 for a sample of n = 100 ANSWER: d DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 31. Under what circumstances can a very small treatment effect be statistically significant? a. if the sample size is large and the sample variance is small b. if the sample size and variance are each large c. if the sample size is small and the sample variance is large d. if the sample size and variance are each small ANSWER: a DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 32. How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen’s d?

a. Larger sample variance increases both the estimated standard error and measures of effect size. b. Larger sample variance increases the estimated standard error but decreases measures of effect size. c. Larger sample variance decreases the estimated standard error but increases measures of effect size. d. Larger sample variance decreases both the estimated standard error and measures of effect size.

ANSWER: b DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 33. A researcher selects a sample from a population with µ = 30 and uses the sample to evaluate the effect of a treatment.

Copyright Cengage Learning. Powered by Cognero.

Page 8

After treatment, the sample has a mean of M = 32 and a variance of s2 = 6. If Cohen’s d is used to measure the size of the treatment effect, which of the following would have no effect on the value of Cohen’s d? a. an increased sample size

b. an increased sample mean c. an increase sample variance d. Each of these of these aspects will influence the value of Cohen’s d.

ANSWER: a DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 34. Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that µ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare? a. The larger sample is more likely to reject the null hypothesis and will produce a larger value for Cohen’s d.

b. The larger sample is more likely to reject the null hypothesis, but the two samples will have the same value for Cohen’s d. c. The larger sample is less likely to reject the null hypothesis and will produce a larger value for Cohen’s d.

d. The larger sample is less likely to reject the null hypothesis, but the two samples will have the same value for Cohen’s d.

ANSWER: b DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 35. A sample of n = 16 scores produces a t statistic of t = +2.00. If the sample is used to measure effect size with r2, which value will be obtained for r2?

a. r2 = 0.10 b. r2 = 0.20 c. r2 = 0.11 d. r2 = 0.21 ANSWER: d DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 36. Consider a sample with M = 16 and s2 = 25. A researcher is testing the null hypothesis that µ = 20. Which statement is correct? a. The treatment has a large effect size (Cohen’s d).

b. The treatment has a moderate effect size (Cohen’s d). c. The treatment has a small effect size (Cohen’s d). d. The treatment has a statistically significant effect.

ANSWER: a Copyright Cengage Learning. Powered by Cognero.

Page 9

DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 37. The results of a hypothesis test are reported as follows in a scientific report: t(38) = –3.13, p < 0.05. Based on this information, which statement below is not correct? a. The sample size was n = 39.

b. The conclusion reached by the researcher was to reject the null hypothesis. c. The sample mean was greater than the hypothesized population mean. d. The probability of a Type I error is less than 5%.

ANSWER: c DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 38. A sample is selected from a population with µ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen’s d? a. d = 0.125

b. d = 0.25 c. d = 0.50 d. Cohen’s d cannot be computed without knowing the sample size.

ANSWER: c DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 39. The results of a hypothesis test are reported as follows in a scientific report: t(17) = +2.76, p < 0.05. Based on this information, which statement below is not correct? a. The sample size is n = 18.

b. The sample mean is greater than the hypothesized population mean. c. The probability that there is a statistically significant effect is less than 5%. d. The conclusion reached by the researcher was to reject the null hypothesis.

ANSWER: c DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 40. Which of the following is consistent with what r2 represents as a measure of effect size? a. the portion of variability in a sample attributable to a treatment effect relative to the total variability in the sample b. the portion of variability in a sample attributable to a treatment effect after correcting for sample size

c. the statistical significance of a treatment effect d. the statistical significance of a treatment effect correcting for the alpha level ANSWER: a Copyright Cengage Learning. Powered by Cognero.

Page 10

DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 41. Which bit of information is not obtainable from the results of a t-test written up in a statistical report? a. the alpha level used in the hypothesis test b. whether the null hypothesis is rejected or fails to be rejected c. the degrees of freedom used in the hypothesis test d. Each of these bits of information is obtainable from the results of a t-test written up in a statistical report.

ANSWER: d DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 42. If a sample of n = 22 scores is being used to make an 90% confidence interval estimate of the population mean (µ), which values of t should be used? a. t = ±1.325

b. t = ±1.323 c. t = ±1.717 d. t = ±1.721 ANSWER: d DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 43. A sample of n = 7 scores is selected from a population with an unknown mean (µ). The sample has a mean of M = 40 and a variance of s2 = 63. Which of the following is the correct 95% confidence interval for µ? a. µ = 40 ± 7.341

b. µ = 40 ± 22.023 c. µ = 40 ± 7.095 d. µ = 40 ± 21.285 ANSWER: a DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 44. All else constant, which combination of factors would increase the width of a confidence interval most? a. a smaller sample size and a smaller confidence interval b. a larger sample size and a smaller confidence interval c. a smaller sample size and a larger confidence interval d. a larger sample size and a larger confidence interval ANSWER: c DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 11

REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 45. All else constant, which of the following would not have an effect on the width of a confidence interval? a. an increased sample mean b. an increased sample size c. an increased percentage of confidence d. an increased sample variance ANSWER: a DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 46. The results of a hypothesis test are reported as follows in a scientific report: t(15) = 2.70, p < 0.05. Based on this report, how many individuals were in the sample? a. n = 14

b. n = 15 c. n = 16 d. n = 5 ANSWER: c DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 47. Which of the following results from a hypothesis test involving the computation of a t-statistic is structured correctly based on standards for presenting hypothesis tests in scientific reports?

a. t(19) = 2.30, r2 = 0.42, p < .05 b. t(19) = 2.30, p < 0.05, r2 = 0.42 c. r2 = 0.42, t(19) = 2.30 , p < 0.05 d. t = 2.30, df = 19, p < 0.05, r2 = 0.42 ANSWER: b DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 48. If a treatment is expected to increase scores on a variable for which the mean is expected to be µ = 100, what is the null hypothesis?

a. µwith treatment > 100 b. µwith treatment < 100 c. µwith treatment > 100 d. µwith treatment < 100 ANSWER: d DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 12

REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 49. If a treatment is expected to decrease scores on a variable for which the mean is expected to be µ = 50, what is the null hypothesis?

a. µwith treatment > 50 b. µwith treatment < 50 c. µwith treatment > 50 d. µwith treatment < 50 ANSWER: c DIFFICULTY: Understand REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 50. It is expected that a treatment will reduce scores on a variable. If α = 0.05, what is the critical t value for a one-tailed hypothesis test with n = 15? a. t = 1.761

b. t = –1.761 c. t = 1.746 d. t = –1.746 ANSWER: b DIFFICULTY: Understand REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 51. When the population variance or standard deviation is not known, a researcher must use a t statistic instead of a zscore when conducting a hypothesis test.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 52. Compared to a z-score, a hypothesis test with a t statistic requires less information from the sample. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 53. The estimated standard error is a measure of central tendency.

Copyright Cengage Learning. Powered by Cognero.

Page 13

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 54. For a hypothesis test with alpha level held constant, as sample size increases the critical values obtained from the t distribution increasingly resemble the critical values obtained from the z distribution.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 55. A sample of n = 4 scores has a variance of s2 = 16 and an estimated standard error of 2. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 56. If a treatment is expected to decrease scores in a population with µ= 30, then the alternative hypothesis is µ ≤ 30. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 57. A random sample with n = 20 scores has df = 19. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 58. As sample size decreases, the critical t values for a two-tailed t-test with α = 0.05 will move closer to t = 0. a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 14

ANSWER: False DIFFICULTY: Apply REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Apply 59. For a one-tailed hypothesis test with α = 0.01 and a sample of n = 28 scores, the critical t value is either t = +2.473 or t = –2.473.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 60. As sample size increases, the distribution of t statistics becomes flatter and more spread out. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 61. A directional hypothesis test has a critical region that consists of the extreme ends of both the left and right side of the t distribution.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 62. For a two-tailed hypothesis test with α = 0.05 and a sample of n = 16, the boundaries for the critical region are t = ±2.120.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 63. If a treatment is expected to increase scores among a population with µ= 20, then the alternative hypothesis is µwith treatment > 20.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 15

ANSWER: True DIFFICULTY: Understand REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Understand 64. The t-score distribution for df = 4 resembles the z-score distribution in shape more than a t-score distribution for df = 20.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 65. If two samples, each with n = 20 scores are selected from the same population and both have the same mean (M = 53), then they will also generate the same t statistic.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 66. If other factors are held constant, as the sample size and sample variance increase, the estimated standard error decreases.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.1 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 67. It is possible for the probability of a Type I error (p-value) obtained from a t-test to be 0. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.3 The t Statistic: An Alternative to z KEYWORDS: Bloom’s: Understand 68. If other factors are held constant, the larger the value of the sample variance, the lesser the likelihood of rejecting the null hypothesis.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 16

ANSWER: True DIFFICULTY: Understand REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Understand 69. If other factors are held constant, the larger the sample size is, the greater the likelihood of rejecting the null hypothesis.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Understand 70. In a hypothesis test, a small value for the sample variance increases the likelihood that a statistically significant treatment effect will be detected.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Understand 71. If a hypothesis test using a sample of n = 16 scores produces a t statistic of t = 2.15, then the correct decision is to reject the null hypothesis for a two-tailed hypothesis test with α = 0.05.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 72. Two samples are selected from a population, and a treatment is administered to the samples. If both samples have the same mean and the same variance, a researcher is more likely to reject the null hypothesis and find a significant treatment effect with a sample of n = 100 than with a sample of n = 4.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 73. A research report describing the effect of a treatment states “t(15) = +2.31, p < 0.05.” For this study, there is less than a 5% probability that the treatment is effective.

a. True Copyright Cengage Learning. Powered by Cognero.

Page 17

b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 74. A research report states “t(18) = +3.00, p < 0.05.” For this test, r2 = .33. a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 75. The null hypothesis for a research study states that µ = 70. If a researcher obtains a sample with M = 73 and s2 = 9, then Cohen’s d = 0.33.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 76. Although t tests are affected by sample size, sample size does not influence measures of effect size, such as r2 or Cohen’s d.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 77. To estimate a population mean with a confidence interval, a researcher must estimate a range of values for t. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 78. A confidence interval is a range of values centered around a sample statistic. a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 18

ANSWER: True DIFFICULTY: Remember REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Remember 79. All else constant, a 90% confidence interval for µ will be wider than a 95% confidence interval. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Understand 80. For a one-tailed test evaluating a treatment that is hypothesized to decrease scores, a researcher obtains t(8) = -1.80.

For α = 0.05, the correct decision is to reject the null hypothesis.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Apply 81. A sample is selected from a population with µ = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s2 = 64. a. For a sample of n = 4 scores, conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen’s d to measure the size of the treatment effect. Use a two-tailed test with α = 0.05. b. For a sample of n = 16 scores, conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen’s d to measure the size of the treatment effect. Use a two-tailed test with α = 0.05. c. Describe how increasing the size of the sample affects the likelihood of rejecting the null hypothesis and the measure of effect size. a. The standard error is 4 and t = +1.25. With df = 3, the critical value is t = ±3.182. Fail to reject the ANSWER: null hypothesis. Cohen’s d = 5/8 = 0.625. b. The standard error is 2 and t = +2.50. With df = 15, the critical value is t = ±2.131. Reject the null hypothesis. Cohen’s d = 5/8 = 0.625. c. Increasing sample size increases the likelihood of rejecting the null hypothesis but has no influence on measures of effect size like Cohen’s d.

DIFFICULTY: Apply REFERENCES: 9.2 Hypothesis Tests with the t Statistic KEYWORDS: Bloom’s: Apply 82. A sample of n = 16 individuals is selected from a population with µ = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33. The researcher expects the treatment will increase scores on a variable. a. Assuming the sample variance is s2 = 16, conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r2 to measure the size of the treatment effect. Use a one-tailed test with α = 0.01. b. Assuming the sample variance is s2 = 64, conduct a hypothesis test to evaluate the significance of the treatment effect Copyright Cengage Learning. Powered by Cognero.

Page 19

and calculate r2 to measure the size of the treatment effect. Use a one-tailed test with α = 0.01. c. Describe how increasing variance affects the likelihood of rejecting the null hypothesis and the measure of effect size.

ANSWER:

a. The standard error is 1 and t = +3.00. With df = 15, the critical value is t > 2.602. Reject the null hypothesis. r2 = 9/24 = 0.375 b. The standard error is 2 and t = +1.50. With df = 15, the critical value is t > 2.602. Fail to reject the null hypothesis. r2 = 2.25/17.25 = 0.13. c. Increasing sample variance decreases the likelihood of rejecting the null hypothesis and decreases measures of effect size like r2.

DIFFICULTY: Apply REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Apply 83. A sample of n = 16 scores has a mean of M = 58 with SS = 540. Use the sample to construct the 95% confidence interval for µ.

ANSWER:

The sample variance is s2 = 36 and the estimated standard error is 1.5. With df = 15 and 95% confidence, use t = ± 2.1311. The interval is µ = 58 ± 2.131(1.5) and extends from 54.8035 to 61.1965.

DIFFICULTY: Apply REFERENCES: 9.3 Measuring Effect Size for the t Statistic KEYWORDS: Bloom’s: Apply 84. A sample of n = 9 participants is obtained from a population with µ = 29, and a treatment is administered to the individuals in the sample. After treatment, the scores for the nine participants are as follows: 23, 33, 26, 28, 30, 26, 27, 25, 25. a. Are the data sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = 0.05. b. Write the results of this hypothesis test for a scientific report. c. Are the data sufficient to conclude that the treatment significantly decreased scores? Use a one-tailed test with α = 0.05. d. Write the results of this hypothesis test for a scientific report.

ANSWER:

a. M = 27 and SS = 72. The standard error is 1 and t = –2.00. With critical boundaries of ±2.306. Fail to reject H0. b. The treatment (M = 27, SD = 3) has no effect on scores, t(8) = –2.00, p > 0.05. c. t = –2.00 is beyond the critical boundary of –1.860. Reject H0. d. The treatment (M = 27, SD = 3) significantly reduced scores, t(8) = –2.00, p < 0.05, one tailed.

DIFFICULTY: Apply REFERENCES: 9.4 Directional Hypotheses and One-Tailed Tests KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 20

Chapter 10 1. Which of the following research situations would be most likely to use an independent-measures design? a. examine the development of vocabulary as a group of children mature from age 2 to age 3 b. examine the long-term effectiveness of a stop-smoking treatment by interviewing individuals 2 months and 6 months after the treatment ends

c. compare the mathematics skills for 9th-grade boys relative to 9th-grade girls d. compare the blood-pressure readings before medication and after medication for a group of patients with high blood pressure

ANSWER: c DIFFICULTY: Apply REFERENCES: 10.1 Introduction to the Independent-Measures Design KEYWORDS: Bloom’s: Apply 2. Which of the following is true regarding assumptions underlying the independent-measures t formula for hypothesis testing? a. As sample sizes increase, the assumption that observations within each sample must be independent becomes less important. b. As sample sizes increase, the assumption that the two populations from which the samples are selected must be normal becomes more important. c. As the discrepancy in sample sizes increases, the assumption that observations within each sample must be independent becomes more important. d. As the discrepancy in sample sizes increases, the assumption that the two populations from which the samples are selected must have equal variances becomes more important.

ANSWER: d DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 3. Which of the following is the correct null hypothesis for an independent-measures t test? a. µ1 – µ2 = 0 b. M1 – M2 = 0 c. µ1 – µ2 ≠ 0 d. M1 – M2 ≠ 0 ANSWER: a DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 4. An independent-measures research study uses n = 15 participants in one group and n = 12 participants in a second group to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test? a. df = 27

b. df = 24 c. df = 25 Copyright Cengage Learning. Powered by Cognero.

Page 1

d. df = 26 ANSWER: c DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 5. A research study has two samples, each with n = 6, and the two experimental treatments used in each sample are being compared using an independent-measures t statistic. What is the df value for the t statistic in this study? a. df = 14

b. df = 12 c. df = 11 d. df = 10 ANSWER: d DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 6. An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test? a. df = 18

b. df = 19 c. df = 38 d. df = 39 ANSWER: c DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 7. An independent-measures study comparing two treatment conditions produces a t statistic with df = 16. If the two samples are the same size, how many participants were in each of the samples? a. n = 9

b. n = 10 c. n = 8 d. n = 18 ANSWER: a DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 8. Which of the following is the correct alternative hypothesis for an independent-measures t test? a. µ1 – µ2 = 0 b. M1 – M2 = 0 c. µ1 – µ2 ≠ 0 Copyright Cengage Learning. Powered by Cognero.

Page 2

d. M1 – M2 ≠ 0 ANSWER: c DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 9. A researcher reports an independent-measures t statistic with df = 16. How many participants were in the entire study? a. n = 17 b. n = 18 c. n = 14 d. n = 34 ANSWER: b DIFFICULTY: Apply REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 10. One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has a variance of s2 = 10. If the pooled variance is computed for these two samples, then the value obtained for the variance will be _____. a. closer to 6 than to 10

b. closer to 10 than to 6 c. exactly halfway between 6 and 10 d. This cannot be determined by the information provided ANSWER: c DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 11. One sample has a sample size of n = 8 and SS = 168. A second sample has a sample size of n = 6 and SS = 126. What is the pooled variance for these two samples?

a. s2p = 17.36 b. s2p = 21.00 c. s2p = 18.38 d. s2p = 24.50 ANSWER: d DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 12. One sample has a variance of s2 = 12 and a second sample has a variance of s2 = 8. Which of the following most accurately describes the pooled variance for the two samples? a. closer to 8 than to 12

b. closer to 12 than to 8 c. somewhere between 8 and 12 Copyright Cengage Learning. Powered by Cognero.

Page 3

d. around 16 ANSWER: c DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 13. One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can be concluded about the pooled variance for these two samples? a. It will be closer to 20 than to 30.

b. It will be closer to 30 than to 20. c. It will be exactly halfway between 20 and 30. d. This cannot be determined by the information provided.

ANSWER: b DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 14. Two samples, each with n = 5 scores, have a pooled variance of s2p = 40. What is the estimated standard error for the sample mean difference?

a. s(M1 - M2) = 4 b. s(M1 - M2) = 8 c. s(M1 - M2) = 10 d. s(M1 - M2) = 20 ANSWER: a DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 15. Two samples each have n = 4 scores. If the first sample has a variance of s2 = 10 and the second sample has a variance of s2 = 6, what is the estimated standard error for the sample mean difference?

a. s(M1 - M2) = 1 b. s(M1 - M2) = 2 c. s(M1 - M2) = 4 d. This cannot be determined by the information provided.

ANSWER: b DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 16. A researcher is examining whether daily exercise influences mood. The researcher assigns n = 12 individuals to exercise for three months and finds an average mood score of M = 22 with SS = 182 after three months for individuals in this group. A second group of n = 7 individuals assigned to a control group for the three months has a mood score of M = 19 with SS = 90. Which of the following is most consistent with the results of conducting a two-tailed independentCopyright Cengage Learning. Powered by Cognero.

Page 4

measures t test with α = .05? a. t = +2.12 and fail to reject the null hypothesis

b. t = +2.12 and reject the null hypothesis c. t = +1.58 and fail to reject the null hypothesis d. t = +1.58 and reject the null hypothesis ANSWER: c DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 17. A researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123 after three months for individuals in this group. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independentmeasures t test with α = .05? a. t = –1.83 and fail to reject the null hypothesis

b. t = –1.83 and reject the null hypothesis c. t = –1.61 and fail to reject the null hypothesis d. t = –1.61 and reject the null hypothesis ANSWER: b DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 18. An independent-measures study with n = 5 in each sample produces a sample mean difference of 4 points and a pooled variance of 40. What is the value for the t statistic? a. t = +1

b. t = +4 c. t = +2 d. t = +3 ANSWER: a DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 19. Two samples, each with n = 16 scores, produce an estimated standard error of s(M1 - M2) = 4 and a t statistic of t = +2.00. What is the sample mean difference?

a. M1 – M2 = 2 b. M1 – M2 = 4 c. M1 – M2 = 8 d. M1 – M2 = 16 ANSWER: c DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic Copyright Cengage Learning. Powered by Cognero.

Page 5

KEYWORDS:

Bloom’s: Understand

20. The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points. If there are n = 8 scores in each sample, what is the value for the t statistic? a. t = +3

b. t = +2 c. t = +1 d. t = +4 ANSWER: a DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 21. What is the average value expected for the independent-measures t statistic if the null hypothesis is true? a. t = 0 b. t = ±1 c. t = ±2 d. t = ±3 ANSWER: a DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 22. An independent-measures research study uses two samples, each with n = 10 participants. If the data produce a t statistic of t = 2.015, which of the following is the correct decision for a two-tailed hypothesis test? a. reject the null hypothesis with α = 0.05 but fail to reject with α = 0.01

b. reject the null hypothesis with either α = 0.05 or α = 0.01 c. fail to reject the null hypothesis with either α = 0.05 or α = 0.01 d. This cannot be answered with the information provided.

ANSWER: c DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 23. An independent-measures research study uses two samples, each with n = 15 participants. If the data produce a t statistic of t = 2.660, which of the following is the correct decision for a two-tailed hypothesis test? a. reject the null hypothesis with α = 0.05 but fail to reject with α = 0.01

b. reject the null hypothesis with either α = 0.05 or α = 0.01 c. fail to reject the null hypothesis with either α = 0.05 or α = 0.01 d. This cannot be answered with the information provided.

ANSWER: a DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 6

24. A researcher conducts a research study to examine whether there is a difference between two treatments regarding anxiety. Which of the following is consistent conceptually with the null hypothesis? a. The second treatment is less effective than the first treatment regarding anxiety.

b. The first treatment is less effective than the second treatment regarding anxiety. c. There is a difference between the two treatments among the general population regarding anxiety. d. There is no difference between the two treatments among the general population regarding anxiety.

ANSWER: d DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 25. A researcher reports t(22) = 5.30, p < 0.01, two tails for an independent-measures experiment. How many individuals participated in the entire experiment? a. n = 20

b. n = 21 c. n = 23 d. n = 24 ANSWER: d DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 26. The results of an independent-measures research study are reported as t(22) = 2.12, p < 0.05, two tails. For this study, what t values formed the boundaries for the critical region? a. t = ±2.080

b. t = ±2.074 c. t = ±2.069 d. t = ±2.064 ANSWER: b DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 27. An independent-measures research study with n = 5 participants in each treatment produces sample variances of s2 = 8 and s2 = 10, and a 2-point difference between the two treatment means. What is the value of Cohen’s d? a. d = 0.75

b. d = 0.67 c. d = 0.33 d. d = 0.12 ANSWER: b DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 7

28. Two samples, each with n = 9 scores, produce an independent-measures t statistic of t = +2.00. If the effect size is measured using r2, what is the value of r2?

a. r2 = 0.33 b. r2 = 0.20 c. r2 = 0.25 d. r2 = 0.50 ANSWER: b DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 29. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is s2p = 16, what is the value of Cohen’s d? a. d = 0.25

b. d = 0.50 c. d = 1.00 d. This cannot be determined with the information provided.

ANSWER: c DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 30. A researcher predicts that scores in treatment A will be lower than scores in treatment B. Which of the following is the correct alternative hypothesis for a one-tailed test evaluating this prediction?

a. A > B b. A < B c. A > B d. A < B ANSWER: b DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 31. An independent-measures study produces sample means of M1 = 20 and M2 = 17. If both samples have n = 18 and Cohen’s d = 0.50, what is the value for the pooled variance?

a. s2p = 16 b. s2p = 4 c. s2p = 6 d. s2p = 36 ANSWER: d DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 8

REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 32. Which of the following is not an assumption underlying the independent-measures t formula for hypothesis testing. a. The observations within each sample must be independent. b. The two populations from which the samples are selected must be normal. c. The two samples must have equal sample sizes. d. The two populations from which the samples are selected must have equal variances.

ANSWER: c DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 33. A researcher predicts that scores in treatment A will be higher than scores in treatment B. If the mean for the n = 10 participants in treatment A is 4 points higher than the mean for the n = 10 participants in treatment B and the data produce t = 1.985, which decision should be made?

a. reject H0 if  = 0.05 and if  = 0.01 b. reject H0 if  = 0.05 but fail to reject H0 if  = 0.01 c. fail to reject H0 if  = 0.05 and if  = 0.01 d. fail to reject H0 if  = 0.05 but reject H0 if  = 0.01 ANSWER: b DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 34. A researcher predicts that scores in treatment A will be higher than scores in treatment B. Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?

a. A > B b. A < B c. A > B d. A <  ANSWER: d DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 35. The narrower the confidence interval, the more precise it is. Which combination of factors will produce the most precise estimate of the difference between two population means? a. two samples of n = 20 and 80% confidence

b. two samples of n = 20 and 90% confidence c. two samples of n = 50 and 80% confidence d. two samples of n = 50 and 90% confidence ANSWER: c Copyright Cengage Learning. Powered by Cognero.

Page 9

DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 36. Two separate samples are being used to estimate the population mean difference between two treatment conditions.

Which of the following would produce the widest confidence interval?

a. n1 = n2 = 10 with a pooled variance of s2p = 10 b. n1 = n2 = 10 with a pooled variance of s2p = 100 c. n1 = n2 = 20 with a pooled variance of s2p = 10 d. n1 = n2 = 20 with a pooled variance of s2p = 100 ANSWER: b DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 37. One sample has n = 18 with SS = 102 and M = 12. A second sample has n = 5 with SS = 171 and M = 8. Which of the following is the 95% confidence interval for the mean difference in confidence between the two samples? a. 5 ± 6.0956

b. 4 ± 3.7856 c. 4 ± 6.0956 d. 5 ± 3.7856 ANSWER: b DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 38. Which of the following confidence intervals indicates a significant difference between treatments with α = 0.05? a. estimate that µ1 – µ2 is in an interval between 2 and 10 with 95% confidence b. estimate that µ1 – µ2 is in an interval between –2 and 8 with 95% confidence c. estimate that µ1 – µ2 is in an interval between 0 and 4 with 95% confidence d. This cannot be determined by the information provided.

ANSWER: a DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 39. For the independent-measures t statistic, what is the effect of increasing the sample variances? a. an increase in the likelihood of rejecting H0 and an increase in measures of effect size b. an increase in the likelihood of rejecting H0 and a decrease in measures of effect size c. a decrease in the likelihood of rejecting H0 and an increase in measures of effect size d. a decrease in the likelihood of rejecting H0 and a decrease in measures of effect size ANSWER:

d

Copyright Cengage Learning. Powered by Cognero.

Page 10

DIFFICULTY: Understand REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Understand 40. For the independent-measures t statistic, what is the effect of increasing the difference between sample means? a. an increase in the likelihood of rejecting H0 and an increase in measures of effect size b. an increase in the likelihood of rejecting H0 and a decrease in measures of effect size c. a decrease in the likelihood of rejecting H0 and an increase in measures of effect size d. a decrease in the likelihood of rejecting H0 and a decrease in measures of effect size ANSWER: a DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 41. For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples? a. an increase in the likelihood of rejecting H0 and an increase in measures of effect size b. an increase in the likelihood of rejecting H0 and little or no influence on measures of effect size c. a decrease in the likelihood of rejecting H0 and an increase on measures of effect size d. a decrease the likelihood of rejecting H0 and little or no influence on measures of effect size ANSWER: b DIFFICULTY: Understand REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Understand 42. Which of the following sets of data would produce the largest value for Cohen’s d? a. n = 10 for both samples, a pooled variance of s2p = 16, and a mean difference of 3 points b. n = 10 for both samples, a pooled variance of s2p = 16, and a mean difference of 4 points c. n = 20 for both samples, a pooled variance of s2p = 36, and a mean difference of 5 points d. This cannot be determined by the information provided.

ANSWER: b DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 43. Which of the following sets of data would produce the largest value for an independent-measures t statistic? a. Sample means of M = 10 and M = 12, with sample variances of s2 = 20 and s2 = 25. b. Sample means of M = 10 and M = 12, with sample variances of s2 = 120 and s2 = 125. c. Sample means of M = 10 and M = 20, with sample variances of s2 = 20 and s2 = 25. d. Sample means of M = 10 and M = 20, with sample variances of s2 = 120 and s2 = 125.

ANSWER: c DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 11

REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 44. Which of the following sets of data would produce the largest value for an independent-measures t statistic, assuming the difference between sample means is held constant?

a. The two samples both have n = 15, with sample variances of s2 = 20 and s2 = 25. b. The two samples both have n = 15, with variances of s2 = 120 and s2 = 125. c. The two samples both have n = 30, with sample variances of s2 = 20 and s2 = 25. d. The two samples both have n = 30, with variances of s2 = 120 and s2 = 125.

ANSWER: c DIFFICULTY: Apply REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 45. Which combination of factors is most likely to produce a statistically significant value for an independent-measures t statistic? a. large sample sizes and large sample variances

b. large sample sizes and small sample variances c. small sample sizes and large sample variances d. small sample sizes and small sample variances ANSWER: b DIFFICULTY: Understand REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Understand 46. Which of the following sets of data is most likely to produce a statistically significant mean difference when conducting an independent samples t test? a. a sample mean difference of 5 points with n = 5 for each sample

b. a sample mean difference of 5 points with n = 10 for each sample c. a sample mean difference of 10 points with n = 5 for each sample d. a sample mean difference of 10 points with n = 10 for each sample ANSWER: d DIFFICULTY: Apply REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 47. Which set of sample characteristics is most likely to produce a statistically significant value for the independentmeasures t statistic and a large effect size when conducting a hypothesis test? a. a small sample mean difference and small sample variances

b. a large sample mean difference and small sample variances c. a small sample mean difference and large sample variances d. a large sample mean difference and large sample variances ANSWER: b Copyright Cengage Learning. Powered by Cognero.

Page 12

DIFFICULTY: Apply REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 48. Which of the following elements is always presented last in a statistical report statement describing the results of an independent-measures t test? a. effect size

b. degrees of freedom c. computed t statistic d. probability of making a Type I error if the null hypothesis is rejected ANSWER: a DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and the Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 49. What is assumed by the homogeneity of variance assumption? a. whether two samples have equal variances b. whether two samples do not have equal variances c. whether two populations have equal variances d. whether two populations do not have equal variances ANSWER: c DIFFICULTY: Remember REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Remember 50. A researcher conducts a research study to examine whether there is a difference between two treatments regarding depression. Which of the following is consistent conceptually with the alternative hypothesis? a. The second treatment is less effective than the first treatment regarding depression.

b. The first treatment is less effective than the second treatment regarding depression. c. There is a difference between the two treatments among the general population regarding depression. d. There is no difference between the two treatments among the general population regarding depression.

ANSWER: c DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 51. A research study compares the mean weight for a sample of n = 36 participants before they begin a dieting routine diet to their mean weight six weeks later. This is an example of an independent-measures design.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 10.1 Introduction to the Independent-Measures Design KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 13

52. There is one source of error that needs to be accounted for in the denominator of the independent-measures t test equation.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 53. A researcher expects that a newly developed shoe used by a sample of n = 6 individuals will reduce running speeds compared to a sample of n = 11 individuals using a control condition shoe. The critical region for the one-tailed hypothesis test with α = 0.05 is t = +1.753.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 54. An independent-measures study with n = 20 scores in each condition will produce an independent-measures t statistic with df = 18.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 55. If two samples are the same size, then the pooled variance will equal the average of the two sample variances. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 56. One sample has n = 7 scores with SS = 40, and a second sample has n = 5 scores with SS = 80. The pooled variance for these two samples is 120/12 = 10.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 14

57. Individual differences in personality, attitudes, and past experiences are examples of sources of error that contribute to the estimated standard error in the denominator of an independent samples t test equation.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Understand 58. An F-Max value near 1.00 indicates that the homogeneity of variance assumption underlying independent samples t tests has not been violated.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 59. When conducting a hypothesis test using an independent-measures t statistic, a researcher must compute the pooled variance before calculating the estimated standard error.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 60. For the independent-measures t statistic equation, the numerator of the equation measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 61. If one sample has n = 4 and SS = 90 and a second sample has n = 8 and SS = 150, then the estimated standard error for the sample mean difference is 9 points.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

62. A research study comparing self-esteem scores among the same individuals at different time intervals is an example of an independent-measures design.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.1 Introduction to the Independent-Measures Design KEYWORDS: Bloom’s: Understand 63. If two sample sizes are not equal, the pooled variance value will be closer to the individual sample variance that has a larger variance value.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 64. Two samples, one with n = 2 and another with n = 3, have a pooled variance of s2p = 30. The estimated standard error for the sample mean difference is s(M1 - M2) = 5.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 65. Conceptually, the independent samples t test equation assesses the ratio of the actual difference between two sample means relative to how much difference should exist, on average, between two sample means when the null hypothesis is true.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 66. Using the pooled variance formula when computing the estimated standard error in an independent samples t test corrects for the bias that otherwise exists typically when averaging across two individual sample variances.

a. True b. False ANSWER: True DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

REFERENCES: 10.2 The Hypotheses and the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 67. Larger values for two sample variances decreases the likelihood that an independent-measures t test will find a statistically significant difference, as well as the computed value for Cohen’s d.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 68. Larger sample sizes increase the likelihood that an independent-measures t test will find a statistically significant difference, as well as the computed value for Cohen’s d.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 69. A larger difference between two sample means increases the likelihood that an independent-measures t test will find a statistically significant difference, as well as the computed value for Cohen’s d.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 10.5 The Role of Sample Variance and Sample Size in the Independent-Measures t Test KEYWORDS: Bloom’s: Apply 70. The results from an independent-measures t hypothesis test are reported as “t(14) = 2.10, p > 0.05, two tails.” For this test, the null hypothesis was rejected.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 71. The results from an independent-measures t hypothesis test are reported as “95% CI [0.65, 6.30].” For this test, a statistically significant difference between sample means emerged.

a. True b. False ANSWER: True DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 17

REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 72. An independent-measures study produces t(9) = +3.00, p < 0.05. For this study, if effect size is measured with r2, then r2 = 0.50.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 73. If two separate samples have M1 = 10 and M2 = 18 with a pooled variance of s2p = 16, then Cohen’s d = 0.50. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 74. An independent-measures study has M1 = 45 and M2 = 49 with a pooled variance of s2p = 4. For this study, Cohen’s d should be reported as = –2.00.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 75. An independent-measures research study uses a total of 18 participants to compare two treatment conditions. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values used to construct the confidence interval will be ±1.746.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 76. If the value of 0 falls within a computed confidence interval for a hypothesis test, then the decision should be to fail to reject the null hypothesis.

a. True b. False ANSWER:

True

Copyright Cengage Learning. Powered by Cognero.

Page 18

DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 77. For an independent-measures study, the width of a confidence interval estimating µ1 – µ2 does not depend on the size of the difference between M1 and M2.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Understand 78. The 95% confidence interval for the difference between two treatment means extends from –2.50 to +5.50. Based on this information, you can conclude that there is no statistically significant difference between the treatments at the .05 level of significance.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 79. For a hypothesis test in which the independent-measures t statistic is computed, Hartley’s F-Max test is used to determine whether a statistically significant difference exists between two sample means.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 80. The t values that define the critical region for a two-tailed independent samples t test using α = 0.05 with sample sizes of n = 17 and n = 8 are t = ±2.060.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Understand 81. A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual. The data are as follows: Copyright Cengage Learning. Powered by Cognero.

Page 19

Control n = 10 M = 12 SS = 120.5

Exercise n = 15 M = 15.5 SS = 190.0

a. Does the exercise program have a significant effect? Use an alpha level of .05, two tails. b. Compute Cohen’s d to measure the size of the treatment effect.

ANSWER:

a. The pooled variance is s2p = 13.5 and the estimated standard error is s(M1 - M2) = 1.50. t = +2.33; Reject the null hypothesis, and conclude that the exercise program does have an effect on balance and strength. b. d = 3.50/3.67 = 0.95

DIFFICULTY: Apply REFERENCES: 10.4 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 82. An educational psychologist studies the positive effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below: Frequent Quizzes Two Exams n = 11 n=7 M = 73 M = 66.5 a. If the first sample (frequent quizzing condition) variance is s2 = 51 and the second sample (two exams condition) is s2 = 59, do the data indicate that frequent quizzing has a significant positive effect on retention of class material? Use a onetailed test at the α = 0.05 level of significance. b. If the alpha level for the hypothesis test was changed from α = 0.05 to α = 0.01, do the data indicate that frequent quizzing has a significant positive effect on retention of class material? Use a one-tailed test at the α = 0.01 level of significance. c. If the first sample variance has s2 = 67 and the second sample has s2 = 61, do the data indicate that testing frequency has a significant positive effect on retention of class material? As in part A, use a one-tailed test with α = 0.05. d. Describe how the alpha level and the size of the variance affects the outcome of the hypothesis test.

ANSWER:

a. The pooled variance = 54, the estimated standard error = 3.55, and t(16) = +1.83. With α = 0.05 and df = 16, the critical boundary is +1.746 given that this is a one-tailed hypothesis test. The decision is to reject the null hypothesis and conclude that frequent testing significantly increased retention of class material. b. The pooled variance = 54, the estimated standard error = 3.55, and t(16) = +1.83. With α = 0.01 and df = 16, the critical boundary is +2.583 given that the alpha value for the hypothesis test is now smaller.

The decision is to fail to reject the null hypothesis and conclude that frequent testing does not significant increase retention of class material. c. The pooled variance is now 64.75, the estimated standard error is 3.89, and t(16) = +1.67. With α = 0.05 and df = 16, the critical boundary is +1.746 given that this is a one-tailed hypothesis test. The decision is to fail reject the null hypothesis and conclude that frequent testing does not significantly increase retention of class material. d. The critical region becomes more extreme with α = 0.01 compared to α = 0.05, making it more likely that the null hypothesis will fail to be rejected. Larger sample variances increase the estimated standard error which forms the denominator of the independent samples t test equation, making it less likely that

Copyright Cengage Learning. Powered by Cognero.

Page 20

the null hypothesis will be rejected.

DIFFICULTY: Apply REFERENCES: 10.3 Hypothesis Tests with the Independent-Measures t Statistic KEYWORDS: Bloom’s: Apply 83. The following data are from an independent-measures experiment comparing two treatment conditions: Treatment 1 6 13 8 4 13 4 11 5

Treatment 2 19 9 18 10 12 14 19 11

a. Do these data indicate a significant difference between the treatments at the α = 0.05 level of significance? b. Compute r2 to measure the size of the treatment effect. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

ANSWER:

a. For treatment 1, M = 8 and SS = 104. For treatment 2, M = 14 and SS = 120. The pooled variance is 16, the estimated standard error is 2, and t(14) = +3.00. The decision is to reject H0 and conclude that there is a difference between the two treatment conditions. b. r2 = 9/23 = 0.391. c. The data indicate a significant difference between treatments, t(14) = +3.00, p < .05, r2 = 0.391.

DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply 84. A major company would like to assess the impact of using a professional trainer to conduct a confidencebuilding workshop with its salespeople. A sample of 16 workers is obtained. Half (n = 8) attend the workshop and the other half (n = 8) serve as a control group. Two weeks later, each of the participants is given a questionnaire measuring their level of self-confidence. The data are as follows: Control Workshop M = 20 M = 22 SS = 100 SS = 124 a. Use the sample data to construct an 90% confidence interval for the mean difference in confidence between the control group and the workshop conditions. b. What conclusion should be drawn based on the creation of the confidence interval in part A?

ANSWER:

a. The pooled variance is 16 and the estimated standard error is 2. With df = 14 and 90% confidence, use t = ±1.761. The confidence interval is 1 – 2 = 2 ± 1.7641(2) and extends from –1.53 to +5.53. b. The value of 0 lies within the computed confidence interval, which indicates that 0 is an acceptable value for the sample mean difference. This is equivalent to failing to reject the null hypothesis and concluding that there is no difference in self-confidence between conditions.

Copyright Cengage Learning. Powered by Cognero.

Page 21

DIFFICULTY: Apply REFERENCES: 10.4 Effect Size and Confidence Intervals for the Independent-Measures t KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 22

Chapter 11 1. For which of the following situations would a repeated-measures research design be appropriate? a. comparing mathematical skills for girls versus boys at age 10 b. comparing pain tolerance with and without acupuncture needles c. comparing self-esteem for students who participate in school athletics versus those who do not d. comparing verbal solving skills for science majors versus art majors at a college ANSWER: b DIFFICULTY: Apply REFERENCES: 11.1 Introduction to Repeated-Measures Designs KEYWORDS: Bloom’s: Apply 2. A researcher plans to conduct a research study comparing two treatment conditions with a total of 20 participants.

Which of the following designs would produce 20 scores in each treatment? a. an independent-measures design

b. a repeated-measures design c. a matched-subjects design d. Each of these options would produce 20 scores in each treatment.

ANSWER: b DIFFICULTY: Apply REFERENCES: 11.1 Introduction to Repeated-Measures Designs KEYWORDS: Bloom’s: Apply 3. A researcher conducts a repeated-measures study to evaluate the efficacy of therapy in increasing positive coping skills.

The researcher examines positive coping skills before and after therapy with a sample of n = 6 participants and obtains a sample mean difference of MD = 10 with an estimated standard error of sMD = 4.78. Which of the following is the correct decision for a one-tailed hypothesis test in which therapy is expected to increase positive coping skills? a. reject the null hypothesis with α = 0.05 but not with α = 0.01

b. reject the null hypothesis with both α = 0.05 and α = 0.01 c. fail to reject the null hypothesis with both α = 0.05 and α = 0.01 d. fail to reject the null hypothesis with α = 0.05 but not with α = 0.01 ANSWER: a DIFFICULTY: Apply REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Apply 4. The following data were obtained from a repeated-measures research study. What is the value of MD for these data?

Subject 1st 2nd #1 10 15 #2 4 8 #3 7 5 #4 6 11 a. MD = 3 Copyright Cengage Learning. Powered by Cognero.

Page 1

b. MD = 3.5 c. MD = 4 d. MD = 4.5 ANSWER: a DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 5. The following data were obtained from a repeated-measures research study. What is the value of SS for the difference scores?

Subject 1st 2nd #1 10 11 #2 4 6 #3 7 9 #4 6 5 a. SS = 10 b. SS = 6 c. SS = 4 d. SS = 1 ANSWER: b DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 6. A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = _____. a. 9 b. 19 c. 20 d. 39 ANSWER: b DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 7. If difference scores begin to pile up away from a sample mean difference score of MD = 0, which of the following statements is true? a. The null hypothesis will likely fail to be rejected.

b. The null hypothesis will likely be rejected. c. The sample size is large. d. The critical region is small.

ANSWER: b DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 2

REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 8. A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment. What is the value of df for the repeated-measures t statistic? a. df = 18

b. df = 19 c. df = 38 d. df = 39 ANSWER: b DIFFICULTY: Apply REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Apply 9. A repeated-measures research study and a separate independent-measures research study both produced a t statistic with df = 10. How many individuals participated in each research study? a. n = 12 for a repeated-measures research study and n = 11 for an independent-measures research study

b. n = 12 for a repeated-measures research study and n = 12 for an independent-measures research study c. n = 11 for a repeated-measures research study and n = 11 for an independent-measures research study d. n = 11 for a repeated-measures research study and n = 12 for an independent-measures research study ANSWER: d DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 10. A repeated-measures research design tends to have which of the following drawbacks? a. the possibility for extraneous variables that occur over the passage of time to influence results b. the need for a larger sample size c. less of an ability to control the extent to which individual differences among research participants influence results d. the need to provide more evidence to support statistical significance than other research designs

ANSWER: a DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 11. Which of the following is an accurate distinction between repeated-measures and independent-measures research designs? a. In repeated-measures research designs, more participants are needed to have sufficient statistical power.

b. In repeated-measures research designs, each participant is measured more than once under a treatment condition. c. In repeated-measures research designs, there is a greater possibility that individuals in one condition are different from those in the other condition due to factors beyond the research focus. d. In repeated-measures research designs, each participant is measured once under a treatment condition.

Copyright Cengage Learning. Powered by Cognero.

Page 3

ANSWER: d DIFFICULTY: Understand REFERENCES: 11.1 Introduction to Repeated-Measures Designs KEYWORDS: Bloom’s: Understand 12. For the repeated-measures t statistic, df = _____. a. n + 2 b. n + 1 c. n – 1 d. n – 2 ANSWER: c DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 13. Which of the following is the correct null hypothesis for a repeated-measures t test? a. MD = 0 b. µD = 0 c. µ1 = µ2 d. M1 = M2 ANSWER: b DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 14. If the null hypothesis is true, which value is expected on average for the repeated-measures t statistic? a. t = 0 b. t = +1 c. t = +1.96 d. t > 1.96 ANSWER: a DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 15. A researcher conducts a repeated-measures study to evaluate the efficacy of therapy in decreasing maladaptive behavior. The researcher examines maladaptive behavior before and after therapy with a sample of n = 6 participants and obtains a sample mean difference of MD = 6 with an estimated standard error of sMD = 3.00. Which of the following is the correct decision for a one-tailed hypothesis test in which therapy is expected to reduce maladaptive behavior? a. reject the null hypothesis with α = 0.05 but not with α = 0.01

b. reject the null hypothesis with both α = 0.05 and α = 0.01 c. fail to reject the null hypothesis with both α = 0.05 and α = 0.01 d. fail to reject the null hypothesis with α = 0.05 but not with α = 0.01 Copyright Cengage Learning. Powered by Cognero.

Page 4

ANSWER: c DIFFICULTY: Apply REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Apply 16. The null hypothesis for a repeated-measures test states which of the following? a. Each individual will have a difference between conditions of MD = 0. b. The overall sample will have a difference between conditions of MD ≠ 0. c. The entire population will have a mean difference of µD = 0. d. Each of these responses is correct.

ANSWER: c DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 17. A repeated-measures study comparing two treatments with n = 4 participants produces a treatment mean difference score of MD = 2 and SS = 75 for the difference scores. What is the estimated standard error for the sample mean difference? a. sMD = 25

b. sMD = 6.25 c. sMD = 5 d. sMD = 2.5 ANSWER: d DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 18. What is the value of the estimated standard error for the following set of D-scores? Scores: 2, 2, 10, 2 a. sMD = 3 b. sMD = 1 c. sMD = 4 d. sMD = 2 ANSWER: d DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 19. Which of the following statements is not consistent with the assumptions necessary when computing a repeatedmeasures t statistic? a. The population distribution of difference scores (D values) does not need to be normal if the sample size is relatively large (n > 30). b. The population distribution of difference scores (D values) must be normal if the sample size is relatively small (n < 30). c. The scores within each treatment must be independent.

Copyright Cengage Learning. Powered by Cognero.

Page 5

d. The scores between each treatment must be independent.

ANSWER: d DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 20. Conceptually, what does the null hypothesis of a one-tailed repeated-measures research study put forth if a treatment is expected to increase scores on a questionnaire, relative to pre-test scores on a questionnaire? a. There is a decrease in scores after treatment.

b. There is an increase in scores after treatment. c. There is no decrease in scores after treatment. d. There is no increase in scores after treatment.

ANSWER: d DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 21. For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s2 = 36. What is the value for the repeated-measures t statistic for these data? a. t = +2.00

b. t = +1.00 c. t = +1.50 d. t = +0.50 ANSWER: a DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 22. Conceptually, what does the alternative hypothesis of a one-tailed repeated-measures research study put forth if a treatment is expected to decrease scores on a questionnaire, relative to pre-test scores on a questionnaire? a. There is a decrease in scores after treatment.

b. There is an increase in scores after treatment. c. There is no decrease in scores after treatment. d. There is no increase in scores after treatment.

ANSWER: a DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Understand 23. A repeated-measures study comparing two treatments with a sample of n = 4 participants produces MD = 3 with SS = 48 for the set of difference scores. What is the repeated-measures t statistic for these data? a. t = +1.73

b. t = +1.50 Copyright Cengage Learning. Powered by Cognero.

Page 6

c. t = +2.00 d. t = +0.19 ANSWER: b DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 24. If a repeated-measures study shows a statistically significant difference between two treatments with α = 0.01, what can the researcher conclude about measures of effect size? a. The value of Cohen’s d is large.

b. The value of Cohen’s d is small. c. The value of both Cohen’s d and r2 are large. d. A statistically significant effect does not necessarily indicate that the effect size will be large.

ANSWER: d DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 25. A sample of difference scores has a mean of MD = 5 with a variance of s2 = 100. If effect size is measured using Cohen’s d, what is the value of d? a. d = 0.50

b. d = 0.05 c. d = 0.25 d. This cannot be determined with the provided information.

ANSWER: a DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 26. For a repeated-measures study comparing two treatment conditions, a researcher obtains Cohen’s d = 0.50 for a sample of n = 4 scores with a variance of s2 = 16. What is the value of the sample mean difference between conditions?

a. MD = 2 b. MD = 4 c. MD = 8 d. MD = 16 ANSWER: a DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 7

27. A researcher obtains t(20) = +2.00 and MD = 9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?

a. r2 = 0.45 b. r2 = 0.30 c. r2 = 0.31 d. r2 = 0.17 ANSWER: d DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 28. A researcher conducts a repeated-measures study to evaluate the efficacy of a therapy in treating pain. The researcher examines pain perceptions before and after therapy with a sample of n = 16 participants and obtains a t statistic of t = +1.94. Pain perception levels are less across participants, on average, following treatment. Which of the following is the correct decision for a hypothesis test using α = .05? a. reject the null hypothesis with a one-tailed test but fail to reject with a two-tailed test

b. reject the null hypothesis with either a one-tailed or a two-tailed test c. fail to reject the null hypothesis with either a one-tailed or a two-tailed test d. fail to reject the null hypothesis with a one-tailed test but reject with a two-tailed test ANSWER: a DIFFICULTY: Apply REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Apply 29. A researcher obtains t = –2.25 for a repeated-measures study using a sample of n = 10 participants. Based on this t value, what is the correct decision for a two-tailed test? a. reject the null hypothesis with α = 0.05 but not with α = 0.01

b. reject the null hypothesis with both α = 0.05 and α = 0.01 c. fail to reject the null hypothesis with both α = 0.05 and α = 0.01 d. fail to reject the null hypothesis with α = 0.05 but not with α = 0.01 ANSWER: c DIFFICULTY: Apply REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design KEYWORDS: Bloom’s: Apply 30. A research report describing the results from a repeated-measures t test includes the following statement: “t(10) = 1.65, p > .05.” Based on this report, how many individuals participated in the research study? a. n = 9

b. n = 10 c. n = 11 d. n = 12 ANSWER:

c

Copyright Cengage Learning. Powered by Cognero.

Page 8

DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 31. A research report describing the results from a repeated-measures t test states: “t(22) = 1.71, p > 0.05.” Which option below is consistent with this statement? a. n = 23 and rejecting the null hypothesis

b. n = 23 and failing to reject the null hypothesis c. n = 22 and rejecting the null hypothesis d. n = 22 and failing to reject the null hypothesis ANSWER: b DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 32. A researcher reports t(5) = +3.00, p < 0.05 for a repeated-measures research study. The sample mean difference score for the sample was MD = 12. Which of the following is the confidence interval for the population mean difference? a. 12 ± 11.014

b. 12 ± 10.284 c. 12 ± 9.788 d. 12 ± 10.000 ANSWER: b DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 33. In general, if the variance of the difference scores increases, what will happen to the value of the t statistic? a. It will increase in magnitude (move farther toward the tail of the distribution). b. It will decrease in magnitude (move toward 0 at the center of the distribution). c. It will stay the same; the t statistic is not affected by the variance of the difference scores. d. It may increase or may decrease; there is no consistent relationship between variance and the size of the t statistic.

ANSWER: b DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 34. A researcher uses a repeated-measures design to compare individuals’ performance before treatment with their performance after treatment. If all the participants show improved performance of approximately 8 points after treatment, what should the researcher find? a. The sample mean difference score is near zero.

Copyright Cengage Learning. Powered by Cognero.

Page 9

b. The t statistic is near zero. c. The variance of the difference scores is near zero. d. This is impossible to determine based on the provided information.

ANSWER: c DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 35. In general, what is the effect of an increase in the variance for the sample of difference scores? a. an increase in the estimated standard error and an increase in the value of t b. an increase in the estimated standard error and a decrease in the value of t c. a decrease in the estimated standard error and an increase in the value of t d. a decrease in the estimated standard error and a decrease in the value of t ANSWER: b DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 36. In general, what characteristics of difference scores are most likely to produce a statistically significant t statistic for a repeated-measures hypothesis test? a. a large sample size and a large variance

b. a large sample size and a small variance c. a small sample size and a large variance d. a small sample size and a small variance ANSWER: b DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 37. What is indicated by a large variance for a sample of difference scores in the context of a repeated-measures hypothesis test? a. a consistent treatment effect and a high likelihood of a statistically significant difference between treatment conditions b. a consistent treatment effect and a low likelihood of a statistically significant difference between treatment conditions c. an inconsistent treatment effect and a high likelihood of a statistically significant difference between treatment conditions d. an inconsistent treatment effect and a low likelihood of a statistically significant difference between treatment conditions

ANSWER: d DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for Copyright Cengage Learning. Powered by Cognero.

Page 10

KEYWORDS:

the Repeated-Measures t Bloom’s: Understand

38. A researcher is using a repeated-measures study to evaluate the difference between two treatments. If the difference between the treatments is consistent from one participant to another, then the data should produce ______. a. a small variance for the difference scores and a small estimated standard error

b. a small variance for the difference scores and a large estimated standard error c. a large variance for the difference scores and a small estimated standard error d. a large variance for the difference scores and a large estimated standard error ANSWER: a DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 39. A researcher reports t(15) = +0.25, p > 0.05 for a repeated-measures research study. The sample mean difference score for the sample was MD = 1. Which of the following is the value for Cohen’s d? a. d = 0.06

b. d = 0.25 c. d = 1.00 d. d = 0.12 ANSWER: a DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 40. Assuming that other factors are held constant, which of the following would increase the likelihood of rejecting the null hypothesis in a hypothesis test using a repeated-measures design? a. decreasing the sample size

b. increasing the sample size c. decreasing the alpha level d. decreasing the difference scores ANSWER: b DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 41. Assuming that other factors are held constant, which of the following sets of data is most likely to produce a statistically significant value for the repeated-measures t statistic?

a. n = 15 and MD = 2 b. n = 15 and MD = 4 c. n = 30 and MD = 2 Copyright Cengage Learning. Powered by Cognero.

Page 11

d. n = 30 and MD = 4 ANSWER: d DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 42. Which of the following describes the effect of increasing sample size in a repeated-measures design? a. Measures of effect size and the likelihood of rejecting the null hypothesis both increase. b. Measures of effect size increase, but the likelihood of rejecting the null hypothesis decreases. c. There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases. d. There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis decreases.

ANSWER: c DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 43. Which of the following describes the effect of an increase in the variance of the difference scores in a repeatedmeasures design? a. Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.

b. Measures of effect size increase, but the likelihood of rejecting the null hypothesis decreases. c. There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases. d. There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis decreases.

ANSWER: a DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 44. Which value is estimated with a confidence interval using the repeated-measures t statistic? a. the mean for a sample of difference scores b. the mean for a population of difference scores c. the difference between two population means d. the difference between two sample means ANSWER: c DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 12

45. A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop. Each student’s grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop. The average GPA improved by MD = 0.60 points with s2 = 0.09. The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population. Which of the following is the 80% confidence interval for these data?

a. µD = 0.60 + 0.0140 b. µD = 0.60 + 0.1674 c. µD = 0.60 + 0.1397 d. µD = 0.60 + 0.1860 ANSWER: c DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 46. Which of the following will not increase the width of a confidence interval constructed for measuring the size of a treatment effect in a repeated-measures research design? a. increasing the percentage of confidence from 80% to 90%

b. reducing the sample size from n = 25 to n = 16 c. increasing the sample mean difference from MD = 2 to MD = 4 d. This cannot be determined based on the provided information.

ANSWER: c DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 47. If sample size is held constant, which of the following will produce the widest confidence interval for measuring the size of a treatment effect in a repeated-measures research study?

a. s2 = 10 for the difference scores with a percentage confidence of 90% b. s2 = 10 for the difference scores with a percentage confidence of 80% c. s2 = 20 for the difference scores with a percentage confidence of 90% d. s2 = 20 for the difference scores with a percentage confidence of 80% ANSWER: c DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 48. Which is a serious concern with a repeated-measures study? a. The results will be influenced by counterbalancing. b. The results will be influenced by order effects. c. The results will be influenced by individual differences rather than treatment differences.

Copyright Cengage Learning. Powered by Cognero.

Page 13

d. The results will be influenced by confounds introduced by researchers.

ANSWER: b DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 49. Compared to an independent-measures design, a repeated-measures study is more likely to find a statistically significant effect because it reduces the contribution of variance due to _____. a. time-related factors

b. order effects c. the effect of the treatment d. individual differences ANSWER: d DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 50. For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design? a. when many subjects are available and individual differences are small

b. when very few subjects are available and individual differences are small c. when many subjects are available and individual differences are large d. when very few subjects are available and individual differences are large ANSWER: d DIFFICULTY: Apply REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Apply 51. In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One major concern in this type of research study is that participation in the first treatment may influence an individual’s score in the second treatment. What is this problem called? a. an individual difference

b. an order effect c. homogeneity of variance d. bi-treatment effect ANSWER: b DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 52. A researcher needs to compare two treatment conditions with a sample size of n = 30 in each treatment. If a repeatedmeasures design is used, the study will require n = 60 participants.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 14

ANSWER: False DIFFICULTY: Apply REFERENCES: 11.1 Introduction to Repeated-Measures Designs KEYWORDS: Bloom’s: Apply 53. One concern for a repeated-measures research study is that the participants in one treatment may have different characteristics than the participants in the other treatment.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.1 Introduction to Repeated-Measures Designs KEYWORDS: Bloom’s: Understand 54. Although a repeated-measures research study measures two scores for each participant, the sample mean and variance used when calculating the t statistic are computed using only one score for each participant.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 55. The correct alternative hypothesis for a two-tailed repeated-measures t test is µD ≠ 0. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 56. For the following data from a repeated-measures study, the sample mean difference is MD = 1.

Participant X1

A B C

1 4 5

X2

5 6 2

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

57. The estimated standard error in the denominator of the repeated-measures t statistic measures the mean difference that is expected for a sample selected from a population with a zero mean difference.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 58. For the repeated-measures t statistic, the value of the estimated standard error in the denominator is computed entirely from the sample data.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 59. The alternative hypothesis in a two-tailed repeated-measures research study puts forth that there is no difference between two treatments for individuals in a population.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 60. A repeated-measures research study and an independent-measures research study both produce a t statistic with df = 20. The repeated-measures study used more subjects than the independent-measures study.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Apply 61. A matched-subjects research design is a type of repeated-measures research design because the participants in each treatment condition are the same people.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

62. Typically, difference scores in a repeated-measures research design are computed by subtracting pre-treatment scores from scores after treatment for each participant.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Understand 63. A statement pertaining to a repeated-measures research design t test is reported in a statistical report as follows: t(16) = 1.36, p > 0.05. The critical region for this hypothesis test was t = ±2.131.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 64. If a set of difference scores with df = 8 has a mean of MD = 3.5 and a variance of s2 = 36, then the estimated standard error for the sample mean difference is sMD = 2 points.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Apply 65. If a set of difference scores with df = 8 has a mean of MD = 3.5 and a variance of s2 = 36, then the sample will produce a repeated-measures t statistic of t = +1.75.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Apply 66. For a repeated-measures study with a total of n = 24 participants, a sample mean difference score of MD = 4 is obtained. If the variance of the difference scores is s2 = 216, the t statistic is t = +0.75.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.3 Hypothesis Tests for the Repeated-Measures Design Copyright Cengage Learning. Powered by Cognero.

Page 17

KEYWORDS:

Bloom’s: Understand

67. For a repeated-measures research study, as the sample mean difference increases, the likelihood of rejecting the null hypothesis also increases.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 68. For a repeated-measures research study, a small variance for the difference scores indicates that the treatment has little or no effect.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 69. Counterbalancing is a way to pre-emptively address the concern that the order in which participants are exposed to treatment conditions in a repeated-measures research study is influencing results.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 70. If all participants in a repeated-measures research study show roughly the same difference between treatments, then the data will produce a statistically significant value for the t statistic.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 71. For a repeated-measures study, if other factors are held constant, then an increase in the sample size will increase the distance of a calculated t statistic from 0.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 18

ANSWER: True DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 72. A set of n = 9 difference scores has a mean of MD = 1 and SS = 32. Cohen’s d for this sample is d = 0.50. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 73. For a repeated-measures research study, if other factors are held constant, then an increase in sample size leads to an increase Cohen’s d.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 74. For a repeated-measures research study, if other factors are held constant, then an increase in the sample variance will decrease Cohen’s d.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 75. A repeated-measures research study with a sample of n = 19 participants produces a repeated-measures t = +2.00. If effect size is measured using r2, then r2 = 0.10.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 19

76. For a repeated-measures research design, the sample mean difference is located exactly in the center of the confidence interval estimate for the population mean difference.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Understand 77. A repeated-measures research study compares two treatment conditions with df = 20. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.729.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 78. One advantage of a repeated-measures research design is that it typically requires fewer participants than an independent-measures design.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 79. One concern for a researcher conducting a repeated-measures research study is that a participant’s score in one treatment may be influenced by practice or experience gained in a previous treatment.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 80. Repeated-measures research designs are particularly well-suited to examine learning or other changes that occur over time within the same participants.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs Copyright Cengage Learning. Powered by Cognero.

Page 20

KEYWORDS:

Bloom’s: Understand

81. A repeated-measures research study usually has greater statistical power than an independent-measures test because the repeated-measures design typically has a smaller variance and a smaller estimated standard error.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Understand 82. Briefly explain the advantages and disadvantages of using a repeated-measures research design as opposed to an independent-measures research design.

Compared to an independent-measures research design, a repeated-measures research design is more ANSWER: likely to reject the null hypothesis because it eliminates variability due to individual differences. Also, a repeated-measures research design uses fewer subjects than an independent-measures research design. However, results from a repeated-measures experiment can be confounded by time-related factors and order effects.

DIFFICULTY: Analyze REFERENCES: 11.5 Comparing Repeated- and Independent-Measures Designs KEYWORDS: Bloom’s: Analyze 83. For the following data from a repeated-measures study: a. Find the difference scores. b. Calculate MD and the variance for the difference scores. c. Calculate the estimated standard error for the mean difference.

Subject Treatment 1 Treatment 2 A 12 14 B 6 16 C 8 10 D 9 11 a. The difference scores are 2, 10, 2, & 2 ANSWER: b. MD = 4 and s2 = 16 c. The estimated standard error is sMD = 2.

DIFFICULTY: Apply REFERENCES: 11.2 The t Statistic for a Repeated-Measures Research Design KEYWORDS: Bloom’s: Apply 84. A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can reduce mental alertness. A sample of n = 9 college students is obtained, and each student’s performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roasted turkey. The average mental alertness score dropped by MD= 14 points after the meal with SS= 1152 for the difference scores.

a. Is there is significant reduction in mental alertness after consuming tryptophan versus before? Use a onetailed test with α = .05. b. Compute r2 to measure the size of the effect.

ANSWER: a. The estimated standard error is sMD = 4 and t(8) = +3.50. Reject H0. Tryptophan appears to reduce Copyright Cengage Learning. Powered by Cognero.

Page 21

mental alertness. b. r2 = 12.25/20.25 = 0.60

DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 85. A researcher would like to evaluate the effectiveness of a pain-relief patch designed for back pain. Prior to testing the patch, each of n = 8 patients rates their current level of back pain on a scale from 1 to 10. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows: Before After 6 2 8 3 9 4 8 1 10 2 5 3 9 8 7 7 a. Compute the mean and variance for the sample of difference scores. b. Do the results indicate that the pain-relief patch has an effect? Use a two-tailed test with α = 0.05 c. Compute Cohen’s d to measure the size of the effect.

ANSWER:

a. MD = –4 and s2 = 8 b. The estimated standard error is sMD = 1 and t(7) = 4/1 = –4.00. Reject H0. The pain-relief patch has an effect on back pain. c. d = 4/√8 = 1.41

DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures t KEYWORDS: Bloom’s: Apply 86. A teacher gives a reading skills test to a third-grade class of n = 25 at the beginning of the school year. To evaluate the changes that occur during the year, students are tested again at the end of the year. Their test scores showed an average improvement of MD = 12.7 points with s2 = 100. a. Construct a 90% confidence interval for the mean difference to describe the size of the improvement. b. Without conducting a hypothesis test, does it appear that the class has an influence on reading skills?

ANSWER:

a. D = 12.7 ± 2(1.711). The interval extends from 9.278 to 16.122 points. b. The class does appear to have an influence on reading skills given that the value of 0 is not contained within the constructed confidence interval. 1

DIFFICULTY: Apply REFERENCES: 11.4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures Copyright Cengage Learning. Powered by Cognero.

Page 22

KEYWORDS:

Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 23

Chapter 12 1. For an ANOVA comparing three treatment conditions, what is stated by the null hypothesis (H0)? a. There are no differences between any of the population means. b. At least one of the three population means is different from another population mean. c. All three of the population means are different from each other. d. One population mean is different from one of the other population means, but not the other population mean.

ANSWER: a DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 2. For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (H1)? a. There are no differences between any of the population means. b. At least one of the three population means is different from another population mean. c. All three of the population means are different from each other. d. One population mean is different from one of the other population means, but not the other population mean.

ANSWER: b DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 3. When comparing more than two condition means, why should an analysis of variance be used instead of multiple t tests?

a. Using multiple t tests increases the risk of a Type I error. b. Using multiple t tests increases the risk of a Type II error. c. The analysis of variance is more likely to detect statistical significance. d. There is no advantage to using an analysis of variance instead of multiple t tests.

ANSWER: a DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 4. In an analysis of variance, differences between participants contribute to which of the following variances? a. both between-treatments variance and within-treatments variance b. between-treatments variance but not within-treatments variance c. within-treatments variance but not between-treatments variance d. neither between-treatments variance nor within-treatments variance ANSWER: a DIFFICULTY: Understand REFERENCES: 12.2 The Logic of Analysis of Variance KEYWORDS: Bloom’s: Understand 5. In an analysis of variance, differences caused by treatment effects contribute to which of the following variances?

Copyright Cengage Learning. Powered by Cognero.

Page 1

a. both between-treatments variance and within-treatments variance b. between-treatments variance but not within-treatments variance c. within-treatments variance but not between-treatments variance d. neither between-treatments variance nor within-treatments variance ANSWER: b DIFFICULTY: Understand REFERENCES: 12.2 The Logic of Analysis of Variance KEYWORDS: Bloom’s: Understand 6. On average, which value is expected for the F-ratio if the null hypothesis is true? a. F = 0 b. F = 1 c. F = k – 1 d. F = N – k ANSWER: b DIFFICULTY: Understand REFERENCES: 12.2 The Logic of Analysis of Variance KEYWORDS: Bloom’s: Understand 7. On average, which value is expected for the F-ratio if the null hypothesis is false? a. F = 0 b. F = 1 c. an F value between 0 and 1 d. an F value much greater than 1 ANSWER: d DIFFICULTY: Understand REFERENCES: 12.2 The Logic of Analysis of Variance KEYWORDS: Bloom’s: Understand 8. In an ANOVA, what is represented by the letter T? a. the sum of the scores in a specific condition b. the sum of the scores in the entire research study c. the number of scores in a specific condition d. the number of scores in an entire research study ANSWER: a DIFFICULTY: Remember REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Remember 9. In an ANOVA, what is represented by the letter N? a. the sum of the scores in a specific condition b. the sum of the scores in the entire research study c. the number of scores in a specific condition Copyright Cengage Learning. Powered by Cognero.

Page 2

d. the total number of scores in the entire research study ANSWER: d DIFFICULTY: Remember REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Remember 10. A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and X2 = 94. For this research study, what is SStotal? a. SStotal = 10 b. SStotal = 24 c. SStotal = 34 d. SStotal = 68 ANSWER: c DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 11. A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and X2 = 94. For this research study, what is SSbetween? a. SSbetween = 10 b. SSbetween = 24 c. SSbetween = 34 d. SSbetween = 68 ANSWER: a DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 12. A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and X2 = 94. For this research study, what is SSwithin? a. SSwithin = 10 b. SSwithin = 24 c. SSwithin = 34 d. SSwithin = 68 ANSWER: b DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 13. An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each condition. For this research study, what is dftotal?

Copyright Cengage Learning. Powered by Cognero.

Page 3

a. dftotal = 2 b. dftotal = 11 c. dftotal = 33 d. dftotal = 35 ANSWER: d DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 14. An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each condition. For this research study, what is dfbetween?

a. dfbetween = 2 b. dfbetween = 11 c. dfbetween = 33 d. dfbetween = 35 ANSWER: a DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 15. An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each condition. For this research study, what is dfwithin?

a. dfwithin = 2 b. dfwithin = 11 c. dfwithin = 33 d. dfwithin = 35 ANSWER: c DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 16. An analysis of variance produces dfbetween = 3 and dfwithin = 24. If each treatment condition has the same number of participants, then how many participants are in each treatment? a. n = 6

b. n = 7 c. n = 8 d. n = 9 ANSWER: b DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 4

17. Which of these comparisons between an ANOVA and a t test is correct? a. An ANOVA can be used to compare three or more conditions, whereas a t test cannot. b. A t test can be used to compare two conditions, whereas an ANOVA cannot. c. An ANOVA examines whether mean differences exist between conditions, whereas a t test does not. d. A t test provides more flexibility in research studies than an ANOVA. ANSWER: a DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 18. An analysis of variances produces dftotal = 29 and dfwithin = 27. For this analysis, how many treatment conditions are being compared? a. k = 1

b. k = 2 c. k = 3 d. This cannot be determined based on the provided information.

ANSWER: c DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 19. Which statement below is not possible as an alternative hypothesis in an analysis of variance? a. µ1 = µ2, but µ3 is different b. µ1 ≠ µ2 ≠ µ3 c. µ1 = µ3, but µ2 is different d. Each of these are possible alternative hypotheses.

ANSWER: d DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 20. In analysis of variance, what is measured by the MS values? a. the mean of the squared deviations b. the mean variability between conditions c. the mean variability within conditions d. the mean of the standard deviations ANSWER: a DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 21. An analysis of variance produces SSbetween = 40 and MSbetween = 20. In this analysis, how many treatment conditions Copyright Cengage Learning. Powered by Cognero.

Page 5

are being compared? a. k = 2

b. k = 3 c. k = 4 d. k = 20 ANSWER: b DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 22. In an analysis of variance, which of the following statements is not true? a. SStotal = SSbetween + SSwithin b. dftotal = dfbetween + dfwithin c. MStotal = MSbetween + MSwithin d. All three choices are true.

ANSWER: c DIFFICULTY: Apply REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Apply 23. Which of the following is expected if the null hypothesis is true for an analysis of variance? a. SSbetween should be about the same value as SStotal b. SSbetween should be about the same value as SSwithin c. MSbetween should be about the same value as MStotal d. MSbetween should be about the same value as MSwithin ANSWER: d DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 24. Which statement below is not consistent with the distribution of F-ratios? a. With very small sample sizes, F-ratio tend to be more spread out. b. With very large sample sizes, F-ratios tend to be clustered closer together. c. F values that make up the F-ratio distribution are always positive. d. With large sample sizes, F-ratios are clustered around 0.

ANSWER: d DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 25. A researcher uses analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment. The F-ratio for this analysis would have which df values?

Copyright Cengage Learning. Powered by Cognero.

Page 6

a. df = 2, 11 b. df = 2, 33 c. df = 2, 35 d. df = 2, 36 ANSWER: b DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 26. An analysis of variance produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 2, 15. For this analysis, what is the F-ratio? a. F = 0.50

b. F = 2.00 c. F = 3.75 d. F = 0.27 ANSWER: c DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 27. An independent-measures research study compares three treatment conditions using a sample of n = 5 in each condition. For this study, the three samples have SS1 = 10, SS2 = 20, and SS3 = 15. Which value would be obtained for MSwithin?

a. MSwithin = 3.21 b. MSwithin = 3.75 c. MSwithin = 5.00 d. MSwithin = 3.33 ANSWER: b DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 28. The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 7 participants in each condition. Note that several values are missing in the table. What is the missing value for MSbetween?

Source SS df MS Between 20 xx xx F = xx Within xx xx 2 Total xx xx a. MSbetween = 2 b. MSbetween = 5 c. MSbetween = 10 Copyright Cengage Learning. Powered by Cognero.

Page 7

d. MSbetween = 40 ANSWER: c DIFFICULTY: Apply REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Apply 29. The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each condition. Note that several values are missing in the table. What is the missing value for MSwithin?

Source SS df MS Between 30 xx xx F = xx Within xx xx xx Total 62 xx a. MSwithin = 2 b. MSwithin = 11 c. MSwithin = 33 d. MSwithin = 15 ANSWER: a DIFFICULTY: Apply REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Apply 30. The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each condition. Note that several values are missing in the table. What is the missing value for SStotal?

Source SS df MS Between 20 xx xx F = 5.00 Within xx xx xx Total xx xx a. SStotal = 22 b. SStotal = 30 c. SStotal = 54 d. SStotal = 74 ANSWER: d DIFFICULTY: Apply REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Apply 31. Which of the following is not consistent with assumptions for the independent-measures ANOVA? a. The populations from which the samples are selected must have equal variances. b. The populations from which samples are selected must be normal, especially as sample sizes decrease.

Copyright Cengage Learning. Powered by Cognero.

Page 8

c. The populations from which samples are selected must be normal, especially as sample sizes increase. d. The observations within each sample must be independent.

ANSWER: c DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 32. A researcher reports an F-ratio with df = 2, 18 from an independent-measures research study. Based on the df values, how many conditions were compared in the study, and what was the total number of individuals participating in the study? a. 2 conditions and 19 participants

b. 2 conditions and 20 participants c. 3 conditions and 21 participants d. 3 conditions and 22 participants ANSWER: c DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 33. A researcher reports an F-ratio with df = 1, 24 for an independent-measures experiment. If all the treatments had the same number of participants, then how many individuals were in each treatment? a. n = 11

b. n = 12 c. n = 13 d. n = 14 ANSWER: c DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 34. Which of the following statements is a correct comparison between Scheffe and Tukey post hoc tests? a. A Scheffe post hoc test tends to require a greater difference between conditions for a statistically significant difference than a Tukey post hoc test. b. A Scheffe post hoc test compares different condition mean values than a Tukey post hoc test.

c. A Scheffe post hoc test tends to be more likely to lead to a Type I error than a Tukey post hoc test. d. A Scheffe post hoc test requires smaller sample sizes than a Tukey post hoc test.

ANSWER: a DIFFICULTY: Understand REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Understand 35. For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each condition, what is the critical value for the F-ratio using α = 0.05? a. F = 3.88 Copyright Cengage Learning. Powered by Cognero.

Page 9

b. F = 3.49 c. F = 3.74 d. F = 3.34 ANSWER: a DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 36. Which of the following describes a typical distribution of F-ratios? a. symmetrical with a mean of zero b. positively skewed with all values greater than or equal to zero c. negatively skewed with all values greater than or equal to zero d. symmetrical with a mean equal to dfbetween ANSWER: b DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 37. If an analysis of variance is used for the following data, what would be the effect of changing the value of M1 to 20?

Sample Data M1 = 15

M2 = 25

SS1 = 90

SS2 = 70

a. a decrease in SSbetween and an increase in the F-ratio b. a decrease in SSbetween and a decrease in the F-ratio c. a decrease in SSwithin and an increase in the F-ratio d. a decrease in SSwithin and a decrease in the F-ratio ANSWER: b DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply 38. If an analysis of variance is used for the following data, what would be the effect of changing the value of SS2 to 100?

Sample Data M1 = 15

M2 = 25

SS1 = 90

SS2 = 70

a. an increase in SSwithin and an increase in the F-ratio b. an increase in SSwithin and a decrease in the F-ratio c. a decrease in SSwithin and an increase in the F-ratio Copyright Cengage Learning. Powered by Cognero.

Page 10

d. a decrease in SSwithin and a decrease in the F-ratio ANSWER: b DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply 39. An independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each condition.

If all three conditions have the same total, T1 = T2 = T3, what is SSbetween?

a. SSbetween = 0 b. SSbetween = 1.00 c. SSbetween = 10 d. This cannot be determined based on the information provided.

ANSWER: a DIFFICULTY: Apply REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 40. Consider that an analysis of variance is conducted for a research study with an overall sample size of n = 18, dfbetween = 3, and SSwithin = 398. If the null hypothesis is rejected, which Tukey honestly significant difference value should be used to determine whether statistically significant differences exist between conditions with an alpha of 0.05? a. HSD = 2.13

b. HSD = 2.81 c. HSD = 4.97 d. HSD = 6.36 ANSWER: a DIFFICULTY: Apply REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Apply 41. Consider that an analysis of variance is conducted for a research study with three conditions. Each condition has n = 7 participants. It is determined that SSbetween = 45 and SSwithin = 90. It is also determined that the first condition has a mean of M1 = 4, the second condition has a mean of M2 = 6, and the third condition has a mean of M3 = 8. Which statement below is consistent with the results of this research study, using an alpha of .05 and Tukey post hoc tests?

a. M1 is statistically different from M3, but M2 is not statistically different from M1 or M3. b. M1 is statistically different from M2 and M3, but M2 is not statistically different from M3. c. M1, M2, and M3 are each statistically different from each other. d. M2 is statistically different from M3, but M1 is not statistically different from M2 or M3.

ANSWER: a DIFFICULTY: Apply REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 11

42. The data below are from an independent-measures experiment comparing three different conditions. Which F-ratio value below is the Scheffe post hoc value computed when comparing conditions 2 and 3 using the data below?

Condition 1 Condition 2 Condition 3 2

2

10

3

6

1

G = 33

1

4

4

ΣX2 = 187

––––––––––––––––––––––––––––––––––––– T=6

T = 12

T = 15

SS = 2

SS = 8

SS = 42

a. F = 8.65 b. F = 1.43 c. F = 0.09 d. F = 0.12 ANSWER: c DIFFICULTY: Apply REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Apply 43. An analysis of variance is used to evaluate the mean differences for a research study comparing four conditions with a separate sample of n = 8 in each condition. If the data produce an F-ratio of F = 4.60, which of the following is the correct statistical decision? a. reject the null hypothesis with α = 0.05 but not with α = 0.01

b. reject the null hypothesis with either α = 0.05 or α = 0.01 c. fail to reject the null hypothesis with either α = 0.05 or α = 0.01 d. There is not enough information to make a statistical decision.

ANSWER: b DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 44. If an analysis of variance is used for the following data, what would be the effect of changing the value of SS1 to 50?

Sample Data M1 = 10

M2 = 20

SS1 = 90

SS2 = 70

a. an increase in SSwithin and an increase in the size of the F-ratio b. an increase in SSwithin and a decrease in the size of the F-ratio c. a decrease in SSwithin and an increase in the size of the F-ratio d. a decrease in SSwithin and a decrease in the size of the F-ratio ANSWER:

c

Copyright Cengage Learning. Powered by Cognero.

Page 12

DIFFICULTY: Apply REFERENCES: 12.6 More about ANVOA KEYWORDS: Bloom’s: Apply 45. If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 25?

Sample Data M1 = 10

M2 = 20

SS1 = 90

SS2 = 70

a. an increase in SSbetween and an increase in the F-ratio b. an increase in SSbetween and a decrease in the F-ratio c. a decrease in SSbetween and an increase in the F-ratio d. a decrease in SSbetween and a decrease in the F-ratio ANSWER: a DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply 46. The following table shows the results of an analysis of variance comparing three treatment conditions. What is the value of 2, the percentage of variance accounted for?

Source SS df MS Between 30 2 15 F = 7.50 Within 60 30 2 Total 90 32 a. 2 = 0.50 b. 2 = 0.33 c. 2= 0.67 d. 2= 0.067 ANSWER: b DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 47. A research report concludes that there are significant differences among treatment conditions, with “F(2, 24) = 8.62, p < 0.01.” If the same number of participants was used in each of the treatment conditions, then how many individuals were in each treatment condition? a. n = 7

b. n = 9 c. n = 10 d. n = 30 ANSWER: b DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 13

REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 48. In which of the following situations would unequal sample sizes in conditions of an ANOVA be problematic? a. if the sample sizes are large and the discrepancy between sample means is large b. if the sample sizes are large and the discrepancy between sample means is not large c. if the populations from which samples are selected are not normally shaped and the discrepancy between condition sample sizes is large d. if the populations from which samples are selected are normally shaped and the discrepancy between condition sample sizes is large

ANSWER: c DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 49. A researcher uses an independent-measures t test to evaluate the mean difference between two treatments and obtains t(12) = 4.00. If the researcher had used an ANOVA to evaluate the data, what F-ratio would be obtained? a. F(1, 12) = 2.00

b. F(1, 12) = 16.00 c. F(1, 11) = 2.00 d. F(1, 11) = 16.00 ANSWER: b DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply 50. The data below are from an independent-measures experiment comparing three different conditions. Which statement below is consistent with the results of a Scheffe post hoc test that compares conditions 1 and 2 using the data below?

Condition 1 Condition 2 Condition 3 2 2 10 3 6 1 G = 33 1 4 4 ΣX2 = 187 ––––––––––––––––––––––––––––––––––––– T=6 T = 12 T = 15 SS = 2 SS = 8 SS = 42 a. The difference between conditions 1 and 2 is not statistically significant, given that the computed F-ratio of F = 0.46 is not in the critical region. b. The difference between conditions 1 and 2 is not statistically significant, given that the computed F-ratio of F = 0.35 is not in the critical region. c. The difference between conditions 1 and 2 is statistically significant, given that the computed F-ratio of F = 3.66 is in the critical region. d. The difference between conditions 1 and 2 is statistically significant, given that the computed F-ratio of F = 4.10 is in the critical region.

ANSWER:

b

Copyright Cengage Learning. Powered by Cognero.

Page 14

DIFFICULTY: Apply REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Apply 51. For an ANOVA, when the null hypothesis is true, the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 52. For an analysis of variance comparing three condition means, there will be three factors. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 53. All things held constant, an F-ratio with a large error term is an indication that the null hypothesis is more likely to be true.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.2 The Logic of Analysis of Variance KEYWORDS: Bloom’s: Understand 54. A research study examining differences in the effectiveness of three treatment conditions in combatting anxiety has three levels.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Apply 55. Typically, the testwise error rate in an ANOVA is less than the experimentwise error rate. a. True b. False ANSWER: True DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

REFERENCES: 12.1 Introduction: An Overview of Analysis of Variance KEYWORDS: Bloom’s: Understand 56. If an ANOVA has dfbetween = 3, then k = 3. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 57. For an analysis of variance comparing four condition means with a separate sample of n = 8 participants in each condition, the F-ratio will have df = 3, 31.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 58. In an analysis of variance, the MSbetween and MSwithin represent the means of the squared variability between and within conditions.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 59. If an analysis of variance produces SSbetween = 30 and MSbetween = 10, then the ANOVA is comparing three treatment conditions.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.3 ANOVA Notation and Formulas KEYWORDS: Bloom’s: Understand 60. Small sample mean differences and large sample variances tend to increase the likelihood that the null hypothesis is rejected in an analysis of variance.

a. True b. False ANSWER: False DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 61. With smaller sample sizes, the distribution of F-ratios is more spread out. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 62. The larger the differences among the sample means, the larger the numerator of the F-ratio will be in an analysis of variance.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 63. SSwithin measures the size of the sample variances in an analysis of variance. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 64. Large sample mean differences and small sample variances tend to increase the likelihood that the null hypothesis is rejected in an analysis of variance.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 65. If an analysis of variance produces an F-ratio value of F = 0, then all the samples have the same mean. a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA Copyright Cengage Learning. Powered by Cognero.

Page 17

66. The number of scores included in an analysis of variance influence measures of effect size, but have little or no influence on the likelihood of rejecting the null hypothesis.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 67. If an ANOVA produces SSbetween = 40 and SSwithin = 60, then η2 = 0.67. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 68. If an ANOVA produces SSbetween = 20 and SSwithin = 40, then η2 = 0.33. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 69. A research report presents the results of an independent-measures ANOVA as follows: F(3, 28) = 5.36, p < 0.01.

There is a statistically significant difference between at least two of the conditions in this research study.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 70. A research report presents the results of an independent-measures ANOVA as follows: F(3, 28) = 4.41, p > 0.01. The null hypothesis was rejected in the hypothesis test pertaining to this research report.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 71. A research report presents the results of an independent-measures ANOVA as follows: F(1, 22) = 4.00, p > 0.05. If Copyright Cengage Learning. Powered by Cognero.

Page 18

the researcher had used an independent-measures t test to evaluate the data, a t value of t = +2.00 would be obtained.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply 72. In an analysis of variance, large sample variances reduce the likelihood of rejecting the null hypothesis. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 73. In an analysis of variance, SSbetween measures the size of the mean differences from one condition to another. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Understand 74. After an ANOVA, a researcher computes 2 to evaluate effect size and obtains 2 = 0.50. If the ANOVA had SStotal = 100, then SSwithin = 50 and SSbetween = 50.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 75. An ANOVA comparing two treatment conditions produces SSwithin = 80 and SSbetween = 50. For these data, 2 = 0.63.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Understand 76. Posttests (or post hoc tests) are only needed if H0 is rejected in an ANOVA comparing more than two treatment conditions.

Copyright Cengage Learning. Powered by Cognero.

Page 19

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Understand 77. Tests like Scheffé and Tukey Honestly Significant Difference post hoc tests are never necessary for an analysis of variance comparing only two treatment conditions.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Understand 78. An ANOVA is used to determine whether any significant difference exists between treatment condition means, and posttests are used to determine exactly which treatment means are significantly different from each other.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Understand 79. A researcher conducts an ANOVA to evaluate the mean difference between two conditions using the data from an independent-measures study and obtains F = 4.00. If the researcher had used an independent-measures t test, then the t statistic calculated would be t = +2.00.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply 80. A researcher uses an independent-measures t test to evaluate the mean difference between two conditions. If the t statistic for the independent-measures t test has df = 12, then an ANOVA evaluating the same data would produce an Fratio with df = 1, 12.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 12.6 More about ANOVA KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 20

81. The data below are from an independent-measures experiment comparing three different treatment conditions regarding attention scores.

Treatment 1 Treatment 2 Treatment 3 0 2 4 0 3 2 G = 36 0 1 4 ΣX2 = 114 3 3 3 0 2 4 0 1 4 ––––––––––––––––––––––––––––––––––––– T=3 T = 12 T = 21 SS = 7.5 SS = 4 SS = 3.5 a. Explain why an ANOVA should be used instead of a series of t tests to evaluate the mean differences among the three treatment conditions. b. Use an analysis of variance with α = .05 to determine whether these data indicate any significant mean differences among the treatment conditions. c. Compute η2, the percentage of variance accounted for by the treatments. d. Write the results of the analysis of variance as appropriate for a statistical report. a. There are more than two treatment conditions. Thus, it would require several t tests to compare all ANSWER: the treatments. This would increase the experimentwise error rate and lead to a greater Type I error risk. b. SSbetween = 27, MSbetween = 13.5, SSwithin = 15, MSwithin = 1, F(2, 15) = 13.5, p < 0.05. Reject the null hypothesis, and conclude that there is a difference between the treatment conditions. c. η2 = 27/42 = 0.643 d. The analysis of variance indicates that there are significant differences among the three treatments regarding attention scores, F(2, 15) = 13.5, p < 0.05, η2 = 0.643.

DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply 82. A researcher used an analysis of variance to compare four treatment conditions with a separate sample of n = 12 participants in each condition. The results of the analysis are shown in the following summary. Fill in all missing values in the table. (Hint: start with the df values.)

Source SS df MS Between Treatments ____ ____ F = 2.50 Within Treatments 88 ____ ____ Total ____ ____ ANSWER: Source SS df MS Between Treatments 15 3 5 F = 2.50 Within Treatments 88 44 2 Total 103 47 DIFFICULTY: Apply REFERENCES: 12.4 Examples of Hypothesis Testing and Effect Size with ANOVA KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 21

83. A psychologist would like to examine the effects of different testing methods on the final performance of college students. One group has regular quizzes, one group has three large exams, and the third group only has a final exam. At the end of the course, the psychologist interviews each student to get a measure of the student’s overall knowledge of the material. a. Do these data indicate any significant differences among the three methods? Test with α = 0.05. b. Compute Tukey’s HSD to determine exactly which methods are significantly different.

Quizzes Exams Final Only 5 3 0 7 6 2 G = 48 4 7 0 ΣX2 = 272 8 4 2 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ T = 24 T = 20 T=4 SS = 10 SS = 10 SS = 4 ANSWER: a. SSbetween = 56, MSbetween = 28, SSwithin = 24, MSwithin = 2.67, F(2, 9) = 10.49, p < 0.05. Reject the null hypothesis and conclude that there is a significant difference among these three methods. b. Tukey’s HSD = 3.23. The Quiz and Final Only conditions are statistically significantly different because the difference between these two group means exceeds 3.23. Moreover, the difference between Exam and Final Only conditions is statistically significant because the difference between these two group means exceeds 3.23. The difference between the Quiz and Exam conditions does not exceed 3.23 and thus is not statistically significant.

DIFFICULTY: Apply REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Apply 84. A. Describe the circumstances in which post hoc tests are used, and explain why these tests are necessary.

B. What is the difference generally between Scheffe and Tukey post hoc tests in the likelihood they indicate statistical significance? a. Post hoc tests are used after an analysis of variance that rejects the null hypothesis is comparing ANSWER: three or more treatments. The decision to reject H0 indicates only that at least one of the treatment means is different from another. Post hoc tests are used to determine which treatment means differ at a statistically significant level. b. Although Scheffe post hoc tests reduce the likelihood of a Type I error, they tend to require a larger mean difference between conditions to reach statistical significance than Tukey post hoc tests.

DIFFICULTY: Apply REFERENCES: 12.5 Post Hoc Tests KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 22

Chapter 13 1. Which of the following is consistent with the null hypothesis regarding the main effect of Factor A, which is comprised of two levels?

a. µA1 = µA2 b. µA1 ≠ µA2 c. µA1 < µA2 d. µA1 > µA2 ANSWER: a DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 2. Which of the following is consistent with the alternative hypothesis regarding the main effect of Factor B, which is comprised of two levels?

a. µB1 = µB2 b. µB1 ≠ µB2 c. µB1 < µB2 d. µB1 > µB2 ANSWER: b DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 3. Which of the following is consistent with the null hypothesis for the interaction of factors A and B in a two-factor analysis of variance? a. µA = µB

b. µA ≠ µB c. The mean differences between treatment conditions are not what would be predicted from the overall main effects of Factors A and B. d. The mean differences between treatment conditions are what would be predicted from the overall main effects of Factors A and B.

ANSWER: d DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 4. Which of the following is consistent with the alternative hypothesis for the interaction of factors A and B in a twofactor analysis of variance? a. µA = µB

b. µA ≠ µB c. The mean differences between treatment conditions are not what would be predicted from the overall main effects of Factors A and B. d. The mean differences between treatment conditions are what would be predicted from the overall main effects Copyright Cengage Learning. Powered by Cognero.

Page 1

of Factors A and B.

ANSWER: c DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom's: Understand 5. Consider that the results of a research study conclude that the “effect of social media use on anxiety depends on gender.” Which statement below is correct based on this conclusion? a. The research study uncovered no main effects of gender or social media use, as well as no interaction between gender and social media use. b. The research study uncovered an interaction between social media use and gender, but no main effects.

c. The research study uncovered a main effect of social media use, but no main effect of gender or interaction between gender and social media use. d. The research study uncovered a main effect of gender and interaction of gender and social media use, but not main effect of social media use.

ANSWER: b DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Apply 6. Two parallel lines in a graph pertaining to separate factors (i.e., A & B) in a two-factor analysis of variance indicate which of the following? a. There is a main effect of factor B.

b. There is a main effect of factor A. c. There is an interaction between factors A and B. d. There is no interaction between factors A and B. ANSWER: d DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 7. Two crossing, non-parallel lines in a graph pertaining to separate factors (i.e., A & B) in a two-factor analysis of variance indicate which of the following? a. There is a main effect of factor B.

b. There is a main effect of factor A. c. There is an interaction between factors A and B. d. There is no interaction between factors A and B. ANSWER: c DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 8. The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. Which value for the missing mean would most clearly result in an A x B interaction?

B1 B2 Copyright Cengage Learning. Powered by Cognero.

Page 2

A1

50

30

A2

60

?

a. M = 40 b. M = 50 c. M = 80 d. M = 60 ANSWER: c DIFFICULTY: Analyze REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Analyze 9. The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. Which value for the missing mean would most clearly result in a main effect for factor A? B1 B2 A1

20

40

A2

50

?

a. M = 40 b. M = 30 c. M = 20 d. M = 10 ANSWER: a DIFFICULTY: Analyze REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Analyze 10. Which statement below is not consistent with the benefits of adding an individual difference variable (i.e., gender) to a single factor (i.e., factor A) ANOVA? a. doing so reduces the within treatments variance

b. doing so reduces the between treatments variance for the single factor c. doing so allows for examination of whether there are differences between the levels of the individual difference variable d. doing so reveals if an interaction exists between the individual difference variable and the single factor

ANSWER: b DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 11. Which of the following is not an assumption of the two-factor ANOVA? a. The observations within each sample must be independent.

Copyright Cengage Learning. Powered by Cognero.

Page 3

b. The populations from which the samples are selected must be normal. c. The observations within each sample must have equal variances. d. The populations from which the samples are selected must have equal variances.

ANSWER: c DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 12. A researcher is interested in the effect of positive affirmations on self-confidence. What is the consequence of adding gender as a factor in the ANOVA?

a. The MSbetween treatments value will increase. b. The MSbetween treatments value will decrease. c. The MSwithin treatments value will increase. d. The MSwithin treatments value will decrease.

ANSWER: d DIFFICULTY: Apply REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Apply 13. A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or not married) and participant sex (i.e., male or female) with regard to health well-being. The researcher decides to compare the difference in health well-being between married men and women. This is an example of testing a(n) _____. a. main effect

b. simple main effect c. interaction d. simple interaction ANSWER: b DIFFICULTY: Apply REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Apply 14. A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or nonmarried) and participant sex (i.e., male or female) regarding well-being. The researcher decides to compare the difference in well-being between married men and women. What would be the null hypothesis for this comparison?

a. µMale = µFemale for married individuals b. µMale ≠ µFemale for married individuals c. µMale = µFemale for non-married individuals d. µMale ≠ µFemale for non-married individuals ANSWER: a DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 4

15. A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or non-married) and participant sex (i.e., male or female) regarding well-being among a sample with n = 6 participants in each condition. The researcher decides to compare the difference in well-being between married men and women. The MSwithin treatments from the original two-factor analysis is MSwithin treatments = 1.00. What is the F-ratio for this comparison using the matrix below, which depicts descriptive statistics regarding married participants? __________________________________________________________________________________________ Participant Sex

Males Females __________________________________________________________________ n=6 n=6 N = 12 M= 4 M=5 G = 54 T = 24 T = 30 a. F = 3 b. F = 4 c. F = 5 d. F = 6 ANSWER: a DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 16. A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or non-married) and participant sex (i.e., male or female) regarding well-being among a sample with n = 6 participants in each condition. The researcher decides to compare the difference in well-being between married men and women. The MSwithin treatments from the original two-factor analysis is MSwithin treatments = 1.00. Using the matrix below to test this simple main effect, which is the appropriate decision using α = .05? __________________________________________________________________________________________ Participant Sex

Males Females __________________________________________________________________ n=6 n=6 N = 12 M=4 M=5 G = 54 T = 24 T = 30 a. Reject the null hypothesis and conclude there is a significant difference in well-being between males and females who are married. b. Reject the null hypothesis and conclude there is a significant difference in well-being between males and females who are not married. c. Fail to reject the null hypothesis and conclude there is not a significant difference in well-being between males and females who are married. d. Fail to reject the null hypothesis and conclude there is not a significant difference in well-being between males and females who are not married.

Copyright Cengage Learning. Powered by Cognero.

Page 5

ANSWER: c DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 17. A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or nonmarried) and participant sex (i.e., male or female) regarding well-being among a sample with n = 6 participants in each condition. What would the critical value for the F-ratio be for a hypothesis test examining the difference in well-being between married men and women using an alpha level of α = 0.01? a. F = 5.85

b. F = 8.10 c. F = 3.49 d. F = 4.35 ANSWER: b DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 18. A researcher uncovers that there is a significant interaction between the factor of marital status (i.e., married or nonmarried) and participant sex (i.e., male or female) regarding well-being among a sample with n = 4 participants in each condition. What would be the degrees of freedom for the simple main effect examining the difference in well-being between married men and women? a. df = 1, 12

b. df = 1, 14 c. df = 2, 12 d. df = 2, 14 ANSWER: a DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 19. The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. Which value for the missing mean would most clearly result in an A × B interaction, as well as a simple main effect of factor A regarding those in condition B2?

B1 B2 A1

50

30

A2

60

?

a. M = 30 b. M = 20 c. M = 10 d. M = 70 ANSWER: d DIFFICULTY: Analyze Copyright Cengage Learning. Powered by Cognero.

Page 6

REFERENCES: 13.3. More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Analyze 20. The following table shows the results of a two-factor ANOVA. Based on this table, what is the value for η2 for the A × B interaction?

Source SS df MS Between 36 3 A 12 1 12 F = 4.00 B 3 1 3 F = 1.00 A×B 21 1 21 F = 7.00 Within 84 28 3 Total 120 31 a. η2 = .12 b. η2 = .16 c. η2 = .40 d. η2 = .20 ANSWER: d DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 21. What is the F value for the critical region for a two-factor analysis of variance hypothesis test with two levels in each factor and n = 7 individuals in each level using an alpha level of 0.05? a. F = 5.61

b. F = 3.40 c. F = 4.26 d. F = 7.82 ANSWER: c DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 22. Which of the following bits of information is referenced last in an APA formatted statistical report of the results regarding a two-factor ANOVA? a. means and standard deviations for all factor conditions

b. partial eta squared as a measure of effect size c. the df for the F-ratio test d. the F-ratio ANSWER: b DIFFICULTY: Understand REFERENCES: 13.2 Hypothesis Testing and Effect Size with the Repeated-Measures ANOVA KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 7

23. Which of the following bits of information is referenced first in an APA formatted statistical report of the results regarding a two-factor ANOVA? a. means and standard deviations for all factor conditions

b. partial eta squared as a measure of effect size c. the df for the F-ratio test d. the F-ratio ANSWER: a DIFFICULTY: Understand REFERENCES: 13.2 Hypothesis Testing and Effect Size with the Repeated-Measures ANOVA KEYWORDS: Bloom’s: Understand 24. Violation of which assumption below for the two-factor ANOVA is not a cause for concern with large sample sizes? a. The populations from which the samples are selected must be normal. b. The observations within each sample must be independent. c. The populations from which the samples are selected must have equal variances. d. A violation of any assumption above would be a concern, even with large sample sizes.

ANSWER: a DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 25. If a simple main effect is examined from a two-factor ANOVA with two levels in each factor and n = 7 individuals in each treatment condition, what df will be used? a. df = 1, 24 b. df = 2, 24 c. df = 1, 27 d. df = 2, 27 ANSWER: a DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 26. In a two-factor analysis of variance, a main effect is defined as _____. a. the mean differences among the levels of one factor b. the mean differences among all treatment conditions across all factors c. the mean difference between two factors d. the difference between the largest treatment mean and the smallest treatment mean ANSWER: a DIFFICULTY: Remember REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Remember 27. A two-factor study with two levels of factor A and three levels of factor B uses a separate group of n = 5 participants in each treatment condition. How many participants are needed for the entire study?

Copyright Cengage Learning. Powered by Cognero.

Page 8

a. n = 5 b. n = 10 c. n = 15 d. n = 30 ANSWER: d DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 28. How many separate groups of participants would be needed for an independent-measures, two-factor research study with 3 levels of factor A and 4 levels of factor B? a. 3

b. 4 c. 7 d. 12 ANSWER: d DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 29. A two-factor ANOVA produces an F-ratio for factor A with df = 1, 36 and an F-ratio for factor B with df = 2, 36.

Which of the following describes the experiment producing these F-ratios? a. 1 level of factor A and 2 levels of factor B

b. 2 levels of factor A and 3 levels of factor B c. 2 levels for both factors d. 3 levels for both factors ANSWER: b DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 30. The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. Which value for the missing mean would result in no main effect for factor B? B1 B2 A1

20

10

A2

40

?

a. M = 20 b. M = 30 c. M = 40 d. M = 50 ANSWER:

d

Copyright Cengage Learning. Powered by Cognero.

Page 9

DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 31. The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. Which value for the missing mean would result in no A × B interaction?

B1 B2 A1

20

30

A2

10

?

a. M = 10 b. M = 20 c. M = 30 d. M = 40 ANSWER: b DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 32. If the mean and variance are computed for each sample in an independent-measures, two-factor experiment, which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA? a. large differences between sample means and small sample variances

b. large differences between sample means and large sample variances c. small differences between sample means and small sample variances d. small differences between sample means and large sample variances ANSWER: a DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Apply 33. In a two-factor experiment with 2 levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. Which result(s) would be produced by this pattern of treatment means? a. a main effect for factor A

b. a main effect for factor B c. an interaction between factors A and B d. main effects for both factors A and B as well as an interaction between factors A and B ANSWER: d DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 10

34. For a research study with 2 levels of factor A, 3 levels of factor B, and n = 5 in each treatment condition, what are the df values for the F-ratio evaluating the main effect for factor A? a. df = 1, 4

b. df = 1, 24 c. df = 1, 29 d. df = 2, 29 ANSWER: b DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 35. In a two-factor ANOVA, which of the following is not computed directly but rather is found by subtraction? a. SSwithin treatments b. SSA c. SSB d. SSA × B ANSWER: d DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 36. For an experiment involving 2 levels of factor A and 4 levels of factor B with a sample of n = 5 in each treatment condition, what is the value for dfwithin treatments?

a. dfwithin treatments = 36 b. dfwithin treatments = 34 c. dfwithin treatments = 32 d. dfwithin treatments = 39 ANSWER: c DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 37. For an experiment involving 3 levels of factor A and 3 levels of factor B with a sample of n = 8 in each treatment condition, what are the df values for the F-ratio for the A × B interaction? a. df = 2, 63

b. df = 4, 63 c. df = 2, 62 d. df = 4, 62 ANSWER: b DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 11

38. The results of a two-factor analysis of variance produce df = 1, 30 for the F-ratio for factor A, and df = 2, 30 for the Fratio for the A × B interaction. Based on this information, how many levels of factor B were compared in the study? a. 1

b. 2 c. 3 d. This cannot be determined with the provided information.

ANSWER: c DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 39. The results of a two-factor analysis of variance produce df = 2, 36 for the F-ratio for factor A and df = 2, 36 for the Fratio for factor B. What are the df values for the F-ratio for the A × B interaction? a. df = 2, 37

b. df = 2, 36 c. df = 4, 37 d. df = 4, 36 ANSWER: d DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 40. The results of a two-factor analysis of variance produce df = 2, 36 for the F-ratio for factor A and df = 2, 36 for the Fratio for factor B. How many participants are in each of the treatment conditions? a. n = 4

b. n = 5 c. n = 6 d. n = 7 ANSWER: b DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 41. A two-factor research study has 2 levels of factor A and 3 levels of factor B with n = 8 participants in each treatment condition. For this study, what is the value for dfbetween treatments?

a. dfbetween treatments = 3 b. dfbetween treatments = 4 c. dfbetween treatments = 5 d. dfbetween treatments = 6 ANSWER: c DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 12

42. What is the relationship among the separate F-ratios in a two-factor ANOVA? a. They may have different df values, but they all have the same denominator. b. They all have the same df values and they all have the same denominator. c. They may have different df values and may have different denominators. d. They all have the same df values, but they may have different denominators.

ANSWER: a DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 43. For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A? a. n = 10

b. n = 20 c. n = 30 d. n = 60 ANSWER: c DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 44. The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B. Based on this information, what can a researcher conclude about the interaction? a. There must be a statistically significant interaction.

b. There probably is a statistically significant interaction. c. The interaction cannot be statistically significant. d. A researcher cannot make any conclusion about the statistical significance of the interaction.

ANSWER: d DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 45. If a two-factor analysis of variance produces a statistically significant interaction, what can you conclude about the main effects? a. Either the main effect for factor A or the main effect for factor B is also statistically significant.

b. Both the main effect for factor A and the main effect for factor B are statistically significant. c. Neither the main effect for factor A nor the main effect for factor B is statistically significant. d. A researcher cannot make any conclusion about the statistical significance of the main effects.

ANSWER: d DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 13

46. A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication. In this twofactor study, factor A is medication versus no medication and factor B is male versus female. The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males. Which pattern of results should be obtained if the medication works as predicted? a. a significant main effect for factor A (medication)

b. a significant interaction c. a significant main effect for factor A and a significant interaction d. The answer is not provided.

ANSWER: c DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 47. The following table shows the results of a two-factor analysis of variance with 2 levels of factor A, 3 levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the F-ratio for the A × B interaction?

Source SS df MS Between 80 xx A 8 xx xx F = xx B xx xx 20 F = xx A×B xx xx xx F = xx Within xx xx xx Total 176 xx a. F = 2 b. F = 4 c. F = 8 d. F = 16 ANSWER: b DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 48. The following table shows the results of a two-factor ANOVA. Based on this table, what is the value for η2 for factor A? Source SS df MS Between 36 3 A 12 1 12 F = 4.00 B 3 1 3 F = 1.00 A×B 21 1 21 F = 7.00 Within 84 28 3 Total 120 31 a. η2 = 0.333 b. η2 = 0.125 c. η2 = 0.121 d. η2 = 0.100 Copyright Cengage Learning. Powered by Cognero.

Page 14

ANSWER: b DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 49. For the following data, what is the value of SSB?

A1

A2

B1 n=5 M=1 SS = 10

B2 n=5 M=2 SS = 20

n=5 M=1 SS = 10

n=5 M=4 SS = 20

a. SSB = 0 b. SSB = 10 c. SSB = 20 d. SSB = 40 ANSWER: c DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 50. For the following data, what is the value of SSwithin?

B1 B2 n=5 n=5 A1 M=1 M=2 SS = 10 SS = 20

A2

n=5 M=1 SS = 10

n=5 M=4 SS = 20

a. SSwithin = 10 b. SSwithin = 20 c. SSwithin = 40 d. SSwithin = 60 ANSWER: d DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 51. In the context of a two-factor ANOVA, the numerator of the F-ratio measures the mean differences that would be expected if there is no treatment effect.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 52. A simple main effect in a two-factor ANOVA with two levels in each factor consists of comparing four treatment conditions to each other.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 53. A single-factor research design can be comprised of three levels or conditions. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 54. For a two-factor analysis of variance with two levels in each factor, the df values for a factor main effect is the same as the df values for a simple main effect.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 55. In a two-factor analysis of variance, the number of cells in a matrix will always be equivalent to the number of factor conditions.

a. True b. False ANSWER: True DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 56. A two-factor, independent-measures ANOVA always involves three hypothesis tests. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent Measures ANOVA KEYWORDS: Bloom’s: Understand 57. In a two-factor ANOVA with two levels in each factor, any simple main effect F-ratio will be computed using a dfbetween value of 1.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 58. If two significant main effects emerge in a two-factor ANOVA, then the interaction between factors must be significant.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.1 An overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 59. Generally, adding an individual difference variable with two levels to a single factor ANOVA increases the likelihood of rejecting the null hypothesis.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 60. If no main effects emerge in a two-factor ANOVA, there must also be no significant interaction between the two factors.

a. True b. False ANSWER: False DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 17

REFERENCES: 13.1 An overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 61. If two factors are independent from each other, it indicates there is an interaction between the two factors in predicting a dependent variable.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.1 An overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 62. The results of a two-factor, independent-measures ANOVA with an equal number of participants in each condition indicates that F(3, 21) = 8.63, p < 0.05.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 63. The results of a two-factor, independent-measures ANOVA with n = 6 participants in each condition indicates that F(5, 24) = 8.63, p < 0.05.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 64. In a two-factor ANOVA with two factors that each contain two levels, there are two total simple main effects that can be examined.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 65. A simple main effect is a mean difference within one column or one row of a two-factor research design. a. True b. False ANSWER: True DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 18

REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 66. A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 67. A two-factor study compares three different treatment conditions (factor 1) for males and females (factor 2). In this study, the main effect for gender is determined by comparing the overall mean score for the males (averaged over the three treatments) and the corresponding overall mean score for the females.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 68. For an independent-measures two-factor experiment, the greater the sample variances, the more likely it is that at least one of the F-ratios will be significant.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Understand 69. A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 70. A two-factor, independent-measures research study with 2 levels of factor A and 3 levels of factor B with n = 10 participants in each treatment condition would require a total of 60 participants.

a. True b. False ANSWER:

True

Copyright Cengage Learning. Powered by Cognero.

Page 19

DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 71. For an independent-measures two-factor analysis of variance, all F-ratios use the same denominator. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factors, Independent-Measures ANOVA KEYWORDS: Bloom’s: Understand 72. For a two-factor analysis of variance, the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 73. A two-factor analysis of variance produces an F-ratio for factor A that has df = 3, 36. This analysis is comparing three different levels of factor A.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 74. A two-factor study compares 2 levels of factor A and 2 levels of factor B with a sample of n = 20 participants in each treatment condition. If the results are evaluated with a two-factor ANOVA, all the F-ratios will have df = 1, 76.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 75. If the F-ratio for factor A has df = 1, 40 and the F-ratio for factor B has df = 3, 40, then the F-ratio for the interaction must have df = 2, 40.

a. True b. False ANSWER:

False

Copyright Cengage Learning. Powered by Cognero.

Page 20

DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 76. If the F-ratio for factor A has df = 1, 36 and the F-ratio for the interaction has df = 3, 36, then the F-ratio for factor B will also have df = 3, 36.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 77. If a two-factor study has 3 levels of factor A and 4 levels of factor B, then dfbetween treatments = 6. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Understand 78. Obtaining a significant interaction means that factor A has a statistically significant main effect, whereas factor B does not.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom's: Understand 79. Whenever a two-factor experiment results in a significant interaction, a researcher should be cautious about interpreting the main effects because an interaction can distort, conceal, or exaggerate the main effects of the individual factors.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom's: Understand 80. A new laundry detergent is supposed to be superior compared to the leading brand in both hot and cold water. If the new detergent works as predicted, then there should be an interaction between the brand of detergent and the temperature of the water.

a. True b. False Copyright Cengage Learning. Powered by Cognero.

Page 21

ANSWER: True DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 81. A researcher conducts a two-factor independent measures research study comparing two treatments (factor D and factor E), each comprised of two levels with n = 4 participants in each level. The results are evaluated with a two-factor ANOVA and condition means are included in the table below. Indicate whether it appears there are main effects and/or an interaction between factors based on the mean averages presented in each example.

A. E1

E2

D1

50

50

D2

50

20 B.

E1

E2

D1

60

30

D2

60

90 C.

E1

E2

D1

30

40

D2

30

40

ANSWER:

A. There are main effects of factors D and E, as well as an interaction of factors D and E. B. There is a main effect of factor D, but no main effect of factor E. There is an interaction of factors D and E. C. There is a main effect of factor E, but no main effect of factor D. There is no interaction of factors D and E.

DIFFICULTY: Apply REFERENCES: 13.1 An Overview of the Two-Factor, Independent-Measures ANOVA KEYWORDS: Bloom’s: Apply 82. A researcher uncovers that there is a significant interaction between the factor of coffee consumption (i.e., coffee drinker or not) and participant sex (i.e., male or female) regarding attention among a sample with n = 5 participants in each condition. A researcher decides to compare the difference in attention between men and women who consume coffee. The MSwithin treatments from the original two-factor analysis is MSwithin treatments = Copyright Cengage Learning. Powered by Cognero.

Page 22

2.00. Is the difference in attention between men and women who consume coffee statistically significant using α = 0.05? Justify your response. __________________________________________________________________________________________ Participant Sex

Males Females __________________________________________________________________ n=5 n=5 N = 10 M=7 M=5 G = 60 T = 35

ANSWER:

T = 25 The SSbetween = 10, and SSwithin is provided as 2. The dfbetween = 1, and the dfwithin is the same dfwithin as the overall two-factor ANOVA, which is equivalent to 16 due to there being a total of 20 participants and four conditions. MSbetween = 10/1 = 10, and MSwithin = 2. The F-ratio is 10/2 = 5. The critical region with df = 1, 16 and α = 0.05 is 4.49. Thus, the conclusion is to reject the null and conclude that there is a difference in attention between men and women who consume coffee, F(1,16) = 5.00, p < 0.05.

DIFFICULTY: Apply REFERENCES: 13.3 More about the Two-Factor ANOVA KEYWORDS: Bloom’s: Apply 83. The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with 2 levels of factor A, 3 levels of factor B, and n = 8 participants in each treatment condition. a. Fill in all missing values in the table. (Hint: start with the df column.) b. Compute η2 (the percentage of variance accounted for) for each of the main effects and for the interaction.

Source SS df MS Between Treatments 124 ____ Factor A ____ ____ ____ FA = 10 _ Factor B ____ ____ ____ FB = ____ A×B 20 ____ ____ FA × B = ____ Within Treatments ____ ____ 4 .

Total ____ ____ ANSWER: .

Source SS df MS Between Treatments 124 5 Factor A 40 1 40 FA = 10 Factor B 64 2 32 FB = 8 A×B 20 2 10 FA × B = 2.5 Within Treatments 168 42 4 Total 292 47 2 b. For factor A,  = 40/208 = 0.192 For factor B, 2 = 64/232 = 0.276 For the A×B interaction, 2 = 20/188 = 0.106 DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply 84. The following data were obtained from a two-factor independent-measures experiment with n = 5 Copyright Cengage Learning. Powered by Cognero.

Page 23

participants in each treatment condition.

B1 B2 M=3 M=6 A1 T = 15 T = 30 SS = 18 SS = 28 M=1 M=4 A2 T=5 T = 20 SS = 8 SS = 20

B3 M=9 T = 45 SS = 26 M=1 T=5 SS = 20

a. State the hypotheses for each of the three separate tests included in the two-factor ANOVA. b. Calculate degrees of freedom and locate the critical region for each of the three tests. c. Calculate the three F-ratios. d. State a conclusion for each test.

ANSWER:

The hypotheses: For factor A: H0: µA1 = µA2 (no A-effect) H1: µA1 ≠ µA2 For factor B: H0: µB1 = µB2 = µB3 (no B-effect) H1: at least one of the B-means is different from another For A × B: H0: The effect of factor A on the dependent variable does not depend on levels of factor B. H1: The effect of factor A on the dependent variable does depend on levels of factor B. b. For factor A, the F-ratio has df = 1, 24 and the critical value is F = 4.26. For factor B and the A × B interaction, the F-ratios have df = 2, 24, and the critical value is F = 3.40. c.

Source df SS MS Between Treatments 5 240 Factor A 1 120 120 FA = 24 Factor B 2 60 30 FB = 6 A×B 2 60 30 FA × B = 6 Within Treatments 24 120 5 Total 29 360 d. The results indicate that there are significant differences among the levels of factor A and factor B, and the interaction between factors A and B is also significant.

DIFFICULTY: Apply REFERENCES: 13.2 An Example of the Two-Factor ANOVA and Effect Size KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 24

Chapter 14 1. What is indicated by a positive value for a correlation? a. increases in X tend to be accompanied by increases in Y b. increases in X tend to be accompanied by decreases in Y c. increases in X tend to be accompanied by decreases in Y up to a point and then are accompanied by increases in Y d. increases in X tend to be accompanied by increases in Y up to a point and then are accompanied by decreases in Y

ANSWER: a DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 2. What would the scatter plot show for data that produce a Pearson correlation of r = +0.88? a. points clustered close to a line that slopes up to the right b. points clustered close to a line that slopes down to the right c. points widely scattered around a line that slopes up to the right d. points widely scattered around a line that slopes down to the right ANSWER: a DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 3. The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle. For these data, which is the most likely value for the Pearson correlation? a. a positive correlation near 0

b. a negative correlation near 0 c. either a positive or negative correlation near 0 d. either a positive or negative correlation near +1.00 or –1.00 ANSWER: c DIFFICULTY: Apply REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Apply 4. Which of the following Pearson correlations shows the greatest strength or consistency of relationship? a. r = –0.90 b. r = +0.74 c. r = +0.85 d. r = –0.33 ANSWER: a DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 1

5. Which of the following Pearson correlations indicates that the data points would be clustered most closely around a straight line? a. r = –0.10

b. r = +0.40 c. r = –0.70 d. r = +0.60 ANSWER: c DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 6. The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers. The correlation between amount of television violence consumed and amount of violent behavior is an example of a _____ correlation. a. positive

b. negative c. zero d. curvilinear ANSWER: a DIFFICULTY: Apply REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Apply 7. A researcher measures IQ and weight for a group of college students. Which kind of correlation is likely to be obtained for these two variables? a. a positive correlation

b. a negative correlation c. a correlation near 0 d. a correlation near 1 ANSWER: c DIFFICULTY: Apply REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Apply 8. A researcher measures driving distance from college and weekly cost of gas for a group of commuting college students.

Which kind of correlation is likely to be obtained for these two variables? a. a positive correlation

b. a negative correlation c. a correlation near 0 d. a correlation near 1 ANSWER: a DIFFICULTY: Apply REFERENCES: 14.1 Introduction Copyright Cengage Learning. Powered by Cognero.

Page 2

KEYWORDS:

Bloom’s: Apply

9. A researcher assesses self-esteem among college students at the beginning of the semester using a selfreport questionnaire. Three months later, at the end of the semester, the researcher assesses self-esteem among the same sample of college students using the exact same self-report measure of self-esteem. The researcher determines that there is a significant positive relationship between self-esteem measured at the beginning and end of the college semester for the students sampled. This demonstrates how correlations can be used to demonstrate _____. a. prediction

b. theoretical support c. validity d. reliability ANSWER: d DIFFICULTY: Apply REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Apply 10. What is indicated by a Pearson correlation of r = +1.00 between X and Y? a. Each time X increases, there is a perfectly predictable increase in Y. b. Each increase in X causes a small increase in Y. c. Each increase in X causes a small decrease in Y. d. Each time X increases, there is a perfectly predictable decrease in Y. ANSWER: a DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 11. A set of n = 10 pairs of scores has ΣX = 20, ΣY = 30, and ΣXY = 74. What is the value of SP for these data? a. SP = 74 b. SP = 24 c. SP = 14 d. SP = 44 ANSWER: c DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 12. Which statement below is consistent conceptually with what a computed Pearson’s r value represents? a. The Pearson’s r value represents the degree to which X and Y scores vary separately relative to how much X and Y scores covary together. b. The Pearson’s r value represents the degree to which X and Y scores covary together relative to how much X and Y scores vary separately. c. The Pearson’s r value represents the degree to which between groups variability exists, relative to within groups variability. d. The Pearson’s r value represents the degree to which within groups variability exists, relative to between groups variability.

Copyright Cengage Learning. Powered by Cognero.

Page 3

ANSWER: b DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 13. What is the value of SP for the following set of data?

XY 14 24 91

a. SP = 5 b. SP = –5 c. SP = 15 d. SP = –15 ANSWER: d DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 14. Which of the following is not an aspect involved in computing the sum of products (SP) of deviations? a. dividing by the total number of participants b. adding the total X and Y scores across all participants c. subtracting the total sum of squares collapsed across all scores d. multiplying the X and Y scores together for each participant ANSWER: c DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 15. A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data? a. r = 0.06

b. r = 0.60 c. r = 0.10 d. r = 0.16 ANSWER: b DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 16. Which of the following best describes the Pearson correlation for these data?

XY 25 51 34 Copyright Cengage Learning. Powered by Cognero.

Page 4

42

a. positive b. negative c. zero d. curvilinear ANSWER: b DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 17. Which of the following actions would have the effect of either changing the size or direction (sign) of a Pearson r value pertaining to a set of X and Y scores? a. dividing each X and Y score by a positive constant value

b. multiplying each X and Y score by a negative constant value c. subtracting a constant value from each X and Y score d. adding a constant value to each X and Y score ANSWER: b DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 18. Suppose the correlation between height and weight for adults is r = +0.40. What proportion (or percent) of the variability in weight can be explained by its relationship with height? a. 40%

b. 60% c. 16% d. 84% ANSWER: c DIFFICULTY: Apply REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Apply 19. A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values are multiplied by 2 and the correlation is computed for the new scores, which value will be obtained for the new correlation? a. r = –0.80

b. r = 0.40 c. r = 0.80 d. r = –0.40 ANSWER: b DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 5

20. For a two-tailed hypothesis test evaluating a Pearson correlation, what is stated by the null hypothesis? a. There is a non-zero correlation for the general population. b. The population correlation is zero. c. There is a non-zero correlation for the sample. d. The sample correlation is zero.

ANSWER: b DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 21. The Pearson correlation is calculated for a sample of n = 20 individuals. If a hypothesis test is used to determine whether the correlation is significant, which df value would be used for the t statistic? a. df = 18

b. df = 19 c. df = 20 d. df = 21 ANSWER: a DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 22. A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores. If the researcher tests the significance of the correlation, which value will be obtained for the t statistic? a. t = 3.75

b. t = 1.50 c. t = 0.77 d. t = 0.60 ANSWER: b DIFFICULTY: Apply REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Apply 23. As the sample size gets larger, the size of the correlation needed for significance _____. a. gets larger b. gets smaller c. stays constant d. This is impossible to determine based on the provided information ANSWER: b DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests With the Pearson Correlation KEYWORDS: Bloom’s: Understand 24. If the following seven scores are ranked from smallest (#1) to largest, which rank should be assigned to a score of X = 6?

Copyright Cengage Learning. Powered by Cognero.

Page 6

Scores: 1, 1, 3, 6, 6, 6, 9 a. 3

b. 4 c. 5 d. 6 ANSWER: c DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Understand 25. If the following nine scores are ranked from smallest (#1) to largest, which rank should be assigned to a score of X = 1?

Scores: 1, 1, 1, 1, 3, 6, 6, 6, 9 a. 1

b. 2 c. 2.5 d. 4 ANSWER: c DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Understand 26. A researcher assesses work ethic among college students using a self-report questionnaire. Moreover, the researcher tracks how many hours students seek out extra support at the tutoring center and with their professors on campus during the semester. The researcher determines that there is a significant positive relationship between self-reported work ethic and the number of hours students seek out extra support at the tutoring center and with their professors during the semester. This demonstrates how correlations can be used to demonstrate _____. a. prediction

b. theoretical support c. validity d. reliability ANSWER: c DIFFICULTY: Apply REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Apply 27. What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks? a. the Spearman correlation b. the point-biserial correlation c. the phi coefficient d. the curvilinear correlation ANSWER: a DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation Copyright Cengage Learning. Powered by Cognero.

Page 7

KEYWORDS:

Bloom’s: Understand

28. Under which circumstances is the phi-coefficient used? a. when one variable consists of ranks and the other is numerical b. when both variables consist of ranks c. when both variables are dichotomous d. when one variable is dichotomous and the other consists of numerical scores ANSWER: c DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Understand 29. Which of the following produces the value for r2, which is used as a measure of effect size in an independent measures t-test? a. squaring the Spearman correlation for the same data

b. squaring the point-biserial correlation for the same data c. squaring the Pearson correlation for the same data d. None of these actions will produce r2.

ANSWER: b DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Understand 30. Which correlation should be used to measure the relationship between gender and grade point average for a group of college students? a. Pearson correlation

b. Spearman correlation c. point-biserial correlation d. phi-coefficient ANSWER: c DIFFICULTY: Apply REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Apply 31. For a group of graduating college seniors, a researcher records each student’s rank in his/her high school graduating class and the student’s rank in the college graduating class. Which correlation should be used to measure the relationship between these two variables? a. Pearson correlation

b. Spearman correlation c. point-biserial correlation d. phi-coefficient ANSWER: b DIFFICULTY: Apply REFERENCES: 14.5 Alternatives to the Pearson Correlation Copyright Cengage Learning. Powered by Cognero.

Page 8

KEYWORDS:

Bloom’s: Apply

32. For the linear equation Y = 2X + 4, if X increases by 1 point, by how much will Y increase? a. 1 point b. 2 points c. 3 points d. 4 points ANSWER: b DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 33. For the linear equation Y = 2X – 3, which of the following points will not be on the line? a. 0, 3 b. 4, 5 c. 2, 1 d. 7, 11 ANSWER: a DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 34. From the regression equation Ŷ = –2X + 6, what can be determined about the correlation between X and Y? a. The correlation will be positive. b. The correlation will be negative. c. The correlation will be large and positive. d. The correlation will be large and negative.

ANSWER: b DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 35. Consider that a researcher is examining the relationship between amounts of physical activity and weight among adults. The researcher goes to a local athletics club to sample individuals who frequently exercise to examine the correlation between physical activity and weight. What is the most prominent concern regarding this research study that may obscure the true nature of the relationship between physical activity and weight among the population of adults? a. outliers

b. restriction of range c. reliability d. violation of the homogeneity of variances assumption ANSWER: b DIFFICULTY: Apply REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Apply Copyright Cengage Learning. Powered by Cognero.

Page 9

36. A set of n = 20 pairs of X and Y scores has SSX = 10, SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X? a. b = 0.33

b. b = 0.25 c. b = 4.00 d. b = 3 ANSWER: d DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 37. A set of X and Y scores are obtained from a sample of n = 36 individuals. A Pearson value of r = 0.50 is obtained for the relationship between the X and Y scores. What is the value for the standard error for r (sr)?

a. sr = 0.15 b. sr = 0.02 c. sr = 0.07 d. sr = 0.09 ANSWER: a DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 38. A Spearman correlation coefficient should be computed to assess the correlation between variables when both variables are measured using a(n) _____ scale of measurement. a. nominal (dichotomous)

b. ordinal c. interval d. ratio ANSWER: b DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Understand 39. The individual residual scores from a sample of participants regarding the difference between the predicted Y values from a regression equation and the actual Y values from the data are provided here: Y - Ŷ = 3, 8, 1, 2, 2. What is the value for the standard error of estimate? a. 3.65

b. 1.45 c. 5.23 d. 4 ANSWER: c DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 10

REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 40. A set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. Which is the regression equation for predicting Y from X? a. Ŷ = 0.25X + 4

b. Ŷ = 4X – 9 c. Ŷ = 0.5X + 3 d. Ŷ = 2X – 3 ANSWER: d DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 41. For the regression equation, Ŷ = –2X + 6, if the X value is above the mean (positive deviation), what can be determined about the predicted Y value? a. The predicted Y value will be above the mean for the Y scores.

b. The predicted Y value will be below the mean for the Y scores. c. The predicted Y value will be equal to the mean for the Y scores. d. The predicted Y value will be above the mean for the Y scores for a period of time and then will move below the mean.

ANSWER: b DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 42. If there is a positive correlation between X and Y in a research study, then the regression equation Y = bX + a will have _____.

a. b > 0 b. b < 0 c. a > 0 d. a < 0 ANSWER: a DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 43. Assuming that SSY is constant in a research study, which of the following correlations would have the largest SSresidual? a. r = –0.10

b. r = +0.40 c. r = –0.70 d. There is no relationship between the correlation and SSresidual.

ANSWER:

a

Copyright Cengage Learning. Powered by Cognero.

Page 11

DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 44. A linear regression equation has b = 3 and a = –6. What is the predicted value of Y for X = 4? a. Ŷ = 6 b. Ŷ = –21 c. Ŷ = –2 d. Ŷ = 8 ANSWER: a DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 45. A researcher conducts a hypothesis test to examine the hypothesis that stress is positively associated with greater impulsive decision-making. Which statement below is consistent with the null hypothesis for this hypothesis test? a. ρ > 0

b. ρ < 0 c. ρ ≥ 0 d. ρ ≤ 0 ANSWER: d DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 46. A set of n = 25 pairs of scores (X and Y values) in a research study has a Pearson correlation of r = 0.80. What percentage of the variance for the Y scores is predicted by its relationship with X? a. 36%

b. 20% c. 80% d. 64% ANSWER: d DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 47. A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores. For the analysis of regression testing the significance of the equation, what are the df values for the F-ratio? a. df = 1, 11

b. df = 1, 12 c. df = 2, 10 d. df = 2, 11 ANSWER: a DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 12

REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 48. For linear regression calculated for a sample of n = 20 pairs of X and Y values, what is the value for degrees of freedom for the predicted portion of the Y-score variance, MSregression? a. df = 1

b. df = 2 c. df = 19 d. df = 18 ANSWER: a DIFFICULTY: Understand KEYWORDS: Bloom’s: Understand 49. The following X and Y scores from a research study produced SSX = 2 and SP = 8. What is the regression equation for predicting Y? XY 12 23 3 10

a. Ŷ = 0.25X + 4.5 b. Ŷ = 0.25X – 4.5 c. Ŷ = 4X + 3 d. Ŷ = 4X – 3 ANSWER: d DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 50. An analysis of regression is used to test the significance of a linear regression equation based on a sample of n = 20 individuals. What are the df values for the F-ratio? a. df = 1, 18

b. df = 1, 19 c. df = 2, 18 d. df = 2, 19 ANSWER: a DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 51. A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable. a. True b. False ANSWER: False DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 13

REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 52. If the value of the Pearson correlation is r = +1.00 or r = –1.00, then all data points in the scatter plot fit perfectly on a straight line.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 53. A Pearson correlation value of r = –0.90 indicates that the data points are clustered far from a line that slopes down to the right.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Understand 54. If a researcher measured hearing acuity and age for a group of people who were 50 to 90 years old, it would be expected that a positive correlation would emerge between hearing acuity and age.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Apply 55. The value obtained for the sum of products, SP, determines the sign (+/–) for the Pearson correlation value. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand 56. A set of X and Y values can be transformed into a set of z-scores. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation Copyright Cengage Learning. Powered by Cognero.

Page 14

KEYWORDS:

Bloom’s: Understand

57. Suppose that there is a correlation of r = 0.41 between the amount of time that each student reports studying for an exam and the student’s grade on the exam. This correlation would indicate that there is a tendency for people who study more to get better grades.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 14.1 Introduction KEYWORDS: Bloom’s: Apply 58. One or two extreme data points can have a dramatic effect on a computed Pearson’s r value for a correlation. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Understand 59. A set of X and Y scores has a Pearson correlation of r = 0.60. For these data, 60% of the variability in Y scores can be predicted from the relationship of the Y variable with the X variable.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Understand 60. A researcher finds a significant positive correlation of r = 0.63 between the amount of time spent watching television and blood pressure for a sample of 40-year-old men. This means that watching more television causes higher blood pressure.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Apply 61. For a two-tailed hypothesis test evaluating the significance of a correlation, the null hypothesis states that the population correlation is zero.

a. True b. False ANSWER: True DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 62. In a test for significance of a Pearson correlation for a sample of n = 30 individuals, a researcher determines the critical value for the hypothesis test by using df = 29.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 63. Assuming that other factors are held constant, a correlation of r = –0.95 between variables in one research study will result in more accurate predictions than a correlation of r = +0.70 in another research study.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Apply 64. A Pearson correlation value (r) indicates the exact degree of accuracy in which a researcher can predict a participant’s score on a second variable from their score on a first variable.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Understand 65. The calculated value for the coefficient of determination is consistent with using correlations as a tool to predict. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.3 Using and Interpreting the Pearson Correlation KEYWORDS: Bloom’s: Understand 66. For a two-tailed hypothesis test evaluating the significance of a correlation, the alternative hypothesis states that the population correlation is zero.

a. True b. False ANSWER: False DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 16

REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 67. The sign of the correlation (+/–) value obtained is generally meaningless for the point-biserial correlation and the phicoefficient.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Understand 68. The standard error of estimate provides a measure of standard distance between the predicted Y values from a regression equation and the actual Y values from the data.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 69. If people are classified by age (over 40/under 40) and by political affiliation (Democrat/Republican), then computing the point-biserial correlation value would be the proper technique to measure the relationship between these two variables.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Apply 70. The line defined by the linear equation Y = –3X + 6 slopes up to the right. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 71. The line produced by the linear equation Y = 4X – 5 crosses the vertical axis at Y = –5. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression Copyright Cengage Learning. Powered by Cognero.

Page 17

KEYWORDS:

Bloom’s: Understand

72. It is possible for none of the actual (observed) data points to be located on the regression line derived from the regression equation.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 73. For a regression equation with a positive slope, if an X value is above the mean for the X scores, then the predicted Y value will be above the mean for the Y scores.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 74. If other factors are held constant and the Pearson correlation value between X and Y is r = 0.80, then the regression equation will produce more accurate predictions than would be obtained if the Pearson correlation value was r = 0.60.

a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply 75. A set of X and Y scores are obtained from a sample of n = 36 individuals. A Pearson value of r = 0.50 is obtained for the relationship between the X and Y scores. Using a two-tailed test with an alpha of α = 0.05, the correct decision should be to reject the null hypothesis.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Understand 76. A set of X and Y scores has SSX = 5, SSY = 7.5, and SP = 15. The regression equation for these scores will have a slope constant of 2.

a. True b. False ANSWER: False DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 18

REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 77. A set of X and Y scores has MX = 4, MY = 10, SSX = 5, and SP = 10. The regression equation for these scores is Y = 2X – 2.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 78. For a regression equation with a slope of b = 4, if MX = 2 and MY = 10, then the Y-intercept value for the equation is 2. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 79. For linear regression, the value of SSresidual is used directly when calculating the standard error of the estimate. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 80. The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1, 9.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Understand 81. Compute the Pearson correlation for the following data.

XY 53 51 95 13 Copyright Cengage Learning. Powered by Cognero.

Page 19

SSX = 32, SSY = 8, SP = 8, r = 0.500 ANSWER: DIFFICULTY: Understand REFERENCES: 14.2 The Pearson Correlation KEYWORDS: Bloom’s: Understand

82. A sample of n = 25 pairs of scores (X and Y values) produces a correlation of r = –0.40.

A. Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the α = 0.05 level of significance.

B. Which proportion of the variance for the Y scores is predicted by the regression equation?

ANSWER:

A. The critical value that needs to be reached to reject the null hypothesis with df = 23 and α = .05 is r = ± 0.396. The Pearson r value provided is r = .40. Thus, the null hypothesis should be rejected, and it should be concluded there is a relationship between the X and Y variables in the population.

B. r2 = 0.16 or 16%

DIFFICULTY: Apply REFERENCES: 14.4 Hypothesis Tests with the Pearson Correlation KEYWORDS: Bloom’s: Apply 83. A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT) and performance on an anagram task. Anagrams are words with the letters scrambled.

Each subject is given a set of 10 anagrams, and the psychologist records how much time is needed to solve all 10 anagrams and correctly unscramble the letters to make all words. The anagram times and each subject’s SAT score are as follows. Note that two subjects failed to complete all 10 anagrams. Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance.

Anagram SAT Subject Time Score 1 104 480 2 195 410 3 50 590 4 93 510 5 failed 420 6 170 460 7 failed 380 8 67 570 9 45 640 10 58 600 ANSWER: After ranking the data for SAT and anagram times, the value of the Spearman correlation is rS= -0.961.

DIFFICULTY: Apply REFERENCES: 14.5 Alternatives to the Pearson Correlation KEYWORDS: Bloom’s: Apply 84. For the data below: a. Find the regression equation for predicting Y from X. b. Calculate the predicted Y for each X value, find each residual (Y – Ŷ), square each residual and add the squared values to obtain SSresidual. c. Calculate the standard error of estimate.

Copyright Cengage Learning. Powered by Cognero.

Page 20

X 1 3 9 7 ANSWER:

Y 1 2 5 4 a. Ŷ = 0.5X + 0.5 b.

X Y Ŷ (Y- Ŷ) (Y- Ŷ)2 1 1 1 0 0 3 2 2 0 0 9 5 5 0 0 7 4 4 0 0 SSresidual = 0 c. The standard error of estimate is 0.

DIFFICULTY: Apply REFERENCES: 14.6 Introduction to Linear Equations and Regression KEYWORDS: Bloom’s: Apply

Copyright Cengage Learning. Powered by Cognero.

Page 21

Chapter 15 1. The data for a chi-square test consists of _____. a. numerical scores b. non-numerical categories c. ranks d. frequencies ANSWER: d DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 2. Which values are specified by the null hypothesis for a chi-square goodness-of-fit test? a. frequencies for a sample b. frequencies for a population c. proportions for a sample d. proportions for a population ANSWER: d DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 3. Which of the following best describes the possible values for a chi-square statistic? a. The chi-square statistic is always a positive whole number. b. The chi-square statistic is always positive but can contain fractions or decimal values. c. The chi-square statistic can be either positive or negative but is always a whole number. d. The chi-square statistic can be either positive or negative and can contain fractions or decimals.

ANSWER: b DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 4. How does the difference between fe and fo influence the outcome of a chi-square goodness-of-fit test? a. The larger the difference, the larger the computed chi-square value and the greater the likelihood of rejecting the null hypothesis. b. The larger the difference, the larger the computed chi-square value and the lower the likelihood of rejecting the null hypothesis. c. The larger the difference, the smaller the computed chi-square value and the greater the likelihood of rejecting the null hypothesis. d. The larger the difference, the smaller the computed chi-square value and the lower the likelihood of rejecting the null hypothesis.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit Copyright Cengage Learning. Powered by Cognero.

Page 1

KEYWORDS:

Bloom’s: Understand

5. What is referred to by the term observed frequencies? a. the frequencies found in the sample data classified into each category b. the frequencies found in the population being examined c. the frequencies computed from the null hypothesis d. the frequencies that are hypothesized for the population being examined ANSWER: a DIFFICULTY: Remember REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Remember 6. What is referred to by the term expected frequencies? a. the frequencies found in the sample data classified into each category b. the frequencies found in the population being examined c. the frequencies computed from the null hypothesis d. the frequencies that are hypothesized for the population being examined ANSWER: c DIFFICULTY: Remember REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Remember 7. Which of the following is an accurate comparison between the expected and observed frequencies for a chi-square test? a. Expected frequencies can contain fractions or decimal values, and observed frequencies are always whole numbers. b. Observed frequencies can contain fractions or decimal values, and expected frequencies are always whole numbers. c. Expected frequencies can contain negative values, and observed frequencies are always positive values.

d. Observed frequencies can contain negative values, and expected frequencies are always positive values.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 8. Which factor below is required in a nonparametric test? a. a normal (symmetrical) distribution b. homogeneity of variance c. numerical scores d. None of these factors are required in a nonparametric test.

ANSWER: d DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 2

9. Candidates for a school board election have put forth four proposals (i.e., Proposal A, Proposal B, Proposal C, Proposal D) regarding plans for a new school. A researcher wants to examine if there is a preference among the four plans among a sample of residents. What is the null hypothesis for this hypothesis test? a. Proposal A = 50%; Proposal B = 50%; Proposal C = 50%; Proposal D = 50%

b. Proposal A ≠ 50%; Proposal B ≠ 50%; Proposal C ≠ 50%; Proposal D ≠ 50% c. Proposal A = 25%; Proposal B = 25%; Proposal C = 25%; Proposal D = 25% d. Proposal A ≠ 25%; Proposal B ≠ 25%; Proposal C ≠ 25%; Proposal D ≠ 25% ANSWER: c DIFFICULTY: Apply REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 10. It is known that males make up approximately 49% of the United States population. A researcher wants to examine whether the proportion of males currently incarcerated in prisons within the United States differs from the proportion of males in the United States. What is the null hypothesis for this hypothesis test? a. The proportion of males incarcerated in prisons within the United States is not 49%.

b. The proportion of males incarcerated in prisons within the United States is 49%. c. The proportion of males incarcerated in prisons within the United States is 50%. d. The proportion of males incarcerated in prisons within the United States is not 50%.

ANSWER: b DIFFICULTY: Apply REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 11. What happens to the critical value for a chi-square goodness-of-fit test if the sample size is increased? a. The critical value increases. b. The critical value decreases. c. The critical value depends on the number of categories, not the sample size. d. The critical value is determined entirely by the alpha level.

ANSWER: c DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 12. What happens to the shape of the chi-square distribution as the df value increases? a. The mode (highest point) of the distribution moves to the right. b. The mode (highest point) of the distribution moves to the left. c. The mode (highest point) of the distribution does not move, but the distribution becomes more spread out. d. The mode (highest point) of the distribution does not move, but the distribution becomes more tightly clustered around the mode.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 3

13. What happens to the critical value for a chi-square test if the number of categories is increased? a. The critical value increases. b. The critical value decreases. c. The critical value depends on the sample size, not the number of categories. d. The critical value is determined entirely by the alpha level.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 14. A researcher obtains a negative value for the chi-square statistic in a chi-square goodness-of-fit test. What can a researcher conclude based on this result? a. The observed frequencies are consistently larger than the expected frequencies.

b. The expected frequencies are consistently larger than the observed frequencies. c. There are large differences between the observed and expected frequencies. d. The researcher made a mistake because a chi-square value cannot be negative.

ANSWER: d DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 15. Which conclusion is appropriate if a chi-square test produces a chi-square statistic near zero? a. There is a good fit between the sample data and the null hypothesis. b. There is a large discrepancy between the sample data and the null hypothesis. c. All of the expected frequencies must also be close to zero. d. The researcher made a mistake because the computed chi-square can never be close to zero.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 16. For a fixed alpha level of significance, how is the critical value for a chi-square test related to degrees of freedom? a. The critical value increases as df increases. b. The critical value decreases as df increases. c. The critical value increases as sample size increases. d. The critical value decreases as sample size increases.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 17. A researcher is using a chi-square test to determine whether people have any preferences among three brands of televisions. The null hypothesis for this test would state that _____.

Copyright Cengage Learning. Powered by Cognero.

Page 4

a. in the sample, one brand is preferred over the other two b. one-third of the sample prefers each brand c. one-third of the population prefers each brand d. in the population, one brand is preferred over the other two ANSWER: c DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 18. Ten years ago, 20% of the U.S. population consisted of people more than 65 years old. A researcher plans to use a sample of n = 200 people to determine whether the population distribution has changed during the past ten years. If a chisquare test is used to evaluate the data, what is the expected frequency for the older-than-65 category? a. 10

b. 20 c. 40 d. 100 ANSWER: c DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 19. A chi-square test for goodness of fit has df = 2. How many categories were used to classify the individuals in the sample? a. 2

b. 3 c. 4 d. 5 ANSWER: b DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 20. A sample of n = 100 people is classified into four categories. If the results are evaluated with a chi-square test for goodness of fit, which is the df value for the chi-square statistic? a. df = 3

b. df = 4 c. df = 99 d. df = 100 ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 21. A researcher used a sample of n = 20 individuals to determine whether there are any preferences among four brands of Copyright Cengage Learning. Powered by Cognero.

Page 5

pizza. Each individual tastes all four brands and selects their favorite brand. If the data are evaluated with a chi-square test for goodness of fit using α = 0.05, then how large does the chi-square statistic need to be to reject the null hypothesis? a. greater than 7.81

b. less than 7.81 c. greater than 30.14 d. less than 30.14 ANSWER: a DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 22. A researcher used a sample of n = 25 individuals to determine whether they are any preferences between five new designs for a smart phone. If the data produce a chi-square statistic of χ2 = 10.00 what decision should the researcher make? a. There is a significant preference at both α = 0.05 and α = 0.01.

b. There is a significant preference at α = 0.05 but not at α = 0.01. c. There is no significant preference at either α = 0.05 or α = 0.01. d. There is no significant preference at α = 0.05 but there is at α = 0.01.

ANSWER: b DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 23. What is indicated by a large value for the chi-square statistic? a. The sample data (observed values) do not match the null hypothesis. b. There is a good fit between the sample data (observed values) and the null hypothesis. c. The observed values from the sample data are consistently larger than the expected values. d. The observed values from the sample data are consistently smaller than the expected values.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 24. How are the degrees of freedom computed for the chi-square test for goodness of fit? a. df = n – 1 b. df = n – 2 c. df = n – C (where C is the number of categories) d. None of these options are correct.

ANSWER: d DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 25. A researcher is examining preferences among three new flavors of water. A sample of n = 60 people is Copyright Cengage Learning. Powered by Cognero.

Page 6

obtained. Each person tastes all three flavors and then picks their favorite. The distribution of preferences is below. Which chi-square value is obtained when conducting a chi-square goodness-of-fit test?

Water Flavor A B C 25

20

15

a. χ2 = 2.50 b. χ2 = 3.00 c. χ2 = 2.00 d. χ2 = 1.50 ANSWER: a DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 26. Under which circumstances will the chi-square test for goodness of fit produce a large value for the chi-square? a. when the sample proportions match the hypothesized population proportions b. when the sample proportions are much different from the hypothesized population proportions c. when the sample mean is close to the population mean d. when there is a large difference between the sample and population mean ANSWER: b DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 27. A researcher is examining preferences among three new flavors of water. A sample of n = 60 people is obtained. Each person tastes all three flavors and then picks their favorite. The distribution of preferences is below. Which chi-square value is obtained when conducting a chi-square goodness-of-fit test, and which decision should be made regarding the hypothesis test using α = 0.05?

Water Flavor A B C 28

14

18

a. χ2 = 6.20; Fail to reject the null hypothesis b. χ2 = 6.20; Reject the null hypothesis c. χ2 = 5.20; Fail to reject the null hypothesis d. χ2 = 5.20; Reject the null hypothesis ANSWER: c DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 28. Which of the following statements accurately describes the chi-square test for independence? a. It is similar to a single-sample t test because it uses one sample to test a hypothesis about two populations.

Copyright Cengage Learning. Powered by Cognero.

Page 7

b. It is similar to a correlation because it uses one sample to evaluate the relationship between two variables using scores. c. It is similar to an independent-measures t test because it uses separate samples to evaluate the difference between separate frequencies. d. It is similar to both a correlation and an independent-measures t test because it can be used to evaluate a relationship between variables or a difference between populations.

ANSWER: d DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 29. A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories. Which test has the larger value for df? a. the test for goodness of fit

b. the test for independence c. Both tests have the same df. d. This cannot be determined, as the df value depends on the sizes of the samples that are used.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 30. Which bit of information needs to be included in a statistical statement that adheres to APA formatting when reporting the results of a chi-square test that is not included in the statistical statements for other types of statistical tests (e.g., t-test, ANOVA)? a. the calculated test value

b. degrees of freedom (df) c. p-value (probability of making a Type I error) d. sample size (n) ANSWER: d DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 31. A researcher would like to examine whether there is a consistent, predictable relationship between political preference and personality. A sample of 100 students is obtained, and each participant answers questions based on political stances, as well as completes a well-validated test of personality. Participants are then classified as being conservative or liberal, as well as having more of a Type A or Type B personality based on their responses. The results are summarized in the following frequency distribution. Which chi-square value is obtained when conducting a chi-square test for independence?

Type A Personality

Political Preference Liberal Conservative 23 20

Copyright Cengage Learning. Powered by Cognero.

Page 8

Type B Personality

31

26

a. χ2 = 0.008 b. χ2 = 0.08 c. χ2 = 0.80 d. χ2 = 1.80 ANSWER: a DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 32. In the observed frequencies for a chi-square test for independence, how often is each participant counted? a. once b. once in each row c. once in each column d. once in each row and once in each column ANSWER: a DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 33. A researcher examines whether 9 out of 10 doctors prefer Brand X as a preventative care method. A sample of 60 doctors is obtained and each is asked to compare Brand X with another leading brand. The data show that 48 of the doctors picked Brand X. If these data are evaluated using a chi-square test for goodness of fit, what is the expected frequency for Brand X?

a. fe = 6 b. fe = 12 c. fe = 48 d. fe = 54 ANSWER: d DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 34. A researcher is using a chi-square test for independence to evaluate the relationship between birth-order position and self-esteem. Each participant is classified as being 1st born, 2nd born, or 3rd born, and self-esteem is categorized as either high or low. For this study, what is the df value for the chi-square statistic? a. df = 1

b. df = 2 c. df = 3 d. df = 4 ANSWER:

b

Copyright Cengage Learning. Powered by Cognero.

Page 9

DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 35. A researcher would like to examine whether there is a consistent, predictable relationship between political preference and personality. A sample of 100 students is obtained, and each participant answers questions based on political stances, as well as completes a well-validated test of personality. Participants are then classified as being conservative or liberal, as well as having more of a Type A or Type B personality based on their responses. The results are summarized in the following frequency distribution. Which chi-square value is obtained when conducting a chi-square test of independence, and which decision should be made regarding the hypothesis test using α = 0.05?

Type A Personality Type B Personality

Political Preference Liberal Conservative 15 40

28

17

a. χ2 = 12.34; Fail to reject the null hypothesis b. χ2 = 12.34; Reject the null hypothesis c. χ2 = 5.15; Fail to reject the null hypothesis d. χ2 = 5.15; Reject the null hypothesis ANSWER: b DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 36. A sample of 100 people is classified by gender (male or female) and by voter registration status (registered voter or not). The sample consists of 80 females and 20 males and has a total of 60 registered voters. If these data are used for a chi-square test for independence, what is the total number of females for the expected frequencies?

a. fe = 40 b. fe = 20 c. fe = 48 d. fe = 80 ANSWER: d DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 37. A sample of 100 people is classified by gender (male or female) and voter registration status (registered voter or not).

The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data were used for a chisquare test for independence, what is the expected frequency for males who are registered voters?

a. fe = 12 Copyright Cengage Learning. Powered by Cognero.

Page 10

b. fe = 20 c. fe = 40 d. This cannot be determined based on the provided information.

ANSWER: a DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 38. A chi-square statistic computed for a hypothesis test is χ2 = 10. If the sample size is n = 100, then the effect size using Cohen’s w is _____. a. 0.10

b. 0.32 c. 0.18 d. 0.23 ANSWER: b DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 39. What is stated by the null hypothesis for the chi-square test for independence? a. There is a relationship between the two populations regarding the two variables. b. There is no relationship between the two populations regarding the two variables. c. Both variables have the same frequency distribution. d. The two variables have different frequency distributions.

ANSWER: b DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 40. A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 2 categories and the second of which is classified into 4 categories. What is the df value for the chi-square statistic? a. df = 7

b. df = 6 c. df = 2 d. df = 3 ANSWER: d DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 41. A chi-square test for independence is being used to evaluate the relationship between two variables. If the hypothesis test has df = 3, what can a researcher conclude about the two variables? a. One variable consists of 2 categories, and the other consists of 3 categories.

Copyright Cengage Learning. Powered by Cognero.

Page 11

b. One variable consists of 2 categories, and the other consists of 4 categories. c. Both variables consist of 2 categories. d. Both variables consist of 3 categories.

ANSWER: b DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 42. A chi-square test for independence is being used to evaluate the relationship between two variables. If the hypothesis test has df = 2, what can a researcher conclude about the two variables? a. One variable consists of 2 categories, and the other consists of 3 categories.

b. One variable consists of 2 categories, and the other consists of 4 categories. c. Both variables consist of 2 categories. d. Both variables consist of 3 categories.

ANSWER: a DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 43. A chi-square test for independence is being used to evaluate the relationship between two variables. If the hypothesis test has df = 1, what can a researcher conclude about the two variables? a. One variable consists of 2 categories, and the other consists of 3 categories.

b. One variable consists of 2 categories, and the other consists of 4 categories. c. Each variable consists of 2 categories. d. Each variable consists of 3 categories.

ANSWER: c DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 44. A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile. Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices. If the researcher obtains a chi-square statistic of χ2 = 4.81, what is the appropriate statistical decision for the test? a. Reject the null hypothesis with α = 0.05 but not with α = 0.01.

b. Reject the null hypothesis with either α = 0.05 or α = 0.01. c. Fail to reject the null hypothesis with either α = 0.05 or α = 0.01. d. There is not enough information to determine the appropriate decision.

ANSWER: c DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 45. A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and Copyright Cengage Learning. Powered by Cognero.

Page 12

registering to vote. The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. If these data were used for a chi-square test for independence, what is the expected frequency for registered females?

a. fe = 12 b. fe = 28 c. fe = 40 d. fe = 42 ANSWER: b DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 46. A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote. The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. If these data were used for a chi-square test for independence, what is the observed frequency for registered males?

a. fo = 12 b. fo = 28 c. fo = 40 d. fo = 42 ANSWER: c DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Apply 47. When the data from a research study form a 2×2 matrix, the phi-coefficient is used to measure effect size for the chisquare test for independence. If other factors are held constant, how does sample size influence the values for the phicoefficient and chi-square? a. A larger sample increases both the phi-coefficient and chi-square value.

b. A larger sample increases the phi-coefficient but has no effect on the chi-square value. c. A larger sample increases the chi-square value but has no effect on the phi-coefficient. d. A larger sample size does not influence the phi-coefficient or chi-square value.

ANSWER: c DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 48. Under which conditions is Cramér’s V used to measure the effect size for a chi-square test for independence? a. when both variables consist of exactly two categories b. when both variables consist of more than two categories c. when either of the two variables consists of exactly two categories d. when either of the two variables consists of more than two categories ANSWER: d Copyright Cengage Learning. Powered by Cognero.

Page 13

DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 49. Which of these examples violates a basic assumption for a chi-square hypothesis test? a. The population distribution for a category is not normal. b. A category includes frequencies or counts instead of scores. c. A participant produces responses that can be counted twice in the same category. d. The expected frequency of a category is less than 10.

ANSWER: c DIFFICULTY: Apply REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Apply 50. Which of these examples violates a basic assumption for a chi-square hypothesis test? a. The population distribution for a category is positively skewed. b. A category includes frequencies or counts instead of scores. c. A participant produces responses that can be counted only once in a single category. d. The expected frequency of a category is less than 5.

ANSWER: d DIFFICULTY: Apply REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Apply 51. Nonparametric tests are used only with data from a nominal scale. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 52. One characteristic of nonparametric tests is that they make few, if any, assumptions about the populations being investigated.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 53. For a chi-square test, the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.

a. True Copyright Cengage Learning. Powered by Cognero.

Page 14

b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 54. For a chi-square test, the observed frequencies are obtained from the sample. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 55. The chi-square distribution tends to be symmetrical with a mean of µ = 0. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 56. When conducting a chi-square goodness-of-fit test to examine whether the null hypothesis that there is no preference regarding the categories of a variable is correct, the expected frequencies for all categories will always be the same.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 57. The degrees of freedom for a chi-square test are not related to the size of the sample pertaining to a research study. a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 58. The chi-square statistic is an example of a parametric test. a. True b. False ANSWER: False DIFFICULTY: Understand Copyright Cengage Learning. Powered by Cognero.

Page 15

REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 59. For a chi-square test of independence with three rows and four columns, the df value when computing Cramér’s V as a measure of effect size is df *= 2.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 60. If the chi-square value obtained in a test for independence is χ2 = 7.00 and the sample size is n = 64, then the phicoefficient computed as a measure of effect size is 0.41.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 61. A researcher examines whether a majority of individuals prefer to wear their seat belts when driving by counting seat belt wearing tendencies among a sample. The statistical test that should be used when conducting the hypothesis test is a chi-square test for independence.

a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 62. The alternative hypothesis for a chi square goodness of fit test examining whether preferences are divided equally regarding a variable puts forth that preferences are not equally divided.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.1 Introduction to Chi-Square: The Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 63. A large value for chi-square tends to indicate a good fit between the sample data and the null hypothesis. a. True b. False ANSWER: False Copyright Cengage Learning. Powered by Cognero.

Page 16

DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 64. For a fixed alpha level of significance used for a hypothesis test, the critical value for a chi-square statistic increases as the degrees of freedom increase.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 65. For a fixed alpha level of significance used for a hypothesis test, the critical value for a chi-square statistic decreases as the size of the sample decreases. a. True b.False a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Understand 66. If using a chi-square test for goodness of fit to test a hypothesis, a researcher must select a sample with an equal number of individuals in each category. a. True b.False a. True b. False ANSWER: False DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 67. A research study tests its hypothesis using a chi-square test for independence which produces a chi-square statistic with df = 2. The data for this research study form a 2×3 matrix with six separate categories. a. True b.False a. True b. False ANSWER: True DIFFICULTY: Apply REFERENCES: 15.3 The Chi-Square Test for Independence Copyright Cengage Learning. Powered by Cognero.

Page 17

KEYWORDS:

Bloom’s: Apply

68. The chi-square test for independence uses the exact same formula as the chi-square goodness-of-fit test. a. True b.False a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 69. The chi-square test for goodness of fit evaluates the distribution for one variable, and the test for independence evaluates the relationship between two variables. a. True b.False a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 70. The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more) separate samples.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 71. The chi-square test for independence can be similar to a correlation or independent-measures t test conceptually regarding the kinds of research questions it is used to examine.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 72. The similarity between the chi-square test for independence and independent-measures t test is that they both examine differences in frequencies between two populations.

a. True Copyright Cengage Learning. Powered by Cognero.

Page 18

b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 73. For a chi-square test for independence with two variables and two categories in each variable, the expected frequencies in each category for the first variable will be the same as those for the second variable.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 74. For a chi-square test for independence with two variables and two categories in each variable, the proportions for each row used to determine the expected frequencies for each category are the same.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand 75. If other factors are held constant, increasing the sample size for a chi-square test for independence will increase the likelihood of rejecting the null hypothesis.

a. True b. False ANSWER: True DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 76. The phi-coefficient can only be used to evaluate the effect size for a chi-square test for independence if the chi-square test has df > 1.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 77. Cramér’s V is used to evaluate the effect size for a chi-square test for independence if the chi-square test has df = 1. a. True Copyright Cengage Learning. Powered by Cognero.

Page 19

b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 78. Although the outcome for measures of effect size such as the phi-coefficient or Cramér’s V are influenced by sample size, the outcome of a chi-square test for independence is not.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 79. Cohen’s w can be used to evaluate the effect size for a chi-square test for goodness of fit test, even if there are more than two categories.

a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 80. A chi-square test should not be used if the observed frequency in any category is less than five. a. True b. False ANSWER: False DIFFICULTY: Understand REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Understand 81. A researcher is interested in consumer preferences among three brands of yogurt. A sample of 90 participants is obtained, and each participant is asked to taste each brand and then select their favorite. The resulting frequency data are as follows: Brand A 37

Brand B 21

Brand C 32

Do the data indicate any significant preferences among the three brands? Use α = 0.05 The null hypothesis states that the three brands are equally preferred in the population. The expected ANSWER: frequency is 30 for each category, and Χ2 = 4.46. With df = 2, the critical value is 5.99. The decision is to fail to reject the null hypothesis and conclude that there are no significant preferences among the three brands.

DIFFICULTY: Apply Copyright Cengage Learning. Powered by Cognero.

Page 20

REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 82. A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks their favorite. The distribution of preferences is as follows: A 12

Ice Cream Flavor B C 18

D 28

22

Do these data indicate any significant preferences among the four flavors? Use α = 0.05.

The null hypothesis states that there are no preferences among the four flavors. The expected ANSWER: frequencies are 20 for each flavor, and Χ2 = 6.80. With df = 3, the critical value is 7.81. The decision is to fail to reject the null hypothesis and conclude that there are no significant preferences among the four ice cream flavors.

DIFFICULTY: Apply REFERENCES: 15.2 An Example of the Chi-Square Test for Goodness of Fit KEYWORDS: Bloom’s: Apply 83. A researcher is interested in the relationship between birth order and personality. A sample of n = 100 participants is obtained, all of whom grew up in families as one of three children. Each participant is given a personality test, and the researcher also records the person’s birth-order position (1st, 2nd, or 3rd born). The frequencies from this research study are shown in the following table.

A. Should the researcher conclude that there is a significant relation between birth order and personality? Use α = 0.05.

B. Calculate Cramér’s V as a measure of effect size.

Birth Position 1st 2nd 3rd Outgoing Reserved ANSWER:

13

31

16

17 19 4 A. The null hypothesis states that there is no relationship between birth order and personality.

With df = 2, the critical value is 5.99. The expected frequencies are: Birth Position 1st 2nd 3rd Outgoing

18

30

12

Reserved

12

20

8

Χ2 = 6.88. Reject H0 and conclude that there is a relationship between birth order and

personality.

B. Cramér’s V = √(6.88/100(2) = 0.19 Copyright Cengage Learning. Powered by Cognero.

Page 21

DIFFICULTY: Apply REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Apply 84. A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 200 students is obtained, and each student is given a standardized English test and a standardized math test. Based on the test results, students are classified as high or low for verbal skills and for math skills. The results are summarized in the following frequency distribution: Verbal Skills High Low High Math 59 41 Low Math

31

69

a. Based on these results, should the researcher conclude that there is a significant relationship between verbal skills and math skills? Use α = 0.05. b. Compute the phi-coefficient to measure the strength of the relationship.

ANSWER: a. The null hypothesis states that there is no relationship between the two variables. With α = 0.05 and df = 1, the critical value is 3.84. The expected frequencies are as follows:

High Math

Verbal Skills High Low 45 55

Low Math

45

55

For these data, Χ2 = = 15.84. Reject H0 and conclude that there is a relationship between verbal skills and math skills. b. The phi-coefficient is √15.84/200 = 0.28.

DIFFICULTY: Apply REFERENCES: 15.4 Effect Size and Assumptions for the Chi-Square Tests KEYWORDS: Bloom’s: Apply 85. In which situations should a researcher use a chi-square test instead of a correlation or t-test to conduct a hypothesis test? When should a chi-square goodness of fit test be used relative to a chi-square test for independence?

In general, a chi-square test should be used when the data for variables within a hypothesis test consists ANSWER: of counts or frequencies, relative to scores. In general, a chi-square test should be used when data are assessed using a nominal or ordinal scale of measurement, and a correlation or t test is more prudent if variables are assessed using an interval or ratio scale of measurement. A chi-square goodness of fit test compares observed frequencies for one variable to expected frequencies delineated by the null hypothesis. In contrast, a chi-square test for independence is used to assess the relationship between variables. For instance, a chi-square test for independence should be used to examine the relationship between two variables measured within a sample of individuals or to examine the relationship between variables among two separate samples.

DIFFICULTY: Understand REFERENCES: 15.3 The Chi-Square Test for Independence KEYWORDS: Bloom’s: Understand Copyright Cengage Learning. Powered by Cognero.

Page 22