Introductory Statistics, 8th Edition International Student Version Prem S. Mann Test Bank

Type:

Test Bank

Resource:

Introductory Statistics

Edition:

8th Edition

Author(s):

Prem S. Mann

1. Under descriptive statistics, we study A) the description of decision making tricks B) the methods for organizing, displaying, and describing data C) how to describe the probability distribution D) samples to assist in decision making Ans: B Difficulty level: low Objective: Explain what constitutes descriptive statistics.

2. Under inferential statistics, we study A) the methods to make decisions about one or more populations based on sample results B) how to make decisions about a mean, median, or mode C) how a sample is taken from a population D) tables composed of summary measures Ans: A Difficulty level: low Objective: Explain what constitutes inferential statistics.

3. In statistics, a population consists of: A) all people living in a country B) all people living in the area under study C) all subjects or objects whose characteristics are being studied D) a selection of a limited number of elements Ans: C Difficulty level: low Objective: Describe the difference between a population and a sample.

4. In statistics, we define a sample as: A) people living in one city only B) the target population Ans: D Difficulty level: low population and a sample.

C) all items under investigation D) a portion of the population Objective: Describe the difference between a

5. In statistics, conducting a survey means: A) collecting information from elements C) drawing pictures and graphs B) making mathematical calculations D) none of these Ans: A Difficulty level: low Objective: Define the term "sample survey."

6. In statistics, conducting a census means: A) making decisions based on sample results B) checking if a variable is qualitative or quantitative C) collecting information from all members of the population D) collecting a sample with replacement Ans: C Difficulty level: low Objective: Define the term "census."

Page 1

Chapter 1

7. In statistics, a representative sample is a sample that: A) contains the characteristics of the population as closely as possible B) represents the results of a sample exactly C) contains all people living in an area D) contains elements collected with replacement Ans: A Difficulty level: low Objective: Explain what constitutes a representative sample from a population.

8. A random sample is a sample drawn in such a way that: A) each member of the population has a 0.10 chance of being included in the sample B) all elements of a population are included C) some members of the population have no chance of being included in the sample D) each member of the population has some chance of being included in the sample Ans: D Difficulty level: low Objective: Differentiate between a random sample and a nonrandom sample.

9. A simple random sample is a sample drawn in such a way that: A) each member of the population has some chance of being included in the sample B) every tenth element of an arranged population is included C) each sample of the same size has an equal chance of being selected D) each member of the population has a 0.10 chance for being included in the sample Ans: C Difficulty level: low Objective: Differentiate between a random sample and a nonrandom sample.

10. A data set is a: A) set of decisions made about the population B) set of graphs and pictures C) collection of observations on one or more variables D) score collected from an element of the population Ans: C Difficulty level: low Objective: Explain the meaning of a member, variable, measurement, and data set with reference to given tabular information.

11. An observation is a: A) graph observed for a data set B) value of a variable for a single element C) table prepared for a data set D) sample observed from the population Ans: B Difficulty level: low Objective: Explain the meaning of a member, variable, measurement, and data set with reference to given tabular information.

Page 2

Chapter 1

12. A quantitative variable is the only type of variable that can: A) assume numeric values for which arithmetic operations make sense B) be graphed C) be used to prepare tables D) have no intermediate values Ans: A Difficulty level: low Objective: Define the term "quantitative variable."

13. A discrete variable is a variable that can assume: A) categorical values only C) an uncountable set of values B) a countable set of values only D) non-numerical values Ans: B Difficulty level: low Objective: Distinguish between discrete and continuous variables.

14. A continuous variable is a variable that can assume: A) categorical values only C) an uncountable set of values B) a countable set of values only D) non-numerical values Ans: C Difficulty level: low Objective: Distinguish between discrete and continuous variables.

15. A qualitative variable is the only type of variable that: A) can assume numerical values B) cannot be graphed C) can assume an uncountable set of values D) cannot be measured numerically Ans: D Difficulty level: low Objective: "Define the term ""qualitative (or categorical) variable,"" providing practical examples."

16. Time-series data are collected: A) on the same element for the same variable at different points in time B) on a variable that involves time, e.g., minutes, hours, weeks, months, etc.

C) for a qualitative variable D) on different elements for the same period of time Ans: A Difficulty level: low Objective: Define the term "time-series" data.

17. Cross-section data are collected: A) on the same variable for the same variable at different points in time B) on different elements at the same point in time C) for a qualitative variable D) on different elements for the same variable for different periods of time Ans: B Difficulty level: low Objective: Define the term "cross-section" data.

Use the following to answer questions 18-21: The telephone bills for the past month for four families are $48, $65, $39, and $81.

Page 3

Chapter 1

18. The value of  x is: Ans: 233 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

19. The value of  x 2 is: Ans: 14,611 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

20. The value of (  x ) is: 2

Ans: 52,900 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

21. The value of  ( x − 5) is: Ans: 210 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

Use the following to answer questions 22-25: The test scores of five students are 85, 64, 95, 75, and 93.

22. The value of  x is: Ans: 412 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

23. The value of  x 2 is: Ans: 34,620 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

24. The value of (  x ) is: 2

Ans: 169,744 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

Page 4

Chapter 1

25. The value of  ( x − 10 ) is: Ans: 362 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

Use the following to answer questions 26-32: Consider the following five pairs of m and f values: m 6 9 7 13 7

f 3 5 5 6 8

26. The value of  m is: Ans: 42 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

27. The value of  mf is: Ans: 232 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

28. The value of  m 2 is: Ans: 384 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

29. The value of  f 2 is: Ans: 159 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

30. The value of  m 2 f is: Ans: 2,164 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

Page 5

Chapter 1

31. The value of  mf 2 is: Ans: 1,370 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

32. The value of  ( m − 3) f is: Ans: 1,015 Difficulty level: medium Objective: Summation notation 2

Use the following to answer questions 33-39: Consider the following six pairs of x and y values: x 8 11 15 5 20 21

y 10 16 20 7 28 21

33. The value of  y is: Ans: 102 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

34. The value of  xy is: Ans: 1,592 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

35. The value of  xy 2 is: Ans: 34,802 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

36. The value of  x 2 y is: Ans: 27,712 Difficulty level: low Objective: Perform elementary computations involving sigma notation and two variables.

Page 6

Chapter 1

37. The value of  x 2 is: Ans: 1,374 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

38. The value of  y 2 is: Ans: 2,080 Difficulty level: low Objective: Perform elementary computations involving sigma notation and one variable.

39. The value of  ( x − 2) 2 y is: Ans: 24,101 Difficulty level: medium Objective: Perform elementary computations involving sigma notation and one variable.

40. Whether or not a university's enrollment increased from last year to this year is an example of qualitative or quantitative data?

Ans: Qualitative Difficulty level: low Objective: Categorize variables as being quantitative or qualitative.

41. Total insect population among 12 U.S. national parks in 2003 is an example of time-series or cross-section data?

Ans: Cross-section Difficulty level: low Objective: Categorize data as being cross-section data or time-series data.

42. Is the variable "lengths of top-ten hit songs" discrete or continuous?

Ans: Continuous Difficulty level: low Objective: Distinguish between discrete and continuous variables.

43. A statistician wants to determine the average annual Gross National Product for countries in Africa. He samples the 20 largest (in terms of population) African countries over 10 years, and gets their quarterly G.N.P results for each quarter of each year. The statistician is criticized because the sample is not representative. Explain why.

Ans: The statistician took the 20 largest countries. I representative sample should include some smaller countries also.

Difficulty level: medium Objective: Explain what constitutes a representative sample from a population.

Page 7

Chapter 1

44. A statistician wants to determine the total annual medical costs incurred by all U.S. states from 1981 to 2001 as a result of health problems related to smoking. She polls each of the 50 states annually to obtain health care expenditures, in dollars, on smoking-related illnesses. Does this study constitute a survey or a census. Explain.

Ans: Census. She collected data from all 50 states in the population.

Difficulty level: medium Objective: Categorize data as being collected from a population or a sample.

45. Classify the following as cross-section or time-series data.

Monthly telephone bill for each family in an apartments complex.

Ans: Cross-section data Difficulty level: medium time-series data.

Objective: Categorize data as being cross-section data or

46. Classify the variable as discrete or continuous.

Duration of your last 30 cell phone calls.

Ans: Continuous Difficulty level: low variables.

Objective: Distinguish between discrete and continuous

47. The two types of variables are continuous and ______.

Ans: discrete Difficulty level: low Objective: Distinguish between discrete and continuous variables.

48. An independent group wants to determine if the consumption of gasoline has increased due to changes in price. The group randomly selects 320 gas stations from 12 different states and collects data from the month of the year when gas is the cheapest and from the month of the year when gas is the most expensive. The data shows no significant difference in gas consumption between the two months.

In this example, what is the variable being studied?

A) The 320 gas stations chosen.

C) The consumption of gasoline.

B) The 12 different states.

D) The price of gasoline.

Ans: C Difficulty level: low Objective: Explain what constitutes a variable in a statistical study, identifying it in practical situations.

49. The Ohio lottery involves selecting 5 numbers from 5 different bins. This is an example of sampling A) with replacement.

B) without replacement.

Ans: A Difficulty level: low Objective: Explain the difference between random sampling with and without replacement.

Page 8

Chapter 1

50. The Megabucks lottery involves selecting 3 numbers from a single bin. This is an example of sampling A) with replacement.

B) without replacement.

Ans: B Difficulty level: low Objective: Explain the difference between random sampling with and without replacement.

Page 9

1. Raw data are the data that: A) are presented in the form of a frequency table B) give information on each individual sample member separately C) are arranged in increasing order D) are arranged in a random order Ans: B Difficulty level: low Objective: Explain what is meant by the term "raw data."

2. We obtain the relative frequency of a category by: A) dividing the frequency of that category by the sum of all frequencies B) multiplying the frequency of that category by 100 C) dividing the frequency of that category by 100 D) dividing the sum of all frequencies by the frequency of that category Ans: A Difficulty level: medium Objective: Construct a relative frequency and percentage distribution.

3. We obtain the percentage of a category by: A) multiplying the frequency of that category by 100 B) multiplying the relative frequency of that category by 100 C) dividing the frequency of that category by 100 D) dividing the sum of all frequencies by the frequency of that category Ans: B Difficulty level: medium Objective: Construct a relative frequency and percentage distribution.

Use the following to answer questions 4-8: The following table gives the frequency distribution of the highest degrees held by 25 professionals.

Highest Degree Bachelor’s Master’s Doctorate

f 12 9 4

4. The number of persons with a Master's degree as their highest degree is: Ans: 9 Difficulty level: low Objective: Construct a frequency distribution table for qualitative data.

5. The number of persons who possess a Doctorate is: Ans: 4 Difficulty level: low Objective: Construct a frequency distribution table for qualitative data.

Page 1

Chapter 2

6. The percentage of persons with a Bachelor's degree as the highest degree is: Ans: 48% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

7. The percentage of persons who hold a Doctorate is: Ans: 16% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

8. The percentage of persons who do not hold a Doctorate is: Ans: 84% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

Use the following to answer questions 9-13: The following table gives the frequency distribution of opinions of 50 persons in regard to an issue.

Opinion In favor Against No opinion

f 20 19 11

9. The percentage of persons who have no opinion is: Ans: 22% Difficulty level: low Objective: Organizing qualitative data 10. The relative frequency, expressed to two decimal places, of the "Against" category is: Ans: 0.38 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

11. The sample size is: Ans: 50 Difficulty level: low qualitative data.

Objective: Construct a frequency distribution table for

12. The percentage of persons who are either against this issue or have no opinion is: Ans: 60% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

Page 2

Chapter 2

13. The percentage of persons who are either in favor of this issue or have no opinion is: Ans: 62% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

14. In a frequency distribution, the classes should always: A) be overlapping C) have a width of 10 B) have the same frequency D) be non-overlapping Ans: D Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

15. The number of classes in a frequency distribution depends on the size of the data set. In general, the: A) larger the data set, the larger the number of classes B) larger the data set, the smaller the number of classes C) number of classes should be equal to the number of values in the data set divided by 5 D) smaller the data set, the larger the number of classes Ans: A Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

16. When preparing a frequency distribution, the lower limit of the first class should always be: A) a number that is greater than the smallest value in the data set B) equal to 10 C) a number that is less than or equal to the smallest value in the data set D) equal to zero Ans: C Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

17. A distribution curve that is right-skewed has: A) both tails of the same length C) a shorter tail on the right side B) a longer tail on the left side D) a longer tail on the right side Ans: D Difficulty level: low Objective: Describe the shape of a histogram.

18. A symmetric distribution curve: A) has a longer tail on the right side C) is identical on both sides of the mean B) has a longer tail on the left side D) is triangular in shape Ans: C Difficulty level: low Objective: Describe the shape of a histogram.

Page 3

Chapter 2

19. The procedure for obtaining the midpoint of a class is to: A) add the lower limit to the upper limit of the previous class B) subtract the lower limit from the upper limit C) multiply the sum of the two class limits by 2 D) divide the sum of the two class limits by 2 Ans: D Difficulty level: low Objective: Calculate class midpoint (class mark).

20. The procedure for obtaining the relative frequency of a class is to: A) divide the frequency of that class by the sum of all frequencies B) multiply the frequency of that class by 100 C) divide the frequency of that class by 100 D) divide the sum of all frequencies by the frequency of that class Ans: A Difficulty level: medium Objective: Construct a relative frequency and percentage distribution.

21. The procedure for obtaining the percentage for a class is to: A) multiply the frequency of that class by 100 B) multiply the relative frequency of that class by 100 C) divide the relative frequency of that class by 100 D) divide the sum of all frequencies by 100 Ans: B Difficulty level: medium Objective: Construct a relative frequency and percentage distribution.

22. In a frequency histogram, the frequency of a class is the: A) height of the corresponding bar B) width of the corresponding bar C) height multiplied by the width of the corresponding bar D) height divided by the width of the corresponding bar Ans: A Difficulty level: low Objective: Create a frequency histogram.

23. We can construct a frequency histogram for: A) qualitative data only C) qualitative and quantitative data B) any kind of data D) continuous data Ans: D Difficulty level: low Objective: Create a frequency histogram.

24. In a frequency distribution, the correct notation for the sum of the frequencies is: A)  f B) f C) x D) y Ans: A

Difficulty level: low

25. A rectangular histogram has: A) a longer tail on the right side B) a longer tail on the left side Ans: D Difficulty level: low

Objective: Create a frequency histogram.

C) shorter tails on both sides D) the same frequency for each class Objective: Create a frequency histogram.

Page 4

Chapter 2

Use the following to answer questions 26-35: The following table gives the frequency distribution of test scores for a math class of 30 students.

Score 61 to 70 71 to 80 81 to 90 91 to 100

f 1 7 13 9

26. The number of classes in this frequency table is: Ans: 4 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

27. The width of each class in this frequency table is: Ans: 10 Difficulty level: low Objective: Find class width.

28. The midpoint of the fourth class is: Ans: 95.5 Difficulty level: low Objective: Calculate class midpoint (class mark).

29. The lower boundary of the first class is: Ans: 60.5 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

30. The upper boundary of the third class is: Ans: 90.5 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

31. The sample size is: Ans: 30 Difficulty level: low quantitative data.

Objective: Construct a frequency distribution table for

32. The relative frequency of the second class, rounded to three decimal places, is: Ans: 0.233 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

Page 5

Chapter 2

33. The percentage of students who scored 80 or less on the test, rounded to two decimal places, is: Ans: 26.67% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

34. The lower limit of the fourth class is: Ans: 91 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

35. The upper limit of the fourth class is: Ans: 100 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

Use the following to answer questions 36-45: The following table gives the frequency distribution of rents paid per month by 500 families selected from a city.

Rent 301 to 400 401 to 500 501 to 600 601 to 700 701 to 800 801 to 900

f 26 49 75 102 141 107

36. The number of classes in this frequency table is: Ans: 6 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

37. The width of each class in this frequency table is: Ans: 100 Difficulty level: low Objective: Find class width.

38. The midpoint of the second class is: Ans: 450.5 Difficulty level: low Objective: Calculate class midpoint (class mark).

Page 6

Chapter 2

39. The lower boundary of the fifth class is: Ans: 700.5 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

40. The upper boundary of the fourth class is: Ans: 700.5 Difficulty level: low Objective: Construct a frequency distribution table for quantitative data.

41. The sample size is: Ans: 500 Difficulty level: low quantitative data.

Objective: Construct a frequency distribution table for

42. The relative frequency of the sixth class, rounded to three decimal places, is: Ans: 0.214 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

43. The percentage of families who paid a rent of $500 or less per month, rounded to one decimal place, is: Ans: 15.0% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

44. The lower limit of the third class is: Ans: 501 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

45. The upper limit of the second class is: Ans: 500 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

Page 7

Chapter 2

Use the following to answer questions 46-51: The following table gives the frequency distribution of the number of telephones owned by a sample of 50 households selected from a city.

Number of f Telephones Owned 0 3 1 20 2 14 3 3 4 10

46. The relative frequency of the second class, rounded to two decimal places, is: Ans: 0.4 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

47. The number of households which own more than one telephone is: Ans: 27 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

48. The percentage of households which own three or more telephones is: Ans: 26% Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

49. The number of households which own one or two telephones is: Ans: 34 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

50. The percentage of households which do not own a telephone is: Ans: 6% Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

51. The number of classes for this frequency distribution table is:: Ans: 5 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

Page 8

Chapter 2

Use the following to answer questions 52-57: The following table gives the frequency distribution of the number of rooms for a sample of 100 houses.

Number of Rooms 2 3 4 5 6 7 8

f 8 10 20 24 18 10 10

52. The relative frequency of the fourth class, rounded to two decimal places, is: Ans: 0.24 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

53. The percentage of houses that have three or fewer rooms is: Ans: 18% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

54. The percentage of houses that contain five or more rooms is: Ans: 62% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

55. The number of houses that contain four or five rooms is: Ans: 44 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

56. The relative frequency of the fifth class, rounded to two decimal places, is: Ans: 0.18 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

57. The number of classes for this frequency distribution table is: Ans: 7 Difficulty level: low Objective: Construct a frequency distribution using single-valued classes.

Page 9

Chapter 2

58. We construct an ogive to graph a: A) frequency distribution C) relative frequency distribution B) cumulative frequency distribution D) stem-and-leaf display Ans: B Difficulty level: low Objective: Draw an ogive for the cumulative percentage distribution.

59. The graph of a cumulative frequency distribution is a(n): A) frequency histogram B) stem-and-leaf display C) line graph D) ogive Ans: D Difficulty level: low Objective: Draw an ogive for the cumulative percentage distribution.

Use the following to answer questions 60-66: The following table gives the cumulative frequency distribution of annual incomes (in thousands of dollars) for a sample of 200 families selected from a city.

Income ($1000's) 10 to less than 25 10 to less than 40 10 to less than 55 10 to less than 70 10 to less than 85 10 to less than 100

f 25 79 149 167 191 200

60. The cumulative relative frequency of the fourth class, rounded to three decimal places, is: Ans: 0.835 Difficulty level: low Objective: Construct a cumulative frequency distribution table.

61. The sample size is: Ans: 200 Difficulty level: low

Objective: Construct a cumulative frequency distribution table.

62. The cumulative percentage for the second class, rounded to one decimal place, is: Ans: 39.5% Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

63. The percentage of families with an income of less than $55,000, rounded to one decimal place, is: Ans: 74.5% Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

Page 10

Chapter 2

64. The percentage of families with an income of $70,000 or more, rounded to one decimal place, is: Ans: 16.5% Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

65. The number of families with an income of $40,000 or less is: Ans: 79 Difficulty level: low Objective: Construct a cumulative frequency distribution table.

66. The number of families with an income of $85,000 or more is: Ans: 9 Difficulty level: low Objective: Construct a cumulative frequency distribution table.

Use the following to answer questions 67-72: The following table gives the cumulative frequency distribution of the commuting time (in minutes) from home to work for a sample of 400 persons selected from a city.

Time (minutes) 0 to less than 10 0 to less than 20 0 to less than 30 0 to less than 40 0 to less than 50 0 to less than 60

67. The sample size is: Ans: 400 Difficulty level: low

f 67 158 223 291 350 400

Objective: Construct a cumulative frequency distribution table.

68. The percentage of persons who commute for less than 30 minutes, rounded to two decimal places, is: Ans: 55.75% Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

69. The cumulative relative frequency of the fourth class, rounded to four decimal places, is: Ans: 0.7275 Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

Page 11

Chapter 2

70. The percentage of persons who commute for 40 or more minutes, rounded to two decimal places, is: Ans: 27.25% Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

71. The percentage of persons who commute for less than 50 minutes, rounded to two decimal places, is: Ans: 87.50% Difficulty level: low Objective: Construct a cumulative relative frequency distribution table.

72. The number of persons who commute for 20 or more minutes is: Ans: 242 Difficulty level: low Objective: Construct a cumulative frequency distribution table.

73. For the observation 4, the stem is: Ans: 0 Difficulty level: low Objective: Construct a stem-and-leaf display.

74. For the observation 34, the leaf is: Ans: 4 Difficulty level: low Objective: Construct a stem-and-leaf display.

75. You ask 27 people what kind of pet they own. Seven people have dogs, five have cats, three have birds, and the remainder have no pets. The relative frequency of dog owners, rounded to three decimal places, is: Ans: 0.259 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

76. Fifteen programmers were asked what computer language was used in their first programming class. The raw data appears below: Java C++ Fortran

Visual Basic C++ Visual Basic

Visual Basic Java Fortran Fortran Java Visual Basic C Visual Basic Visual Basic

The percentage of people, rounded to two decimal places, who did not answer "Fortran" is: Ans: 80.00% Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

Page 12

Chapter 2

77. In a game of four-handed Hearts, all 52 cards of a standard deck are dealt, so that each player starts each round with 13 cards in a hand. Suppose player A's hand has three clubs, six diamonds, two hearts, and two spades. What is the relative frequency of spades, rounded to two decimal places, dealt to player A? Ans: 0.15 Difficulty level: low Objective: Construct a relative frequency and percentage distribution.

Use the following to answer questions 78-81: A highway patrolman records the following speeds (in mph) for 25 cars that pass through his radar within a five-minute interval. Here is the histogram of that data:

78. What is the width of each class?

Ans: 5 Difficulty level: low Objective: Find class width.

79. How many observations fall in the fourth interval?

Ans: 10 Difficulty level: low Objective: Create a frequency histogram.

80. The relative frequency of drivers whose speed is less than 55 mph, rounded to two decimal places, is?

Ans: 0.40 Difficulty level: low Objective: Create a relative frequency histogram.

Page 13

Chapter 2

81. The speed limit on this street is 60 mph. What percentage of drivers are traveling at or above the speed limit?

Ans: 20% Difficulty level: low Objective: Create a relative frequency histogram.

Use the following to answer questions 82-84: Suppose you have the following stem-and-leaf display:

1 2 3 4

1 3 1 2 8 5 4

Stem: Tens

Leaf: Ones

82. What is the value of smallest data point in this data set?

Ans: 11 Difficulty level: low Objective: Construct a stem-and-leaf display.

83. How many observations are in this data set?

Ans: 7 Difficulty level: low Objective: Construct a stem-and-leaf display.

84. What is the sum of the data values in the bottom two branches in this display?

Ans: 79 Difficulty level: low Objective: Construct a stem-and-leaf display.

Use the following to answer questions 85-88: Here is a dot plot of the daily high temperature (in Fahrenheit) from a sample of 25 U.S. cities: Collection 1

62

64

Dot Plot

66 68 70 72 74 high_tem perature

76

78

Page 14

Chapter 2

85. Which high temperature has the highest frequency?

Ans: 74 Difficulty level: low Objective: Create a dot plot.

86. What is the relative frequency of high temperatures, rounded to two decimal places, that are 71 degrees or lower?

Ans: 0.56 Difficulty level: low Objective: Create a dot plot.

87. How many cities had a high temperature of 72?

Ans: 0 Difficulty level: low Objective: Create a dot plot.

88. What percentage of cities had a high temperature of more than 74 degrees?

Ans: 24% Difficulty level: medium Objective: Create a dot plot.

Page 15

Chapter 2

89. In 2007/2008 basketball season, Steve Nash scored 485 field goals, 179 3-point field goals, and 222 free-throw goals. Find the pie chart that better describes the data.

A)

B)

C)

D)

Page 16

Chapter 2

Ans: A Difficulty Level: Easy Objective: Construct a pie chart.

Difficulty level: low

Page 17

Chapter 2

90. The following table shows the countries whose teams have won the UEFA Champions League.

Country Spain England Italy Germany Netherlands Other

Frequency 12 11 11 6 6 8

a) Calculate the relative frequency of each country. Round your answers to three decimal places b) Select the pie chart that better describes the data.

I

II

III Ans: a) Country Spain England Italy Germany Netherlands Other

Relative Frequency 0.222 0.204 0.204 0.111 0.111 0.148

b) I Difficulty Level: Medium Difficulty level: medium Objective: Construct a pie chart.

Page 18

Chapter 2

91. The number of touchdowns of a college football team is: 38 36 30 33 37 30 35 34 43 27 36 31 22 28 36 a) Complete the frequency distribution.

Class Interval 21 - 24 25 - 28 29 - 32 33 - 36 37 - 40 41 - 44 Total

Frequency ---5 ------3 1 20

38

21

26

26

27

Relative Frequency ---0.250 ------0.150 0.050 1.000

b) Select the bar graph that matches the data.

I

II

III

Ans: a) Class Interval 21 - 24 25 - 28 29 - 32 33 - 36 37 - 40 41 - 44 Total

Frequency 2 5 3 6 3 1 20

b) I Difficulty Level: Medium Difficulty level: medium Objective: Construct a bar graph.

Page 19

Relative Frequency 0.100 0.250 0.150 0.300 0.150 0.050 1.000

Chapter 2

92. Find the histogram that better describes the data.

Value x 1 2 3 4 5 Total

I

Ans: I Difficulty Level: Easy

Frequency 4 5 4 3 2 18

II

Difficulty level: low

Page 20

Relative Frequency 0.22 0.28 0.22 0.17 0.11 1.000

III

Objective: Construct a bar graph.

Chapter 2

93. The maximum number of goals scored by a national team in the last 14 FIFA's World Cups is shown below. Select the bar graph that matches with the data.

14

15

15

16

16

17

23

18

15

14

15

19

14

27

I II

Ans: II Difficulty level: low

Objective: Construct a bar graph.

Page 21

1. The mean of a data set is the: A) value of the middle term in a ranked data set B) sum of all values divided by the number of values C) difference between the maximum and minimum values D) average of the deviations of values from the average Ans: B Difficulty level: low Objective: Measures of central tendency for ungrouped data 2. The median of a data set is the: A) value of the middle term in a ranked data set B) value that occurs with maximum frequency C) sum of all values divided by the number of values D) average of the deviations of values from the average Ans: A Difficulty level: low Objective: Measures of central tendency for ungrouped data 3. You just dropped an outlier from a data set. The value of the mean: A) is now more than the value of the median B) is now less than the value of the median C) is now less than the value of the mode D) can't be determined from the given information Ans: D Difficulty level: low Objective: Outliers in a set of data 4. An outlier influences which of the following summary measures the most?

A) mean B) median C) mode D) median and mode Ans: A Difficulty level: low Objective: Outliers in a set of data 5. Which of the following is the only measure that can be calculated for qualitative data?

A) mean B) range C) mode D) median Ans: C Difficulty level: low Objective: Measures of center and dispersion for qualitative data 6. If a data set is right-skewed with one peak in the histogram, then which of the following is true?

A) the values of the mean, median, and mode are the same B) the mean is greater than the median, which is greater than the mode C) the mean and median are equal, but the mode is different D) the mode is greater than the median, which is greater than the mean Ans: B Difficulty level: low Objective: Skewed data

Page 1

Chapter 3

7. If a distribution is symmetric with one peak, then: A) the values of the mean, median, and mode are identical B) the mean is greater than the median, which is greater than the mode C) the values of the mean and median are equal but the mode is different D) the mode is greater than the median, which is greater than the mean Ans: A Difficulty level: low Objective: Symmetrical data Use the following to answer questions 8-10: The annual salaries of six employees of a company are as follows: $22,000

$35,000

$22,000

$46,000

$57,000

$51,000

8. The mean salary of these employees is: Ans: $38,833.33 Difficulty level: low Objective: Measures of central tendency for ungrouped data 9. The median salary of these employees is: Ans: $40,500 Difficulty level: low Objective: Measures of central tendency for ungrouped data 10. The mode of the salaries of these employees is: Ans: $22,000 Difficulty level: low Objective: Measures of central tendency for ungrouped data Use the following to answer questions 11-13: The points scored by a team in five basketball games are as follows: 118

124

77

99

112

11. The mean for this data set is: Ans: 106 Difficulty level: low Objective: Measures of central tendency for ungrouped data 12. The median for this data set is: Ans: 112 Difficulty level: low Objective: Measures of central tendency for ungrouped data 13. The mode of this data set is: A) 47 B) 77 C) 112 D) this data set does not have a unique mode Ans: D Difficulty level: low Objective: Measures of central tendency for ungrouped data

Page 2

Chapter 3

14. The mean age of five members of a family is 40 years. The ages of four of the five members are 61, 60, 27, and 23. The age of the fifth member is: A) 32 B) 27 C) 29 D) 35 Ans: C Difficulty level: low Objective: Mean of a set of data 15. The scores of eight students taking a mathematics test are 87, 93, 76, 7, 84, 90, 95, and 93. The best measure of central tendency in this case is the: A) median B) mean C) box-and whisker D) variance Ans: A Difficulty level: low Objective: Measures of central tendency for ungrouped data 16. The mean score of 15 male students taking a test is 76 and the mean score of 12 female students taking the same test is 73. The combined mean score of the 27 male and female students is A) 69.15 B) 80.19 C) 74.67 D) 77.43 Ans: C Difficulty level: medium Objective: Mean of a set of data 17. The summary measure obtained by taking the difference between the minimum and maximum values in a data set is the: A) median B) standard deviation C) variance D) range Ans: D Difficulty level: low Objective: Measures of dispersion for ungrouped data 18. Outliers influence which of the following summary measures?

A) standard deviation D) A and B only B) interquartile range E) A and C only C) range Ans: E Difficulty level: low Objective: Outliers in a set of data 19. The value of the standard deviation of a data set is: A) never zero B) never negative C) never positive D) always positive Ans: B Difficulty level: low Objective: Measures of dispersion for ungrouped data 20. The quantity x −  is called the: A) standard deviation B) deviation of x from the mean C) variance D) range Ans: B Difficulty level: low Objective: Measures of center and dispersion for qualitative data

Page 3

Chapter 3

21. The measurement units of the standard deviation are always: A) the same as those of the original data B) the square of the measurement units of the original data C) 50% of the measurement units of the original data D) the square root of the sum of the squares of the original data set Ans: A Difficulty level: low Objective: Standard deviation 22. The procedure for obtaining the variance from the standard deviation is to: A) take the square root of the standard deviation B) square the standard deviation C) divide the standard deviation by 2 D) multiply the standard deviation by 2 Ans: B Difficulty level: low Objective: Measures of dispersion for ungrouped data 23. A numerical measure calculated from population data is called a(n): A) parameter B) statistic C) empirical rule D) probability distribution Ans: A Difficulty level: low Objective: Population parameters Use the following to answer questions 24-26: The annual salaries of six employees of a company are as follows: $22,000

$35,000

$22,000

$46,000

$57,000

$51,000

24. The range of these salaries is: Ans: 35,000 Difficulty level: low Objective: Measures of dispersion for ungrouped data 25. The variance of these salaries, rounded to the nearest dollar, is: Ans: $222,166,667 Difficulty level: medium Objective: Measures of dispersion for ungrouped data 26. The standard deviation of these salaries, rounded to the nearest dollar, is: Ans: $14,905 Difficulty level: medium Objective: Measures of dispersion for ungrouped data Use the following to answer questions 27-29: The temperatures (in degrees Fahrenheit) observed during seven days of summer in Los Angeles are: 78

99

68

91

105

75

85

Page 4

Chapter 3

27. The range of these temperatures is: Ans: 37 Difficulty level: low Objective: Measures of dispersion for ungrouped data 28. The variance of these temperatures, rounded to three decimals, is: Ans: 177.476 Difficulty level: medium Objective: Measures of dispersion for ungrouped data 29. The standard deviation, rounded to three decimals, of these temperatures is: Ans: 13.322 Difficulty level: medium Objective: Measures of dispersion for ungrouped data Use the following to answer questions 30-32: The times (in minutes) taken by a sample of nine students to complete a statistics test are: 52

47

57

33

39

43

52

41

36

30. The range of these times is: Ans: 24 Difficulty level: low Objective: Measures of dispersion for ungrouped data 31. The variance of these times, rounded to three decimal places, is: Ans: 65.528 Difficulty level: medium Objective: Measures of dispersion for ungrouped data 32. The standard deviation of these times, rounded to three decimal places, is: Ans: 8.095 Difficulty level: medium Objective: Measures of dispersion for ungrouped data Use the following to answer questions 33-37: You have just recorded the waiting times for a random sample of 50 customers who visited Elmo's Pizza Shop. The following table gives the frequency distribution of waiting times (in minutes) for these customers.

Waiting Time 10 to less than 16 16 to less than 22 22 to less than 28 28 to less than 34 34 to less than 40 40 to less than 46

f 6 10 18 8 7 1

Page 5

Chapter 3

33. The value of  mf is: Ans: 1,268 Difficulty level: low

Objective: Summary statistics for grouped data

34. The value of  m 2 f is: Ans: 34,994 Difficulty level: low

Objective: Summary statistics for grouped data

35. The mean waiting time, rounded to two decimal places, is: Ans: 25.36 minutes Difficulty level: medium Objective: Summary statistics for grouped data 36. The variance of waiting times, rounded to two decimal places, is: Ans: 57.91 minutes Difficulty level: medium Objective: Summary statistics for grouped data 37. The standard deviation of waiting times, rounded to two decimal places, is: Ans: 7.61 minutes Difficulty level: medium Objective: Summary statistics for grouped data Use the following to answer questions 38-42: The following table gives the frequency distribution of prices for a sample of 30 college textbooks.

Price 20 to less than 30 30 to less than 40 40 to less than 50 50 to less than 60 60 to less than 70

f 4 7 13 3 3

38. The value of  mf is: Ans: 1,290 Difficulty level: low

Objective: Summary statistics for grouped data

39. The value of  m 2 f is: Ans: 59,150 Difficulty level: low

Objective: Summary statistics for grouped data

40. The mean price of these textbooks, rounded to two decimal places, is: Ans: $43.00 Difficulty level: low Objective: Summary statistics for grouped data

Page 6

Chapter 3

41. The variance of the textbook prices, rounded to two decimal places, is: Ans: 126.90 Difficulty level: low Objective: Summary statistics for grouped data 42. The standard deviation of the textbook prices, rounded to two decimal places, is: Ans: $11.26 Difficulty level: medium Objective: Summary statistics for grouped data 43. According to Chebyshev's theorem, the minimum percentage of values that fall within 3 standard deviations of the mean is: A) 86% B) 90% C) 87% D) 89% Ans: D Difficulty level: medium Objective: Use of standard deviation 44. According to Chebyshev's theorem, the minimum percentage of values that fall within 1.5 standard deviations of the mean is: A) 53.56% B) 57.06% C) 55.56% D) 52.56% Ans: C Difficulty level: medium Objective: Use of standard deviation 45. Chebyshev's theorem is applicable to: A) a bell-shaped distribution D) A and B only B) a skewed distribution E) A, B and C C) a multimodal distribution Ans: E Difficulty level: low Objective: Use of standard deviation 46. The empirical rule is applicable to: A) a bell-shaped distribution B) a skewed distribution C) a multimodal distribution Ans: A Difficulty level: low

D) E)

A and B only A, B, and C

Objective: Use of standard deviation

47. According to the empirical rule, the percentage of values that fall within one standard deviation of the mean is approximately: A) 63% B) 72% C) 68% D) 59% Ans: C Difficulty level: low Objective: Use of standard deviation 48. According to the empirical rule, the percentage of values that fall within two standard deviations of the mean is approximately: A) 93% B) 95% C) 94% D) 91% Ans: B Difficulty level: low Objective: Use of standard deviation 49. According to the empirical rule, the percentage of values that fall within three standard deviations of the mean is approximately: A) 99.4% B) 99.7% C) 97.9% D) 97.3% Ans: B Difficulty level: low Objective: Use of standard deviation

Page 7

Chapter 3

50. According to the empirical rule, the percentage of values that fall outside two standard deviations of the mean is approximately: A) 5% B) 9% C) 7% D) 4% Ans: A Difficulty level: medium Objective: Use of standard deviation 51. The mean age of all high school teachers in New York state is 41 years and the standard deviation is 6 years. According to Chebyshev's theorem, the percentage of teachers in New York who are 23 to 59 years old is at least: A) 88.89 B) 77.78 C) 84.39 D) 90.89 Ans: A Difficulty level: medium Objective: Use of standard deviation 52. The mean age of all high school teachers in New York state is 50 years and the standard deviation is 7 years. According to Chebyshev's theorem, the percentage of teachers in New York who are 25.5 to 74.5 years old is at least: A) 91.84 B) 83.67 C) 87.34 D) 93.84 Ans: A Difficulty level: medium Objective: Use of standard deviation 53. The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 39 years and a standard deviation of 7 years. According to the empirical rule, the percentage of teachers in this state who are 32 to 46 years old is approximately: A) 75% B) 68% C) 95% D) 62% Ans: B Difficulty level: low Objective: Use of standard deviation 54. The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 45 years and a standard deviation of 7 years. According to the empirical rule, the percentage of teachers in this state who are 24 to 66 years old is approximately: A) 99.4% B) 97.9% C) 98.3% D) 99.7% Ans: D Difficulty level: low Objective: Use of standard deviation 55. The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 43 years and a standard deviation of 6 years. According to the empirical rule, the percentage of teachers in this state who are 31 to 55 years old is approximately: A) 97% B) 94% C) 89% D) 95% Ans: D Difficulty level: low Objective: Use of standard deviation 56. The mean income of all MBA degree holders working in Los Angeles is $65,000 per year and the standard deviation of their incomes is $8,000 per year. According to Chebyshev's theorem, the percentage of MBA degree holders, working in Los Angeles, with an annual income of $33,000 to $97,000 is at least: A) 87.50 B) 95.75 C) 89.25 D) 93.75 Ans: D Difficulty level: medium Objective: Use of standard deviation

Page 8

Chapter 3

57. The mean income of all MBA degree holders working in Los Angeles is $86,000 per year and the standard deviation of their incomes is $10,500 per year. According to Chebyshev's theorem, the percentage of MBA degree holders, working in Los Angeles, with an annual income of $49,250 to $122,750 is at least:: A) 91.84 B) 86.39 C) 87.34 D) 93.84 Ans: A Difficulty level: medium Objective: Use of standard deviation 58. The annual incomes of all MBA degree holders working in Los Angeles have a bell-shaped distribution with a mean of $71,000 and a standard deviation of $8,000.

According to the empirical rule, the percentage of MBA degree holders working in Los Angeles who have an annual income of $63,000 to $79,000 is approximately: A) 86% B) 68% C) 64% D) 89% Ans: B Difficulty level: low Objective: Use of standard deviation 59. The annual incomes of all MBA degree holders working in Los Angeles have a bell-shaped distribution with a mean of $72,000 and a standard deviation of $6,000.

According to the empirical rule, the percentage of MBA degree holders working in Los Angeles who have an annual income of $54,000 to $90,000 is approximately: A) 97.9% B) 99.4% C) 94.9% D) 99.7% Ans: D Difficulty level: low Objective: Use of standard deviation 60. The annual incomes of all MBA degree holders working in Los Angeles have a bell-shaped distribution with a mean of $78,000 and a standard deviation of $11,000.

According to the empirical rule, the percentage of MBA degree holders working in Los Angeles who have an annual income of $56,000 to $100,000 is approximately: A) 75% B) 95% C) 88% D) 97% Ans: B Difficulty level: low Objective: Use of standard deviation 61. The quartiles divide a ranked data set into: A) 2 equal parts B) 4 equal parts C) 100 equal parts D) 10 equal parts Ans: B Difficulty level: low Objective: Measures of position 62. The percentiles divide a ranked data set into: A) 2 equal parts B) 4 equal parts C) 100 equal parts D) 10 equal parts Ans: C Difficulty level: low Objective: Measures of position 63. The value of the third quartile for a data set is 65. This means that: A) 25% of the values in that data set are smaller than 65.

B) 75% of the values in that data set are smaller than 65.

C) 75% of the values in that data set are greater than 65.

D) 50% of the values in that data set are greater than 65.

Ans: B Difficulty level: low Objective: Measures of position

Page 9

Chapter 3

64. The value of the 65th percentile for a data set is 82. This means that: A) 35% of the values in that data set are smaller than 82.

B) 65% of the values in that data set are greater than 82.

C) 65% of the values in that data set are smaller than 82.

D) 82% of the values in that data set are greater than 82.

Ans: C Difficulty level: low Objective: Measures of position 65. The percentile rank of a value in a data set is 43. This means that: A) 43% of the values in that data set are greater than that value B) 43% of the values in that data set are greater than 43 C) 57% of the values in that data set are smaller than that value D) 43% of the values in that data set are smaller than that value Ans: D Difficulty level: low Objective: Measures of position Use the following to answer questions 66-70: The waiting times (in minutes) for 11 customers at a supermarket are: 14

9

15

4

4

7

9

11

14

2

6

66. The first quartile for these data is: Ans: 4 Difficulty level: low Objective: Measures of position 67. The second quartile for these data is: Ans: 9 Difficulty level: low Objective: Measures of position 68. The third quartile for these data is: Ans: 14 Difficulty level: low Objective: Measures of position 69. The approximate value of the 60th percentile for these data is: Ans: 9 Difficulty level: low Objective: Measures of position 70. The percentile rank for the customer who waited 11 minutes is: A) 80.00% B) 72.72% C) 68.33% D) 63.64% Ans: D Difficulty level: low Objective: Measures of position Use the following to answer questions 71-75: The work experiences (in years) of 14 employees of a company are 8

21

11

4

14

17

11

8

Page 10

8

7

2

11

27

6

Chapter 3

71. The first quartile for these data is: Ans: 7 Difficulty level: low Objective: Measures of position 72. The second quartile for these data is: Ans: 9.5 Difficulty level: low Objective: Measures of position 73. The third quartile for these data is: Ans: 14 Difficulty level: low Objective: Measures of position 74. The approximate value of the 70th percentile for these data is: Ans: 11 Difficulty level: low Objective: Measures of position 75. The percentile rank for the employee with 17 years of experience is: A) 62.96% B) 78.57% C) 68.00% D) 85.71% Ans: B Difficulty level: low Objective: Measures of position 76. Which of the following does a box-and-whisker plot not show?

A) spread of the data B) percent of the data within two standard deviations of the mean C) center of the data set D) skewness of the data set Ans: B Difficulty level: low Objective: Box-and-whisker plots Use the following to answer questions 77-78: Data concerning the time between failures (in hours of operation) for a computer printer have been recorded, and the first quartile equals 38 hours, the second quartile equals 59 hours, and the third quartile equals 87 hours.

77. The value for the lower inner fence equals Ans: –35.5 Difficulty level: low Objective: Box-and-whisker plots 78. The value for the upper inner fence equals Ans: 160.5 Difficulty level: low Objective: Box-and-whisker plots

Page 11

Chapter 3

Use the following to answer questions 79-90: The following data represent the ages of 15 people buying lift tickets at a ski area.

15 34

25 31

26

17

38

16

74

41

30

24

28

40

20

79. What is the mean of these data, rounded to two decimal places?

Ans: 30.60 Difficulty level: low Objective: Measures of central tendency for ungrouped data 80. What is the median of these data?

Ans: 28 Difficulty level: low Objective: Measures of central tendency for ungrouped data 81. What is the range of these data?

Ans: 59 Difficulty level: low Objective: Measures of dispersion for ungrouped data 82. What is the variance of these data, rounded to two decimal places?

Ans: 214.54 Difficulty level: medium Objective: Measures of dispersion for ungrouped data 83. What is the standard deviation of these data, rounded to two decimal places?

Ans: 14.65 Difficulty level: medium Objective: Measures of dispersion for ungrouped data 84. What is the value of the first quartile?

Ans: 20 Difficulty level: low Objective: Measures of position 85. What is the value of the third quartile?

Ans: 38 Difficulty level: low Objective: Measures of position 86. What is the value of the interquartile range?

Ans: 18 Difficulty level: low Objective: Measures of dispersion for ungrouped data 87. What is the value of the lower inner fence?

Ans: -7 Difficulty level: low Objective: Box-and-whisker plots

Page 12

Chapter 3

88. What is the value of the upper inner fence?

Ans: 65 Difficulty level: low Objective: Box-and-whisker plots 89. Are there any outliers in this data set? If so, what are they?

Ans: yes: 74 Difficulty level: low Objective: Box-and-whisker plots 90. Create a boxplot of the data. Describe the features of the distribution.

Ans: Difficulty level: medium

Objective: Box-and-whisker plots

91. Based on the box-and-whisker plot,

complete the table.

Minimum ----

Q1 ----

Median ----

Q3 ----

Maximum ----

Ans: Minimum 0 Difficulty Level: Easy

Q1 10

Median 17

Difficulty level: low

Page 13

Q3 23.5

Maximum 28

Objective: Box-and-whisker plots

Chapter 3

92. Let s1, s2, and s3 be the standard deviations of the bell-shaped graphs I, II, and III, respectively. Place them in increasing order.

A) s3 , s1 , s3 B) s3 , s1 , s3 C) s1 , s3 , s3 D) s3 , s3 , s1 Ans: B Difficulty Level: Medium Difficulty level: medium Objective: Measures of dispersion for ungrouped data

Page 14

1. A statistical experiment is a process that, when performed: A) results in one and only one of two observations B) results in at least two of many observations C) may not lead to the occurrence of any outcome D) results in one and only one of many observations Ans: D Difficulty level: Low Objective: Identify the sample space used in the description of an experiment.

2. A sample point is A) a collection of many sample spaces B) a point that represents a population in a sample C) an element of a sample space D) a collection of observations Ans: C Difficulty level: low Objective: Identify the sample space used in the description of an experiment.

3. An event A) is the same as a sample space B) includes exactly one outcome Ans: C Difficulty level: low

C) includes one or more outcomes D) includes all possible outcomes Objective: Define an event.

4. A simple event A) is a collection of exactly two outcomes B) includes one and only one outcome C) does not include any outcome D) includes all possible outcomes Ans: B Difficulty level: low Objective: Distinguish between simple and compound events.

5. A compound event includes A) at least three outcomes B) at least two outcomes Ans: B Difficulty level: low compound events.

C) one and only one outcome D) all outcomes of an experiment Objective: Distinguish between simple and

6. The experiment of tossing a coin 3 times has A) 2 outcomes B) 8 outcomes C) 6 outcomes D) 5 outcomes Ans: B Difficulty level: medium Objective: Identify the sample space used in the description of an experiment.

Page 1

Chapter 4

7. A box contains a few red, a few black, and a few white marbles. Two marbles are randomly drawn from this box and the color of these marbles is observed. The total number of outcomes for this experiment is A) 3 B) 6 C) 9 D) you can't tell until you know exactly how many marbles are in the box Ans: C Difficulty level: low Objective: Identify the sample space used in the description of an experiment.

8. You randomly select two households and observe whether or not they own a telephone answering machine. Which of the following is a simple event?

A) Exactly one of them owns a telephone answering machine.

B) At least one of them owns a telephone answering machine.

C) At most one of them owns a telephone answering machine.

D) Neither of the two owns a telephone answering machine.

Ans: A Difficulty level: low Objective: Define an event.

9. You toss a coin nine times and observe 3 heads and 6 tails. This event is a: A) compound event C) multiple outcome B) simple event D) multinomial sample point Ans: B Difficulty level: low Objective: Distinguish between simple and compound events.

10. The probability of an event is always A) greater than zero C) between 0 and 1, inclusive B) less than 1 D) greater than 1 Ans: C Difficulty level: low Objective: Explain the basic properties of probability.

11. According to the relative frequency concept of probability, the probability of an event is A) 1 divided by the total number of outcomes for the experiment B) the number of times the given event is observed divided by the total number of repetitions of the experiment C) the number of outcomes favorable to the given event divided by the sample space D) the sample space divided by the number of outcomes favorable to the given event Ans: B Difficulty level: low Objective: Apply the relative frequency concept of the probability approach to compute the probability of an event.

12. You select one person from a group of eight males and two females. The two events "a male is selected" and "a female is selected" are A) independent C) not equally likely B) equally likely D) collectively exhaustive Ans: C Difficulty level: low Objective: Explain the basic properties of probability.

Page 2

Chapter 4

13. Which of the following values cannot be the probability of an event?

A) 0.33 B) 2.47 C) 0.25 D) 1.00 Ans: B Difficulty level: low Objective: Explain the basic properties of probability.

14. A conditional probability is a probability A) of a sample space based on a certain condition B) that an event will occur given that another event has already occurred C) that an event will occur based on the condition that no other event is being considered D) that an event will occur based on the condition that no other event has already occurred Ans: B Difficulty level: low Objective: Compute the conditional probability of an event in the context of an application.

15. A marginal probability is a probability of A) a sample space B) an outcome when another outcome has already occurred C) an event without considering any other event D) an experiment calculated at the margin Ans: C Difficulty level: Low Objective: Compute and interpret the marginal probabilities in the context of an application.

16. Two mutually exclusive events A) always occur together B) can sometimes occur together C) cannot occur together D) can occur together, provided one has already occurred Ans: C Difficulty level: low Objective: Determine if events are mutually exclusive.

17. Two events are independent if the occurrence of one event A) affects the probability of the occurrence of the other event B) does not affect the probability of the occurrence of the other event C) means that the second event cannot occur D) means that the second event is certain to occur Ans: B Difficulty level: low Objective: Apply the definition of independence to determine if two events are independent.

Page 3

Chapter 4

18. Two complementary events A) taken together do not include all outcomes for an experiment B) taken together include all outcomes for an experiment C) can occur together D) are always independent Ans: B Difficulty level: low Objective: Determine the probability of the complement of an event in the context of an application.

19. Two events A and B are independent if A) P(A) is equal to P(B) C) P(A|B) is equal to P(A) B) P(B|A) is equal to P(A) D) P(A|B) is equal to P(B) Ans: C Difficulty level: low Objective: Apply the definition of independence to determine if two events are independent.

20. If P( A  B) = P( A) P( B) , then events A and B are A) complementary B) mutually exclusive C) independent D) subjective Ans: C Difficulty level: low Objective: Apply the definition of independence to determine if two events are independent.

Use the following to answer questions 21-26: The following table gives the two-way classification of 500 students based on sex and whether or not they suffer from math anxiety.

Sex Male Female

Suffer From Math Anxiety Yes No 167 73 168 92

21. If you randomly select one student from these 500 students, the probability that this selected student is a female is: (round your answer to three decimal places, so 0.0857 would be 0.086) Ans: 0.520 Difficulty level: low Objective: Compute and interpret the marginal probabilities in the context of an application.

22. If you randomly select one student from these 500 students, the probability that this selected student suffers from math anxiety is: (round your answer to three decimal places, so 0.0857 would be 0.086) Ans: 0.670 Difficulty level: low Objective: Compute and interpret the marginal probabilities in the context of an application.

Page 4

Chapter 4

23. If you randomly select one student from these 500 students, the probability that this selected student suffers from math anxiety, given that he is a male is: (round your answer to three decimal places, so 0.0857 would be 0.086) Ans: 0.696 Difficulty level: medium Objective: Use a two-way table and tree diagram to help visualize the computation of conditional probability.

24. If you randomly select one student from these 500 students, the probability that this selected student is a female, given that she does not suffer from math anxiety is: (round your answer to three decimal places, so 0.0857 would be 0.086) Ans: 0.558 Difficulty level: medium Objective: Use a two-way table and tree diagram to help visualize the computation of conditional probability.

25. Which of the following pairs of events are mutually exclusive?

A) Female and male D) Male and no B) Female and no E) Male and yes C) Female and yes F) No and yes Ans: A Difficulty level: low Objective: Determine if events are mutually exclusive.

26. Are the events "Has math anxiety" and "Person is female" independent or dependent?

Detail the calculations you performed to determine this.

Ans: Dependent.

P(Has math anxiety{for all students}) = 0.670 P(Female) = 0.520 P(Has math anxiety | Female) = 0.548 Since P(Has math anxiety | Female) is very different from P(Has math anxiety), the two variables are not independent.

Difficulty level: medium Objective: Use a two-way table to aid in determining if two events are independent.

27. In a group of 88 students, 16 are seniors. If you select one student randomly from this group, the probability (rounded to three decimal places) that this student is a senior is: Ans: 0.182 Difficulty level: Low Objective: Apply the classical probability approach to compute the probability of a simple event.

28. In a group of 436 families, 259 own homes. If you select one family randomly from this group, the probability (rounded to three decimal places) that this family owns a house is: Ans: 0.594 Difficulty level: Low Objective: Apply the classical probability approach to compute the probability of a simple event.

Page 5

Chapter 4

29. You roll an unbalanced die 850 times, and a 3-spot is obtained 148 times. The probability (rounded to three decimal places) of not obtaining a 3-spot for this die is approximately: Ans: 0.826 Difficulty level: Low Objective: Apply the classical probability approach to compute the probability of a simple event.; Determine the probability of the complement of an event in the context of an application.

30. A quality control staff selects 192 items from the production line of a company and finds 21 defective items. The probability (rounded to three decimal places) that an item manufactured by this company is not defective is: Ans: 0.891 Difficulty level: Low Objective: Apply the classical probability approach to compute the probability of a simple event.; Determine the probability of the complement of an event in the context of an application.

Use the following to answer questions 31-44: A pollster asked 1000 adults whether Republicans or Democrats have better domestic economic policies. The following table gives the two-way classification of there opinions.

Sex Male Female

Republicans 205 185

Democrats 350 190

No Opinion 39 31

The pollster then randomly selected one adult from these 1,000 adults.

31. The probability that the selected adult is a male is: (round your answer to three decimal places) Ans: 0.594 Difficulty level: low Objective: Compute and interpret the marginal probabilities in the context of an application.

32. The probability that the selected adult says Democrats have better domestic economic policies is: (round your answer to three decimal places) Ans: 0.540 Difficulty level: low Objective: Compute and interpret the marginal probabilities in the context of an application.

33. The probability that the selected adult is a female given that she thinks that Republicans have better domestic economic policies is approximately (round your answer to three decimal places): Ans: 0.474 Difficulty level: medium Objective: Compute the conditional probability of an event in the context of an application.

Page 6

Chapter 4

34. The probability that the selected adult has no opinion given that he is a male is approximately (round your answer to three decimal places): Ans: 0.066 Difficulty level: medium Objective: Compute the conditional probability of an event in the context of an application.

35. Which of the following pairs of events are mutually exclusive?

A) Female and democrat D) Democrat and no opinion B) Female and male E) Male and republican C) Female and republican F) Male and no opinion Ans: B, D Difficulty level: low Objective: Determine if events are mutually exclusive.

36. Are the events "Democrat" and "Female" independent or dependent? Detail the calculations you performed to determine this.

Ans: Dependent P(Democrat) = 0.540 P(Female) = 0.406 P(Democrat | Female) = 0.468 P(Female | Democrat) = 0.352 Since the probabilities are so different, they cannot be independent.

Difficulty level: medium Objective: Use a two-way table to aid in determining if two events are independent.

37. The joint probability (rounded to three decimal places) of events "Republicans" and "Male" is: Ans: 0.205 Difficulty level: Low Objective: Apply the multiplication rule along with a two-way table to find the joint probability of two events.

38. The probability (rounded to three decimal places) that a randomly selected adult from these 1,000 adults is a female and holds the opinion that Democrats have better domestic policies is: Ans: 0.190 Difficulty level: Low Objective: Apply the multiplication rule along with a two-way table to find the joint probability of two events.

39. The joint probability (rounded to three decimal places) of events "Male" and "No Opinion" is: Ans: 0.039 Difficulty level: Low Objective: Apply the multiplication rule along with a two-way table to find the joint probability of two events.

Page 7

Chapter 4

40. The joint probability (rounded to three decimal places) of events "Republicans" and "Democrats" is: Ans: 0 Difficulty level: Low Objective: Apply the multiplication rule along with a two-way table to find the joint probability of two events.

41. The probability that the selected adult has no opinion is: (Round your answer to 2 decimal places.)

Ans: 0.07 Difficulty level: Low Objective: Compute and interpret the marginal probabilities in the context of an application.

42. The probability (rounded to three decimal places) that the selected adult is a female or thinks that Democrats have better domestic economic policies is: Ans: 0.756 Difficulty level: medium Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

43. The probability (rounded to three decimal places) that the selected adult has no opinion or is a male is: Ans: 0.625 Difficulty level: medium Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

44. The probability that this adult is a male or doesn't think that Democrats have better domestic economic policies is: (Round your answer to 3 decimal places.)

Ans: 0.810 Difficulty level: high Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

45. The intersection of two events A and B is made up of the outcomes that are: A) either in A or in B or in both A and B C) either in A or in B, but not both B) common to both A and B D) not common to both A and B Ans: B Difficulty level: Low Objective: Illustrate the intersection of two events using a Venn diagram.

46. The probability of the intersection of two events A and B is given by: P( A) P( A | B) P( A) + P( B) A) C) P( A) P( B | A) P( A) + P( B) − P( A and B) B) D) Ans: D Difficulty level: Low Objective: Illustrate the intersection of two events using a Venn diagram.

Page 8

Chapter 4

47. The joint probability of two independent events A and B is: P( A) P( B ) P( A) + P( B) A) C) P( A) P( A | B) P( A) + P( B) + P( A or B) B) D) Ans: C Difficulty level: Low Objective: Apply the multiplication rule along with a two-way table to find the joint probability of two events.

48. The joint probability of two mutually exclusive events is always equal to (rounded to one decimal place) Ans: 0 Difficulty level: medium Objective: Explain why the joint probability of mutually exclusive events must be zero.

49. In a class of 49 students, 11 are math majors. The teacher selects two students at random from this class. The probability (to three decimal places) that both of them are math majors is: Ans: 0.047 Difficulty level: medium Objective: Apply the classical probability approach to compute the probability of a compound event.

50. The athletic department of a school has 12 full-time coaches, and 4 of them are female.

The director selects two coaches at random from this group. The probability (to three decimal places) that neither of them is a female is: Ans: 0.424 Difficulty level: medium Objective: Apply the multiplication rule along with a tree diagram to find the joint probability of two events.

51. The probability that a physician is a pediatrician is 0.16. The administration selects two physicians at random. The probability (rounded to three decimal places) that none of them is a pediatrician is: Ans: 0.706 Difficulty level: medium Objective: Apply the multiplication rule along with a tree diagram to find the joint probability of two events.

52. The probability that an adult possesses a credit card is 0.71. A researcher selects two adults at random. The probability (rounded to three decimal places) that the first adult possesses a credit card and the second adult does not possess a credit card is: Ans: 0.206 Difficulty level: medium Objective: Apply the multiplication rule to calculate the joint probability of two independent events.

Page 9

Chapter 4

53. The probability that a physician is a pediatrician is 0.24. The administration selects three physicians at random. The probability (rounded to three decimal places) that exactly two of them are pediatricians is: Ans: 0.131 Difficulty level: high Objective: Apply the multiplication rule to calculate the joint probability of three events.

54. The probability that an adult possesses a credit card is 0.77. A researcher selects four adults at random. The probability (rounded to three decimal places) that three of the four adults possess a credit card is: Ans: 0.420 Difficulty level: high Objective: Apply the multiplication rule to calculate the joint probability of three events.

55. The probability that a person is a college graduate is 0.34 and that he/she has high blood pressure is 0.13. Assuming that these two events are independent, the probability (to four decimal places) that a person selected at random is a college graduate and has high blood pressure is Ans: 0.0442 Difficulty level: Low Objective: Apply the multiplication rule to calculate the joint probability of two independent events.

56. The probability that a person is a college graduate is 0.40 and that he/she has high blood pressure is 0.18. Assuming that these two events are independent, the probability (to four decimal places) that a person selected at random is a college graduate or has high blood pressure is Ans: 0.5080 Difficulty level: high Objective: Apply the multiplication rule to calculate the joint probability of two independent events.

57. The probability that a corporation made profits in 2005 is 0.80 and the probability that a corporation made charitable contributions in 2005 is 0.25. Assuming that these two events are independent, the probability (rounded to 4 decimal places) that a corporation made profits in 2005 and made charitable contributions in 2005 is: Ans: 0.2000 Difficulty level: Low Objective: Apply the multiplication rule to calculate the joint probability of two independent events.

58. The probability that a corporation made profits in 2005 is 0.78 and the probability that a corporation made charitable contributions in 2005 is 0.23. Assuming that these two events are independent, the probability (rounded to 4 decimal places) that a corporation made profits in 2005 or made charitable contributions in 2005, but not both is: Ans: 0.6512 Difficulty level: high Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

Page 10

Chapter 4

59. The probability that an employee of a company is a male is 0.65 and the joint probability that an employee of this company is a male and single is 0.23. The probability (rounded to three decimal places) that a randomly selected employee of this company is single given he is a male is: Ans: 0.354 Difficulty level: medium Objective: Compute the conditional probability of an event in the context of an application.

60. The probability that a farmer is in debt is 0.76. The joint probability that a farmer is in debt and lives in the Midwest is 0.21. The probability (rounded to three decimal places) that a randomly selected farmer lives in the Midwest, given that he is in debt is: Ans: 0.276 Difficulty level: medium Objective: Calculate the conditional probability of an event in the context of an application.

61. The total number of outcomes for 3 rolls of a 9-sided die is: Ans: 729 Difficulty level: medium Objective: Identify the sample space used in the description of an experiment.

62. A woman owns 15 blouses, 10 skirts, and 4 pairs of shoes. She will randomly select one blouse, one skirt, and one pair of shoes to wear on a certain day. The total number of possible outcomes is: Ans: 600 Difficulty level: medium Objective: Apply the multiplication rule along with a tree diagram to find the joint probability of two events.

63. The union of two events A and B represents the outcomes that are: A) either in A or in B or in both A and B C) neither in A nor in B B) common to both A and B D) not common to both A and B Ans: A Difficulty level: Low Objective: Illustrate the union of two events using a two-way table and a Venn diagram.

64. The probability of the union of two events A and B is the probability that: A) neither event A happens nor event B happens B) both events do not happen together C) both events A and B happen together D) either event A or event B or both A and B happen Ans: D Difficulty level: Low Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

Page 11

Chapter 4

65. The probability of the union of two events A and B is: P( A) P( B | A) P( A) + P( B) + P( A or B) A) C) P( A) P( A | B) P( A) + P( B) − P( A or B) B) D) Ans: B Difficulty level: Low Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

66. The probability of the union of two events A and B, that are mutually exclusive, is: P( A) P( A | B) P( A) + P( B) A) C) P( A) P( B | A) P( A) − P( B) + P( A and B) B) D) Ans: A Difficulty level: Low Objective: Apply the addition rule to find the probability of the union of two mutually exclusive events.

67. The probability that a student at a university is a male is 0.52, that a student is a business major is 0.17, and that a student is a male and a business major is 0.08. The probability that a randomly selected student from this university is a male or a business major is: Ans: 0.61 Difficulty level: medium Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

68. The probability that a family has at least one child is 0.79, that a family owns a camcorder is 0.19, and that a family has at least one child and owns a camcorder is 0.07.

The probability that a randomly selected family has at least one child or owns a camcorder is: Ans: 0.91 Difficulty level: medium Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

69. 44% of the voters are in favor of limiting the number of terms for senators and congressmen, 36% are against it, and 20% have no opinion. If a pollster selects one voter at random, the probability (to two decimal places) that this voter is either in favor of limiting the number of terms for senators and congressmen or has no opinion is: Ans: 0.64 Difficulty level: Low Objective: Apply the addition rule to find the probability of the union of two mutually exclusive events.

70. A company has a total of 575 male employees. Of them, 134 are single, 276 are married, 122 are either divorced or separated, and 43 are widowers. If management selects one male employee at random from the company, the probability (rounded to three decimal places) that this employee is married or a widower is: Ans: 0.555 Difficulty level: Low Objective: Apply the addition rule to find the probability of the union of two mutually exclusive events.; Calculate the conditional probability of an event in the context of an application.

Page 12

Chapter 4

Use the following to answer questions 71-73: A consume researcher inspects 300 batteries manufactured by two companies for being good or defective. The following table gives the two-way classification of these 300 batteries.

Company A Company B

Good 148 122

Defective 2 28

71. If the researcher selects one battery at random from these 300 batteries, the probability (rounded to three decimal places) that this battery is good or made by company B is Ans: 0.993 Difficulty level: medium Objective: Apply the multiplication rule along with a two-way table to find the joint probability of two events.

72. If the researcher selects one battery at random from these 300 batteries, the probability (rounded to three decimal places) that this battery is defective or made by company A is Ans: 0.593 Difficulty level: medium Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

73. If the researcher selects one battery at random from these 300 batteries, the probability (rounded to three decimal places) that this battery is good or made by company A is Ans: 0.907 Difficulty level: medium Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

74. The probability that a person drinks at least five cups of coffee per day is 0.31, and the probability that a person has high blood pressure is 0.09. Assuming that these two events are independent, find the probability (to four decimal places) that a person selected at random drinks less than five cups of coffee per day and has high blood pressure.

Ans: 0.0621 Difficulty level: medium Objective: Apply the multiplication rule along with a tree diagram to find the joint probability of two events.

75. The probability that a person drinks at least five cups of coffee per day is 0.30, and the probability that a person has high blood pressure is 0.09. Assuming that these two events are independent, find the probability (to four decimal places) that a person selected at random drinks less than five cups of coffee per day or has high blood pressure.

Ans: 0.7270 Difficulty level: high Objective: Apply the addition rule along with a two-way table to find the probability of the union of two events.

Page 13

Chapter 4

76. Friends will be called, one after another, and asked to go on a weekend trip with you.

You will call until one agrees to go (A) or four friends are asked. What is the tree diagram for the sample space for this experiment?

A)

B)

C)

D) Ans: C Difficulty Level: Medium Difficulty level: medium Objective: Identify the sample space used in the description of an experiment.

Page 14

Chapter 4

77. Pioneer Of The Nile (A), I Want Revenge (B), and Hold Me Back (C), were the three favorites to win the Kentucky Derby. According to an expert, they should arrive first, second and third, respectively.

The tree diagram for the sample space is given below.

A) Complete the tree diagram from top to bottom B) State the composition of the event E = [exactly two horses arrived in the predicted place]

Part A: B, C, A, C, A, B Part B: E = { } Difficulty Level: Medium Difficulty level: medium sample space used in the description of an experiment.

Page 15

Objective: Identify the

Chapter 4

78. The sample space is given by the first 15 positive integers.

Consider the events: A = [odd integers]

B = [prime integers]

Make a Venn diagram showing these events.

A)

B)

C)

Page 16

Chapter 4

D) Ans: D Difficulty Level: Medium Difficulty level: medium Objective: Identify the sample space used in the description of an experiment.

79. From the probabilities shown in this Venn diagram, determine the probability A does not occur.

A B 0.16

0.23

0.44

0.17

Ans: 0.61 Difficulty Level: Medium Difficulty level: low space using Venn diagrams and/or tree diagrams.

Page 17

Objective: Illustrate the sample

Chapter 4

80. From the probabilities shown in this Venn diagram, determine the probability that A occurs and B does not occur.

A B 0.23

0.18

0.42

0.17

Ans: 0.23 Difficulty Level: Medium Difficulty level: low Objective: Illustrate the sample space using Venn diagrams and/or tree diagrams.; Use a two-way table and tree diagram to help visualize the computation of conditional probability.

81. From the probabilities shown in this Venn diagram, determine the probability that exactly one of the events A and B occurs.

A B 0.02

0.21

0.55

0.22

Ans: 0.57 Difficulty Level: Medium Difficulty level: low Objective: Illustrate the union of two events using a two-way table and a Venn diagram.

Page 18

Chapter 4

82. In general, "n factorial" represents: A) the product of any n numbers C) the product of all integers from n to 1 B) the sum of all integers from n to 1 D) n-1 Ans: C Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 83. The factorial of zero is: Ans: 1 Difficulty level: low counting 84. The factorial of 7 is: Ans: 5,040 Difficulty level: low counting

Objective: Factorials, Combinations, Permutations, and

Objective: Factorials, Combinations, Permutations, and

85. The factorial of (13 - 8) is: Ans: 120 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 86. The factorial of (14 - 14) is: Ans: 1 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 87. The factorial of (5 - 0) is: Ans: 120 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 88. The number of combinations for selecting 6 elements from 13 distinct elements is: Ans: 1,716 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 89. The number of combinations for selecting zero elements from 9 distinct elements is: Ans: 1 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 90. The number of combinations for selecting 7 elements from 7 distinct elements is: Ans: 1 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting

Page 19

Chapter 4

91. A court randomly selects a jury of 8 persons from a group of 21 persons. The total number of combinations is: Ans: 203,490 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 92. An investor randomly selects 9 stocks from 11 stocks for an investment portfolio. The total number of combinations is: Ans: 55 Difficulty level: low Objective: Factorials, Combinations, Permutations, and counting 93. When a person makes an educated guess about the likelihood that an event will occur, it is an example of A) conditional probability.

C) subjective probability.

B) marginal probability.

D) classical probability.

Ans: C Difficulty level: low Objective: Explain the subjective probability approach.

94. The probability of rolling a 1 on a die and flipping heads on a coin at the same time is: Ans: 1/12 Difficulty level: low Objective: Apply the classical probability approach to compute the probability of a compound event.

95. Given the table.

Male Female

Yes 0.097 0.165

No 0.135 0.159

Maybe 0.293 0.151

What is the probability that a randomly selected Male will answer "Yes" or "No"?

Ans: 0.232 Difficulty level: low Objective: Apply the addition rule to find the probability of the union of two mutually exclusive events.

Page 20

1. A random variable is a variable whose value is determined by the: A) outcome of a random experiment C) random space B) random population D) random subjective probability Ans: A Difficulty level: low Objective: Define a random variable.

2. A discrete random variable is a random variable: A) that can assume any value in one or more intervals B) whose set of values is countable C) that is derived from a random population D) that is determined by random probability Ans: B Difficulty level: low Objective: Define a random variable.

3. A continuous random variable is a random variable: A) that can assume any value in one or more intervals B) whose set of values is countable C) that is derived from a random population D) that is determined by random probability Ans: A Difficulty level: low Objective: Define a random variable.

4. Which of the following is not an example of a discrete random variable?

A) The number of days it rains in a month in New York B) The number of stocks a person owns C) The number of persons allergic to penicillin D) The time spent by a physician with a patient Ans: D Difficulty level: low Objective: Provide examples of a discrete random variable.

5. Which of the following is an example of a discrete random variable?

A) The weight of a box of cookies B) The length of a window frame C) The number of horses owned by a farmer D) The distance from home to work for a worker Ans: C Difficulty level: low Objective: Provide examples of a discrete random variable.

Page 1

Chapter 5

6. The probability distribution table of a discrete random variable lists: A) the bottom half of the values that the random variable can assume and their corresponding probabilities B) all of the values that the random variable can assume and their corresponding probabilities C) all of the values that the random variable can assume and their corresponding frequencies D) the top half of the values that the random variable can assume and their corresponding frequencies Ans: B Difficulty level: low Objective: Construct the probability distribution of a discrete random variable.

7. For a discrete random variable x, the probability of any value of x is: A) always greater than 1 C) always in the range zero to 1 B) always less than zero D) never greater than zero Ans: C Difficulty level: low Objective: Construct the probability distribution of a discrete random variable.

8. Which of the following is true for the probability of a discrete random variable x?

A) P ( x )  0 B) P ( x )  1 C) P ( x ) = 2 D) 0  P ( x )  1 Ans: D Difficulty level: low Objective: Construct the probability distribution of a discrete random variable.

9. For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be: A) equal to zero B) in the range zero to 1 C) equal to 0.5 D) equal to 1 Ans: D Difficulty level: low Objective: Determine whether a given table or graph possesses the two characteristics of a probability distribution.

10. Which of the following is true for the probability distribution of a discrete random variable x?

A)  P ( x )  0 B)  P ( x ) = 1 C)  P ( x ) = 2 D)  P ( x )  1 Ans: B Difficulty level: low Objective: Determine whether a given table or graph possesses the two characteristics of a probability distribution.

Use the following to answer questions 11-16: The following table lists the probability distribution of a discrete random variable x: x P(x)

0 0.04

1 0.11

2 0.18

3 0.22

4 0.12

Page 2

5 0.21

6 0.09

7 0.03

Chapter 5

11. The probability of x = 3 is: Ans: 0.22 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

12. The probability that x is less than 5 is: Ans: 0.67 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

13. The probability that x is greater than 3 is: Ans: 0.45 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

14. The probability that x is less than or equal to 5 is: Ans: 0.88 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

15. The probability that x is greater than or equal to 4 is: Ans: 0.45 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

16. The probability that x assumes a value from 2 to 5 is: Ans: 0.73 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

Use the following to answer questions 17-22: The following table lists the probability distribution of a discrete random variable x: x P(x)

2 0.15

3 0.32

4 0.2

5 0.13

6 0.12

7 0.06

8 0.02

17. The probability of x = 7 is: Ans: 0.06 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

Page 3

Chapter 5

18. The probability that x is less than or equal to 4 is: Ans: 0.67 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

19. The probability that x is greater than or equal to 6 is: Ans: 0.2 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

20. The probability that x assumes a value from 3 to 6 is: Ans: 0.77 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

21. The probability that x is greater than 6 is: Ans: 0.08 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

22. The probability that x is less than 4 is: Ans: 0.47 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

Use the following to answer questions 23-27: The following table lists the probability distribution of the number of refrigerators owned by all families in a city. x P(x)

0 0.01

1 0.69

2 0.22

3 0.08

23. The probability that a randomly selected family owns exactly two refrigerators is: Ans: 0.22 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

24. The probability that a randomly selected family owns at most one refrigerator is: Ans: 0.7 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

Page 4

Chapter 5

25. The probability that a randomly selected family owns at least two refrigerators is: Ans: 0.3 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

26. The probability that a randomly selected family owns less than two refrigerators is: Ans: 0.7 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

27. The probability that a randomly selected family owns more than one refrigerator is: Ans: 0.3 Difficulty level: low Objective: Use the probability distribution of a random variable to compute probabilities of events.

28. The mean of a discrete random variable is the mean of its: A) frequency distribution C) probability distribution B) percentage distribution D) second and third quartiles Ans: C Difficulty level: low Objective: Calculate the mean of a discrete random variable.

29. The mean of a discrete random variable is its: A) box-and-whisker measure C) second quartile B) expected value D) upper hinge Ans: B Difficulty level: low Objective: Calculate the mean of a discrete random variable.

30. The formula used to obtain the mean of a discrete random variable is: A)  ( x −  ) P( x) B)  yP( x) C)  mf D)  xP( x) Ans: D Difficulty level: low random variable.

Objective: Calculate the mean of a discrete

31. The standard deviation of a discrete random variable is the standard deviation of its: A) frequency distribution C) probability distribution B) percentage distribution D) first and fourth quartiles Ans: C Difficulty level: low Objective: Calculate the standard deviation of a discrete random variable.

Use the following to answer questions 32-33: The following table lists the probability distribution of a discrete random variable x: x P(x)

0 0.04

1 0.11

2 0.18

3 0.22

4 0.12

Page 5

5 0.21

6 0.09

7 0.03

Chapter 5

32. The mean of the random variable x is: Ans: 3.41 Difficulty level: low Objective: Calculate the mean of a discrete random variable.

33. The standard deviation of the random variable x, rounded to three decimal places, is: Ans: 1.750 Difficulty level: medium Objective: Calculate the standard deviation of a discrete random variable.

Use the following to answer questions 34-35: The following table lists the probability distribution of a discrete random variable x: x P(x)

2 0.15

3 0.32

4 0.2

5 0.13

6 0.12

7 0.06

8 0.02

34. The mean of the random variable x is: Ans: 4.01 Difficulty level: medium Objective: Calculate the mean of a discrete random variable.

35. The standard deviation of the random variable x, rounded to three decimal places, is: Ans: 1.546 Difficulty level: medium Objective: Calculate the standard deviation of a discrete random variable.

Use the following to answer questions 36-37: The following table lists the probability distribution of a discrete random variable x: x P(x)

0 0.19

1 0.38

2 0.22

3 0.12

4 0.06

5 0.03

36. The mean of the random variable x is: Ans: 1.57 Difficulty level: low Objective: Calculate the mean of a discrete random variable.

37. The standard deviation of the random variable x, round to three decimal places, is: Ans: 1.259 Difficulty level: medium Objective: Calculate the standard deviation of a discrete random variable.

Page 6

Chapter 5

Use the following to answer questions 38-39: The following table lists the probability distribution of the number of HD-TVs owned by all families in a city. x P(x)

0 0.07

1 0.41

2 0.3

3 0.14

4 0.08

38. The mean number of HD-TVs owned by these families is: Ans: 1.75 Difficulty level: low Objective: Calculate the mean of a discrete random variable.

39. The standard deviation of the number of HD-TVs owned by these families, rounded to three decimal places, is: Ans: 1.043 Difficulty level: medium Objective: Calculate the standard deviation of a discrete random variable.

40. A Bernoulli trial is: A) the trial of a court case B) a repetition of a binomial experiment C) a repetition of a probability distribution D) the trial of a probability distribution Ans: B Difficulty level: low Objective: Verify that an experiment satisfies the conditions of a binomial experiment.

41. Which of the following is not a condition of the binomial experiment?

A) There are only two trials B) Each trial has two and only two outcomes C) p is the probability of success, q is the probability of failure, and p + q = 1 D) The trials are independent Ans: A Difficulty level: low Objective: Verify that an experiment satisfies the conditions of a binomial experiment.

42. In binomial experiments, the outcome called a "success" is an outcome: A) that is always beneficial C) to which the question refers B) that is linked to success D) that is favorable Ans: C Difficulty level: low Objective: Explain how the assumed value of the "probability of a success" affects the graph of the probability distribution of a binomial random variable.

Page 7

Chapter 5

43. The parameters of the binomial probability distribution are: A) n, p, and q B) n, p, q, and x C) n, p, and x D) n and p Ans: D Difficulty level: low Objective: Explain how the assumed value of the "probability of a success" affects the graph of the probability distribution of a binomial random variable.

44. The binomial probability distribution is symmetric if: A) p is equal to 0.25 C) p is less than 0.50 B) p is equal to 0.50 D) p is greater than 0.50 Ans: B Difficulty level: low Objective: Construct a binomial probability distribution with its graph in an applied context.

45. The binomial probability distribution is right-skewed if: A) p is 0.25 or smaller C) p is less than 0.50 B) p is equal to 0.50 D) p is greater than 0.50 Ans: C Difficulty level: low Objective: Construct a binomial probability distribution with its graph in an applied context.

46. The binomial probability distribution is left-skewed if: A) p is 0.25 or greater C) p is less than 0.50 B) p is equal to 0.50 D) p is greater than 0.50 Ans: D Difficulty level: low Objective: Construct a binomial probability distribution with its graph in an applied context.

47. The mean of a binomial distribution is equal to: A) npq B) np C) square of npq D) square root of npq Ans: B Difficulty level: low Objective: Calculate and interpret the mean and standard deviation of a binomial random variable in the context of an application.

48. The standard deviation of a binomial distribution is equal to: A) npq B) np C) square of npq D) square root of npq Ans: D Difficulty level: low Objective: Calculate and interpret the mean and standard deviation of a binomial random variable in the context of an application.

49. Which of the following is an example of a binomial experiment?

A) Rolling a die 10 times and observing for a number B) Selecting five persons and observing whether they are in favor of an issue, against it, or have no opinion C) Tossing a coin 20 times and observing for a head or tail D) Drawing three marbles from a box that contains red, blue, and yellow marbles Ans: C Difficulty level: low Objective: Verify that an experiment satisfies the conditions of a binomial experiment.

Page 8

Chapter 5

50. Which of the following is not a binomial experiment?

A) Rolling a die 25 times and observing for an even or odd number B) Randomly selecting 50 items from a production line and observing if they are good or defective C) Rolling a die 20 times and observing for a number that is less than or equal to 4 or greater than 4 D) Selecting 50 adults and observing if they are in favor of an issue, against it, or have no opinion Ans: D Difficulty level: low Objective: Verify that an experiment satisfies the conditions of a binomial experiment.

51. Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 3 will stay with the same company for more than five years is: Ans: 0.0434 Difficulty level: medium Objective: Use a tree diagram and/or the binomial formula to compute the probability of an event described by a binomial random variable.

52. Thirty-two percent of adults did not visit their physicians' offices last year. The probability, rounded to four decimal places, that in a random sample of 8 adults, exactly 3 will say they did not visit their physicians' offices last year is: Ans: 0.2668 Difficulty level: medium Objective: Use a tree diagram and/or the binomial formula to compute the probability of an event described by a binomial random variable.

53. Forty-four percent of customers who visit a department store make a purchase. The probability, rounded to four decimal places, that in a random sample of 12 customers who will visit this department store, exactly 7 will make a purchase is: Ans: 0.1393 Difficulty level: medium Objective: Use a tree diagram and/or the binomial formula to compute the probability of an event described by a binomial random variable.

54. Five percent of all credit card holders eventually become delinquent. The probability, rounded to four decimal places, that in a random sample of 21 credit card holders, exactly 3 will become delinquent is: Ans: 0.0660 Difficulty level: medium Objective: Use a tree diagram and/or the binomial formula to compute the probability of an event described by a binomial random variable.

Page 9

Chapter 5

55. Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 4 do not have cavities is: Ans: 0.9006 Difficulty level: medium Objective: Use a tree diagram and/or the binomial formula to compute the probability of an event described by a binomial random variable.

56. Thirty percent of law students who sit for a bar exam pass it the first time. The probability, rounded to four decimal places, that in a random sample of 15 law students who will sit for the bar examination, at most 4 will pass it the first time is: Ans: 0.5155 Difficulty level: medium Objective: Use a tree diagram and/or the binomial formula to compute the probability of an event described by a binomial random variable.

57. 27% of adults did not visit their physicians' offices last year. Let x be the number of adults in a random sample of 30 adults who did not visit their physicians' offices last year. The mean and standard deviation of the probability distribution of x, rounded to two decimal places, are: Part A: The mean is 8.10.

Part B: The standard deviation is 2.43.

Difficulty level: low Objective: Calculate and interpret the mean and standard deviation of a binomial random variable in the context of an application.; Calculate and interpret the mean and standard deviation of a discrete random variable in the context of an application.

58. 57% of children in a school do not have cavities. Let x be the number of children in a random sample of 50 children selected from this school who do not have cavities. The mean and standard deviation of the probability distribution of x, rounded to two decimal places, are: Part A: The mean is 28.50.

Part B: The standard deviation is 3.50.

Difficulty level: low Objective: Calculate and interpret the mean and standard deviation of a binomial random variable in the context of an application.; Calculate and interpret the mean and standard deviation of a discrete random variable in the context of an application.

59. The hypergeometric probability distribution can be used whenever: A) a sample is drawn at random with replacement B) successive trials are independent of each other C) the probability of two outcomes remains constant D) the population is finite and sampling occurs without replacement Ans: D Difficulty level: low Objective: Use the hypergeometric formula to calculate the probability of an event described by a hypergeometric random variable.

Page 10

Chapter 5

60. Which of the following is not a condition to apply the Poisson probability distribution?

A) x is a discrete random variable C) The occurrences are random B) There are n identical occurrences D) The occurrences are independent Ans: B Difficulty level: low Objective: Define the characteristics of a Poisson random variable.

61. The parameter(s) of the Poisson probability distribution is(are): A) n, x, and  B) n and  C)  D)  and x Ans: C Difficulty level: low Objective: Define the characteristics of a Poisson random variable.

62. For  = 4.7, the probability of x = 3, rounded to four decimal places, is: Ans: 0.1574 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

63. For  = 3.5, the probability of P(x < 4), rounded to four decimal places, is: Ans: 0.5366 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

64. For  = 4.7, the probability of P(x > 3), rounded to four decimal places, is: Ans: 0.6903 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

Use the following to answer questions 65-67: A manufacturer packages bolts in boxes containing 100 each. Each box of 100 bolts contains, on average, 6 defective bolts. The quality control staff randomly selects a box at the end of the day from an entire production run.

65. What is the probability, rounded to four decimal places, that the box will contain exactly 7 defective bolts?

Ans: 0.1377 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

66. What is the probability, rounded to four decimal places, that the box will contain at most 6 defective bolts?

Ans: 0.6063 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

Page 11

Chapter 5

67. What is the probability, rounded to four decimal places, that the box will contain less than 7 defective bolts?

Ans: 0.6063 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

Use the following to answer questions 68-70: Historical data indicates that Rickenbacker Airlines receives an average of 2.9 complaints per day.

68. What is the probability, rounded to four decimal places, that on a given day, Rickenbacker Airlines will receive exactly 1 complaints?

Ans: 0.1596 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

69. What is the probability, rounded to four decimal places, that on a given day, Rickenbacker Airlines will receive at least 5 complaints?

Ans: 0.1682 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

70. What is the probability, rounded to four decimal places, that on a given day, Rickenbacker Airlines will receive less than 3 complaints?

Ans: 0.4460 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

71. It costs $7.25 to play a very simple game, in which a dealer gives you one card from a deck of 52 cards. If the card is a heart, spade, or diamond, you lose. If the card is a club other than the queen of clubs, you win $11.50. If the card is the queen of clubs, you win $49.50. The random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. What is the mean of x, rounded to the nearest penny?

Ans: -$3.64 Difficulty level: high Objective: Use the hypergeometric formula to calculate the probability of an event described by a hypergeometric random variable.

Page 12

Chapter 5

72. All 10 of the orangutans at a certain zoo contract a very serious disease which claims 84% of its victims (if an orangutan contracts the disease, the probability that it will die is 0.84). What is the probability, rounded to four decimal places, that exactly 1 of the orangutans at this zoo will survive?

Ans: 0.3331 Difficulty level: medium Objective: Use the hypergeometric formula to calculate the probability of an event described by a hypergeometric random variable.

73. The number of small air bubbles per 3 feet by 3 feet plastic sheet has a Poisson distribution with a mean number of 2.8 per sheet. What percent of these sheets have no air bubbles?

Ans: 0.0608 Difficulty level: medium Objective: Use the Poisson formula to compute the probability of an event given a specific value.

74. The mean number of accidents to occur at a busy intersection during a 24-hour period has a Poisson distribution. If the probability of no accidents during a 24-hour period is 0.1165, what is the mean number of accidents, rounded to two decimal places, per 24-hour period?

Ans: 2.15 Difficulty level: high Objective: Use the Poisson formula to compute the probability of an event given a specific value.

75. Let N = 15, r = 6, and n = 4. Using the hypergeometric probability distribution formula, find P(x = 0). Round your answer to four decimal places.

Ans: 0.0000 Difficulty level: medium Objective: Use the hypergeometric formula to calculate the probability of an event described by a hypergeometric random variable.

76. Let N = 10, r = 6, and n = 7. Using the hypergeometric probability distribution formula, find P(x = 0). Round your answer to four decimal places.

Ans: 0.0333 Difficulty level: medium Objective: Use the hypergeometric formula to calculate the probability of an event described by a hypergeometric random variable.

77. Let N = 15, r = 5, and n = 2. Using the hypergeometric probability distribution formula, find P(x  1). Round your answer to four decimal places.

Ans: 0.9048 Difficulty level: high Objective: Use the hypergeometric formula to calculate the probability of an event described by a hypergeometric random variable.

78. A survey show that out of 1,000 households surveyed, 392 own one car, 432 own two cars, 153 own three cars, and 23 own 4 or more cars. Construct the probability distribution for this data.

Ans:

Page 13

Chapter 5

Number of cars owned 1 2 3 4 or more

Probability 0.392 0.432 0.153 0.023

Difficulty level: high Objective: Construct the probability distribution of a random variable in the context of an application.

79. A survey of 1,000 households gives the probability distribution: Number of cars Probability owned 1 0.428 2 0.322 3 0.228 4 or more 0.022 Is this a valid probability distribution?

A) Yes B) No Ans: A Difficulty level: high Objective: Determine whether a given table or graph possesses the two characteristics of a probability distribution.

Page 14

1. A continuous random variable is a random variable that can: A) assume only a countable set of values B) assume any value in one or more intervals C) have no random sample D) assume no continuous random frequency Ans: B Difficulty level: medium Objective: Describe the charactoristics of a continuous probability distribution 2. The relative frequency density for a class is obtained by dividing the: A) frequency of that class by the class width B) relative frequency of that class by the total frequency C) relative frequency of that class by the class width D) frequency of that class by the relative frequency Ans: C Difficulty level: medium Objective: Describe the characteristics of a continuous probability distribution.

3. For a continuous random variable x, the probability that x assumes a value in an interval is: A) in the range zero to 1 B) greater than 1 C) less than zero D) greater than 2 Ans: A Difficulty level: low Objective: Describe the characteristics of a continuous probability distribution.

4. For a continuous random variable x, the area under the probability distribution curve between any two points is always: A) greater than 1 B) less than zero C) equal to 1 D) in the range zero to 1 Ans: D Difficulty level: low Objective: Describe the characteristics of a continuous probability distribution.

5. For a continuous random variable x, the total probability of all (mutually exclusive) intervals within which x can assume a value is: A) less than 1 B) greater than 1 C) equal to 1 D) between zero and 1 Ans: C Difficulty level: low Objective: Describe the characteristics of a continuous probability distribution.

6. For a continuous random variable x, the total area under the probability distribution curve of x is always: A) less than 1 B) greater than 1 C) equal to 1 D) between zero and 1 Ans: C Difficulty level: low Objective: Describe the characteristics of a continuous probability distribution.

7. The probability that a continuous random variable x assumes a single value is always: A) less than 1 B) greater than zero C) equal to zero D) between zero and 1 Ans: C Difficulty level: medium Objective: Describe the characteristics of a continuous probability distribution.

Page 1

Chapter 6

8. The normal probability distribution is applied to: A) a discrete random variable C) any random variable B) a continuous random variable D) a subjective random variable Ans: B Difficulty level: low Objective: Continuous probability distribution and the Normal Distribution 9. Which of the following is not a characteristic of the normal distribution?

A) The total area under the curve is 1.0 B) The curve is symmetric about the mean C) The value of the mean is always greater than the value of the standard deviation D) The two tails of the curve extend indefinitely Ans: C Difficulty level: low Objective: Describe the characteristics of a normal probability distribution.

10. The total area under a normal distribution curve to the left of the mean is always: A) equal to 1 B) equal to zero C) equal to 0.5 D) greater than .5 Ans: C Difficulty level: low Objective: Continuous probability distribution and the Normal Distribution 11. The total area under a normal distribution curve to the right of the mean is always: A) equal to 1 B) equal to zero C) equal to 0.5 D) greater than .5 Ans: C Difficulty level: low Objective: Describe the characteristics of a normal probability distribution.

12. The tails of a normal distribution curve: A) meet the horizontal axis at z = 3.0 B) never meet or cross the horizontal axis C) cross the horizontal axis at z = 4.0 D) are nonsymmetric Ans: B Difficulty level: medium Objective: Describe the characteristics of a normal probability distribution.

13. The parameters of the normal distribution are: A)  and  B)  , x, and  C)  ,  , and z D)  , x, z, and  Ans: A Difficulty level: medium Objective: Describe the characteristics of a normal probability distribution.

14. For a normal distribution, the spread of the curve decreases and its height increases as: A) the sample size decreases B) the standard deviation decreases C) the ratio of the mean and standard deviation increases D) the mean increases Ans: B Difficulty level: low Objective: Explain the effect that changing the parameter sigma has on the shape of the normal probability distribution.

Page 2

Chapter 6

15. For the standard normal distribution, the mean is: A) 1 and the standard deviation is zero C) zero and the standard deviation is 1 B) 0.5 and the standard deviation is 0.5 D) 1 and the standard deviation is 1 Ans: C Difficulty level: low Objective: Standardizing a normal distribution 16. For the standard normal distribution, the z value gives the distance between the mean and a point in terms of the: A) mean B) standard deviation C) variance D) center of the curve Ans: B Difficulty level: medium Objective: Define a z-score.

17. For a normal distribution, the z value for an x value that is to the right of the mean is always: A) equal to zero B) negative C) greater than 1 D) positive Ans: D Difficulty level: low Objective: Define a z-score.

18. For a normal distribution, the z value for an x value that is to the left of the mean is always: A) equal to zero B) negative C) less than 1 D) positive Ans: B Difficulty level: low Objective: Define a z-score.

19. For a normal distribution, the z value for the mean is always: A) equal to zero B) negative C) equal to 1 D) positive Ans: A Difficulty level: low Objective: Define a z-score.

20. For the standard normal distribution, the area between z = 0 and z = 1.70, rounded to four decimal places, is: Ans: 0.4554 Difficulty level: low Objective: Use the standard normal table to compute the area of a finite region of the standard normal distribution.

21. For the standard normal distribution, the area between z = 0 and z = –1.38, rounded to four decimal places, is: Ans: 0.4162 Difficulty level: low Objective: Use the standard normal table to compute the area of a finite region of the standard normal distribution.

22. For the standard normal distribution, the area to the right of z = 0.53, rounded to four decimal places, is: Ans: 0.2981 Difficulty level: low Objective: Use the standard normal table to compute the area of a right-tail of the standard normal distribution.

Page 3

Chapter 6

23. For the standard normal distribution, the area to the right of z = –2.97, rounded to four decimal places, is: Ans: 0.9985 Difficulty level: low Objective: Use the standard normal table to compute the area of a right-tail of the standard normal distribution.

24. For the standard normal distribution, the area to the left of z = 1.23, rounded to four decimal places, is: Ans: 0.8907 Difficulty level: low Objective: Use the standard normal table to compute the area under the standard normal curve to the left of a positive z.

25. For the standard normal distribution, the area to the left of z = –2.22, rounded to four decimal places, is: Ans: 0.0132 Difficulty level: low Objective: Use the standard normal table to compute the area under the standard normal curve to the left of a positive z.

26. For the standard normal distribution, the area between z = 1.03 and z = 1.30, rounded to four decimal places, is: Ans: 0.0544 Difficulty level: medium Objective: Use the standard normal table to compute the area of a finite region of the standard normal distribution.

27. For the standard normal distribution, the area between z = –2.04 and z = 2.28, rounded to four decimal places, is: Ans: 0.9680 Difficulty level: medium Objective: Use the standard normal table to compute the area of a finite region of the standard normal distribution.

28. For the standard normal distribution, the area between z = –2.35 and z = –1.56, rounded to four decimal places, is: Ans: 0.0499 Difficulty level: medium Objective: Use the standard normal table to compute the area of a finite region of the standard normal distribution.

29. Let x have a normal distribution with a mean of 49.2 and a standard deviation of 4.90.

The z value for x = 56.05, rounded to two decimal places, is: Ans: 1.40 Difficulty level: low Objective: Explain how to convert x-values to corresponding z-values.

Page 4

Chapter 6

30. Let x have a normal distribution with a mean of 123.7 and a standard deviation of 6.01.

The z value for x = 133.67, rounded to two decimal places, is: Ans: 1.66 Difficulty level: low Objective: Explain how to convert x-values to corresponding z-values.

31. Let x have a normal distribution with a mean of 7.8 and a standard deviation of 3.58. The z value for x = 10.27, rounded to two decimal places, is: Ans: 0.69 Difficulty level: low Objective: Explain how to convert x-values to corresponding z-values.

32. Let x have a normal distribution with a mean of –40.3 and a standard deviation of 11.51.

The z value for x = –26.58, rounded to two decimal places, is: Ans: 1.19 Difficulty level: low Objective: Explain how to convert x-values to corresponding z-values.

Use the following to answer questions 33-35: The GMAT scores of all examinees who took that test this year produce a distribution that is approximately normal with a mean of 420 and a standard deviation of 32.

33. The probability that the score of a randomly selected examinee is between 400 and 480, rounded to four decimal places, is: Ans: 0.7036 Difficulty level: medium Objective: Use the process of standardizing a normal distribution to find probabilities.

34. The probability that the score of a randomly selected examinee is less than 370, rounded to four decimal places, is: Ans: 0.0591 Difficulty level: medium Objective: Use the process of standardizing a normal distribution to find probabilities.

35. The probability that the score of a randomly selected examinee is more than 530, rounded to four decimal places, is: Ans: 0.0003 Difficulty level: medium Objective: Use the process of standardizing a normal distribution to find probabilities.

Use the following to answer questions 36-38: The daily sales at a convenience store produce a distribution that is approximately normal with a mean of 1220 and a standard deviation of 130.

Page 5

Chapter 6

36. The probability that the sales on a given day at this store are more than $1,405, rounded to four decimal places, is: Ans: 0.0774 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

37. The probability that the sales on a given day at this store are less than $1,305, rounded to four decimal places, is: Ans: 0.7434 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

38. The probability that the sales on a given day at this store are between $1,200 and $1,300, rounded to four decimal places, is: Ans: 0.2920 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

Use the following to answer questions 39-41: The net weights of all boxes of Top Taste cookies produce a distribution that is approximately normal with a mean of 31.74 and a standard deviation of 0.58.

39. The probability that the net weight of a randomly selected box of these cookies is more than 32.6 ounces, rounded to four decimal places, is: Ans: 0.0691 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

40. The probability that the net weight of a randomly selected box of these cookies is less than 31.58 ounces, rounded to four decimal places, is: Ans: 0.3913 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

41. The probability that the net weight of a randomly selected box of these cookies is between 31.8 and 32.5 ounces, rounded to four decimal places, is: Ans: 0.3638 Difficulty level: high Objective: Use the normal distribution to find the probability of an event in the context of an application.

Use the following to answer questions 42-44: The heights of all female college basketball players produce a distribution that is approximately normal with a mean of 67.55 and a standard deviation of 2.02.

Page 6

Chapter 6

42. The probability that the height of a randomly selected female college basketball player is more than 65.8 inches, rounded to four decimal places, is: Ans: 0.8068 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

43. The probability that the height of a randomly selected female college basketball player is less than 67.2 inches, rounded to four decimal places, is: Ans: 0.4312 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

44. The probability that the height of a randomly selected female college basketball player is between 63.9 and 69.2 inches, rounded to four decimal places, is: Ans: 0.7576 Difficulty level: high Objective: Use the normal distribution to find the probability of an event in the context of an application.

45. The area under the standard normal curve from zero to z is 0.4906 and z is positive. The value of z is: Ans: 2.35 Difficulty level: low Objective: Explain how to find z when the area under the standard normal curve to the left of z is known.

46. The area under the standard normal curve from zero to z is 0.1772 and z is negative. The value of z is: Ans: –0.46 Difficulty level: low Objective: Explain how to find z when the area under the standard normal curve to the left of z is known.

47. The area under the standard normal curve to the right of z is 0.0089 and z is positive. The value of z is: Ans: 2.37 Difficulty level: low Objective: Explain how to find z when the area under the standard normal curve in the right tail is known.

48. The area under the standard normal curve to the left of z is 0.0401 and z is negative. The value of z is: Ans: –1.75 Difficulty level: low Objective: Explain how to find z when the area under the standard normal curve in the left tail is known.

Page 7

Chapter 6

49. We can use the normal distribution to approximate the binomial distribution when: A) the sample size is at least 30 C) np and nq are both more than 5 B) np and nq are both less than 5 D) nx is greater than 30 Ans: C Difficulty level: low Objective: Explain the conditions (involving sample size and probability of a success) under which approximating a binomial distribution by a normal one is valid.

Use the following to answer questions 50-52: We know that 57% of all adults are in favor of abolishing the sales tax and increasing the income tax. Suppose we take a random sample of 420 adults and obtain their opinions on the issue.

50. The probability that exactly 250 will be in favor of abolishing the sales tax and increasing the income tax is approximately: Ans: 0.0228 Difficulty level: low Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

51. The probability that 225 or fewer will be in favor of abolishing the sales tax and increasing the income tax is approximately: Ans: 0.0853 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.Use the normal curve to approximate the binomial distribution in the context of an application.

52. The probability that 250 to 265 will be in favor of abolishing the sales tax and increasing the income tax is approximately: Ans: 0.1547 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

Use the following to answer questions 53-55: We know that football is the favorite sport to watch on television for 36% of adults in the United States. Suppose we take a random sample of 522 adults and obtain their opinions on their favorite sport to watch on television.

53. The probability that 180 to 215 will say that football is their favorite sport to watch on television is approximately: (Round the answer to 4 decimal places.)

Ans: 0.7727 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

Page 8

Chapter 6

54. The probability that 193 or more will say that football is their favorite sport to watch on television is approximately: (Round the answer to 4 decimal places.)

Ans: 0.3381 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

55. The probability that 170 to 190 will say that football is their favorite sport to watch on television is approximately: (Round the answer to 4 decimal places.)

Ans: 0.5465 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

Use the following to answer questions 56-58: In a recent Gallup poll, 52% of parents with children under 18 years of age gave themselves a grade of B for the job they are doing bringing up their kids. Assume that this percentage is true for the current population of all parents with children under 18 years of age. You take a random sample of 1044 such parents and ask them to give themselves a grade for the job they are doing bringing up their kids.

56. The probability that 560 or more will give themselves a grade of B is approximately: (Round the answer to 4 decimal places.)

Ans: 0.1516 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

57. The probability that 550 or less will give themselves a grade of B is approximately: (Round the answer to 4 decimal places.)

Ans: 0.6816 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

58. The probability that 520 to 555 will give themselves a grade of B is approximately: (Round the answer to 4 decimal places.)

Ans: 0.7091 Difficulty level: medium Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

Page 9

Chapter 6

59. The accountant at a department store is analyzing the credit card purchases of 100 of the store's cardholders over the past year. The following table lists the frequency distribution of the continuous random variable x, annual credit card purchases.

Annual Credit Card Frequency Purchases ($) 0 to less than 200 14 200 to less than 400 18 400 to less than 600 15 600 to less than 800 25 800 to less than 1000 15 1000 to less than 1200 13 What is the relative frequency density of the 400 to less than 600 class? Round your answer to 5 decimal places.

Ans: 0.00075 Difficulty level: medium Objective: Illustrate the probability of an event described by a continuous random variable using its probability distribution.

60. There are 250 players in a particular youth soccer league that has 11 teams. The league statistician is tabulating the total goals scored over the past season by each player. She assigns the random variable y to represent these totals, and then assigns the following categories for y: 0 to less than 4, 4 to less than 8, 8 to less than 12, 12 to less than 16, 16 to less than 20, and 20 to less than 24. The relative frequency density for the 8 to less than 12 class is 0.019. How many of the players scored between 8 and less than 12 goals?

Ans: 19 Difficulty level: medium Objective: Illustrate the probability of an event described by a continuous random variable using its probability distribution.

61. You are given that the area under the standard normal curve to the left of z = –2.56 is equal to 0.0052. What is P(–2.56< z < 2.56)?

Ans: 0.9895 Difficulty level: low Objective: Use the standard normal table to compute the area of a finite region of the standard normal distribution.

62. We know that the length of time required for a student to complete a particular aptitude test has a normal distribution with a mean of 41.5 minutes and a variance of 3.1 minutes.

What is the probability, rounded to four decimal places, that a given student will complete the test in more than 36 minutes but less than 44 minutes?

Ans: 0.9213 Difficulty level: medium Objective: Use the normal distribution to find the probability of an event in the context of an application.

Page 10

Chapter 6

63. Suppose that the distribution for a random variable x is normal with mean 15 and standard deviation  , and P( x  0) = 0.0773 . Rounded to two decimal places, what is ?

Ans: 10.54 Difficulty level: high Objective: Compute areas of regions under a non-standard normal distribution.

64. As explained in the textbook, the normal distribution can be used as an approximation to the binomial distribution when np > 5 and nq > 5. Let x be the number of times that heads comes up in n flips of a coin for which the probability of a head is p = 0.152. What is the lowest that n can be in order for us to use the normal approximation for the distribution of x?

Ans: 33 Difficulty level: medium Objective: Explain the conditions (involving sample size and probability of a success) under which approximating a binomial distribution by a normal one is valid.

65. Suppose that the random variable x has a binomial distribution with n = 30 and p = 0.48.

You want to determine P (14  X  19 ) . Using the normal approximation, what is this probability? (Round the answer to 4 decimal places.)

Ans: 0.5977 Difficulty level: high Objective: The Normal Approximation to the Binomial Distribution 66. The ages of adults in a certain community follow a normal distribution with mean 38.5 and standard deviation 6.68. The random variable x represents the age of a randomly selected adult from this community. Given that P ( 35  x  a ) = .17 , what is a to the nearest year?

Ans: 38 Difficulty level: high Objective: Explain how to find x when the area under the standard normal curve in the left tail is known.

67. 95.8% of the parts coming off an assembly line are non-defective. Using the normal approximation to the binomial distribution, what is the probability, rounded to four decimal places, that of 504 parts, fewer than 480 are non-defective?

Ans: 0.3023 Difficulty level: high Objective: Use the normal curve to approximate the binomial distribution in the context of an application.

Page 11

Chapter 6

68. A floor tiling contractor has just sent Tina out on a job without any indication of the size of the job. She does know that, over the years, the number of tiles required for each job has followed a normal distribution with a mean of 581 and a standard deviation of 210.

She can either take the large truck (which is very difficult and expensive to drive) or the small truck to the job site. She is certain that the large truck can hold enough tiles to do the job, but she would prefer to take the small truck if she can. The small truck can carry up to 750 tiles. Because the job site is out of town, she can only make one trip. What is the probability that the small truck will carry enough tiles to do the job?

Ans: 0.7895 Difficulty level: high Objective: Use the normal distribution to find the probability of an event in the context of an application.

69. Let x be a continuous random variable that follows a normal distribution with a mean of 218 and a standard deviation of 26.

Find the value of x so that the area under the normal curve to the left of x is approximately 0.8770. Round your answer to two decimal places.

Ans: 248.16 Difficulty level: medium Objective: Explain how to find x when the area under the standard normal curve in the left tail is known.

70. Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 51.

Find the value of x so that the area under the normal curve to the right of x is approximately 0.2946. Round your answer to two decimal places.

Ans: 227.54 Difficulty level: medium Objective: Explain how to find x when the area under the standard normal curve in the right tail is known.

71. Let x be a continuous random variable that follows a normal distribution with a mean of 226 and a standard deviation of 31.

Find the value of x so that the area under the normal curve between  and x is approximately 0.4959 and the value of x is less than  . Round your answer to two decimal places.

Ans: 144.16 Difficulty level: high Objective: Explain how to find x when the area under the standard normal curve in the left tail is known.

Page 12

Chapter 6

72. Let x be a continuous random variable that follows a normal distribution with a mean of 207 and a standard deviation of 42.

Find the value of x so that the area under the normal curve between  and x is approximately 0.4996 and the value of x is greater than  . Round your answer to two decimal places.

Ans: 348.96 Difficulty level: high Objective: Explain how to find x when the area under the standard normal curve in the right tail is known.

73. According to the Empirical rule, what percent of the data should be between 136 and 260 for a population with mean of 198 and standard deviation of 62?

Ans: 68.26% Difficulty level: low Objective: Interpret the empirical rule for the standard normal distribution.

74. According to the Empirical rule, 68.26% of the data would fall between what two values for a population with mean of 816 and standard deviation of 248?

Ans: 568 and 1,064 Difficulty level: low Objective: Interpret the empirical rule for the standard normal distribution.

75. For a normal curve, changing the mean from 35 to 46 will cause the curve to shift A) to the left.

B) to the right.

C) up.

D) down.

Ans: B Difficulty level: low Objective: Explain the effect that changing the parameter mu has on the shape of the normal probability distribution.

Page 13

1. The population distribution is the probability distribution of the: A) whole population of a country C) population means B) population data D) population probabilities Ans: B Difficulty level: low Objective: Explain the difference between population and sampling distributions.

2. The sampling distribution is the probability distribution of a: A) sample C) sample without replacement B) sample with replacement D) sample statistic Ans: D Difficulty level: low Objective: Explain the difference between population and sampling distributions.

3. The probability distribution of a sample statistic is the: A) frequency distribution of that statistic C) sampling distribution of that statistic B) binomial distribution of that statistic D) Poisson distribution of that statistic Ans: C Difficulty level: low Objective: Explain the difference between population and sampling distributions.

4. A population contains 8 members. The total number of samples of size 4 that you can select (without replacement) from this population is: Ans: 70 Difficulty level: medium Objective: Interpret a sampling distribution.

5. A population contains 14 members. The total number of samples of size 8 that you can select (without replacement) from this population is: Ans: 3,003 Difficulty level: medium Objective: Interpret a sampling distribution.

6. The sampling error is: A) an error that occurs during collection, recording, and tabulation of data B) the difference between the value of a sample statistic and the value of the corresponding population parameter C) an error that occurs when a sample of fewer than 30 members is drawn D) an error that occurs when a sample of 30 or more members is drawn Ans: B Difficulty level: medium Objective: Compute a sampling error.

7. An error that occurs because of chance is called: A) nonsampling error B) sampling error C) mean error D) probability error Ans: B Difficulty level: medium Objective: Distinguish between sampling and nonsampling errors.

Page 1

Chapter 7

8. An error that occurs because of human mistakes is called: A) nonsampling error B) sampling error C) mean error D) probability error Ans: A Difficulty level: low Objective: Identify sources of nonsampling errors.

9. The mean age of all students at a university is 24 years. The mean age of a random sample of 100 students selected from this university is 23.6 years. The difference (23.6 24 = -0.4) is the: A) probability error C) sampling error B) nonsampling error D) population error Ans: C Difficulty level: low Objective: Compute a sampling error.

10. The mean weekly earnings of all employees of a company are $822. The mean weekly earnings of a random sample of 25 employees selected from this company is $837. The difference ($837 - $822 = $15) is the: A) probability error C) sampling error B) nonsampling error D) population error Ans: C Difficulty level: low Objective: Compute a sampling error.

11. The mean price of all magazines published in the United States is $3.65. The mean price of a random sample of 16 magazines is $4.30. The sampling error is: Ans: $0.65 Difficulty level: low Objective: Compute a sampling error.

12. The mean age of all cars registered in the United States is 7.50 years. The mean age of a random sample of 1,000 cars is 6.9. The sampling error is: Ans: –0.6 Difficulty level: low Objective: Compute a sampling error.

13. The mean of the sampling distribution of the sample mean is: A) always equal to the sample mean B) sometimes equal to the population mean C) always equal to the population mean D) always equal to the sampling procedure Ans: C Difficulty level: low Objective: Determine the mean of x-bar.

14. The mean of the sampling distribution of the sample mean is the mean of: A) the means of all possible samples of the same size taken from the population B) the frequency distribution of the population C) the means of all frequency distributions D) one sample Ans: A Difficulty level: medium Objective: Determine the mean of x-bar.

Page 2

Chapter 7

15. If n N is less than or equal to 0.05, the standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation: A) divided by the square of the sample size B) divided by the sample size C) divided by the square root of the sample size D) multiplied by the sample size Ans: C Difficulty level: low Objective: Determine the standard deviation of x-bar.

16. When the sample size is greater than 1, the standard deviation of the sampling distribution of the sample means is always: A) equal to the standard deviation of the population B) smaller than the standard deviation of the population C) greater than the standard deviation of the population D) none of these Ans: B Difficulty level: low Objective: Determine the standard deviation of x-bar.

17. As the sample size increases, the standard deviation of the sampling distribution of the sample mean: A) increases B) decreases C) remains the same D) Unable to determine Ans: B Difficulty level: low Objective: Determine the standard deviation of x-bar.

18. The standard deviation of the sampling distribution of the sample mean for a sample size of n drawn from a population with a mean of  and a standard deviation of  is: A)  B)  C)  D)  2 2n n n n Ans: C Difficulty level: low Objective: Determine the standard deviation of x-bar.

19. For a continuous random variable x, the population mean and the population standard deviation are 82 and 18, respectively. You take a simple random sample of 25 elements from this population. The mean of the sampling distribution of the sample mean is: Ans: 82 Difficulty level: low Objective: Determine the mean of x-bar.

20. For a continuous random variable x, the population mean and the population standard deviation are 139 and 9, respectively. You take a simple random sample of 36 elements from this population. The mean of the sampling distribution of the sample mean is: Ans: 139 Difficulty level: low Objective: Determine the mean of x-bar.

Page 3

Chapter 7

21. For a continuous random variable x, the population mean and the population standard deviation are 69 and 15, respectively. Assuming n N  0.05 , the standard deviation of the sampling distribution of the sample mean for a sample of 16 elements taken from this population, rounded to two decimals, is: Ans: 3.75 Difficulty level: low Objective: Determine the standard deviation of x-bar.

22. For a continuous random variable x, the population mean and the population standard deviation are 95 and 40, respectively. Assuming n N  0.05 , the standard deviation of the sampling distribution of the sample mean for a sample of 49 elements taken from this population, rounded to two decimals, is: Ans: 5.71 Difficulty level: low Objective: Determine the standard deviation of x-bar.

23. The daily sales at a convenience store have a mean of $1,297 and a standard deviation of $134. The mean of the sampling distribution of the mean sales of a sample of 17 days for this convenience store is: Ans: $1,297 Difficulty level: low Objective: Determine the mean of x-bar.

24. The weights of all babies born at a hospital have a mean of 7.3 pounds and a standard deviation of 0.65 pounds. The mean of the sampling distribution of the mean weight of a sample of 41 babies born at this hospital is: Ans: 7.3 Difficulty level: low Objective: Determine the mean of x-bar.

25. The daily sales at a convenience store have a mean of $1280 and a standard deviation of $172. Assuming n N  0.05 , the standard deviation of the sampling distribution of the mean sales of a sample of 16 days for this convenience store, rounded to two decimal places, is: Ans: $43.00 Difficulty level: low Objective: Determine the standard deviation of x-bar.

26. The weights of all babies born at a hospital have a mean of 7.4 pounds and a standard deviation of 0.66 pounds. Assuming n N  0.05 , the standard deviation of the sampling distribution of the mean weight of a sample of 32 babies born at this hospital, rounded to three decimal places, is: Ans: 0.117 Difficulty level: low Objective: Determine the standard deviation of x-bar.

Page 4

Chapter 7

27. If the population from which samples are drawn is normally distributed, then the sampling distribution of the sample mean is: A) not normally distributed B) normally distributed if n is 30 or larger C) always normally distributed D) normally distributed if n is less than 30 Ans: C Difficulty level: low Objective: Identify the characteristics of the sampling distribution of x-bar from a normal population.

28. If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is: A) never normally distributed B) approximately normally distributed if n is 30 or larger C) always normally distributed D) approximately normally distributed if n is less than 30 Ans: B Difficulty level: low Objective: Describe the shape of the sampling distribution of x-bar from a non-normal population.

29. According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal, irrespective of the shape of the population distribution, if: A) n is 30 or larger C) np and nq are both greater than 5 B) n is less than 30 D) n is 50 or larger Ans: A Difficulty level: low Objective: Describe the shape of the sampling distribution of x-bar from a non-normal population.

30. To apply the Central Limit Theorem to the sampling distribution of the sample mean, the required sample is typically large enough if: A) n is greater than 50 C) n is less than 30 B) n is 50 or less D) n is 30 or larger Ans: D Difficulty level: low Objective: Explain the effect of sample size on the standard deviation of x-bar.

31. A continuous random variable x has a normal distribution with a mean of 90 and a standard deviation of 15. The sampling distribution of the sample mean for a sample of 16 elements taken from this population is: A) not normal B) normal C) skewed to the right D) skewed to the left Ans: B Difficulty level: low Objective: Identify the characteristics of the sampling distribution of x-bar from a normal population.

Page 5

Chapter 7

32. A continuous random variable x has a right-skewed distribution with a mean of 45 and a standard deviation of 6. The sampling distribution of the sample mean for a sample of 25 elements taken from this population is: A) approximately normal C) skewed to the right B) normal D) skewed to the left Ans: C Difficulty level: medium Objective: Describe the shape of the sampling distribution of x-bar from a non-normal population.

33. A continuous random variable x has a right-skewed distribution with a mean of 80 and a standard deviation of 12. The sampling distribution of the sample mean for a sample of 50 elements taken from this population is: A) approximately normal C) skewed to the right B) not normal D) skewed to the left Ans: A Difficulty level: low Objective: Describe the shape of the sampling distribution of x-bar from a non-normal population.; Explain the effect of sample size on the standard deviation of x-bar.

34. A continuous random variable x has a left-skewed distribution with a mean of 130 and a standard deviation of 22. The sampling distribution of the sample mean for a sample of 16 elements taken from this population is: A) approximately normal C) skewed to the right B) normal D) skewed to the left Ans: D Difficulty level: medium Objective: Describe the shape of the sampling distribution of x-bar from a non-normal population.

35. A continuous random variable x has a left-skewed distribution with a mean of 155 and a standard deviation of 28. The sampling distribution of the sample mean for a sample of 75 elements taken from this population is: A) approximately normal C) skewed to the right B) not normal D) skewed to the left Ans: A Difficulty level: low Objective: Describe the shape of the sampling distribution of x-bar from a non-normal population.; Explain the effect of sample size on the standard deviation of x-bar.

36. A population has a mean of 98.2 and a standard deviation of 25.2. Assuming n N  0.05 , the probability, rounded to four decimal places, that the sample mean of a sample of size 89 elements selected from this population will be between 91 and 97 is: Ans: 0.3231 Difficulty level: medium Objective: Apply the Central Limit Theorem to compute the probability of x-bar being in an interval, given n ? 30.

Page 6

Chapter 7

37. A population has a mean of 60.5 and a standard deviation of 13.5. Assuming n N  0.05 , the probability, rounded to four decimal places, that the sample mean of a sample of size 35 elements selected from this populations will be between 62.5 and 67.1 is: Ans: 0.1885 Difficulty level: medium Objective: Apply the Central Limit Theorem to compute the probability of x-bar being in an interval, given n ? 30.

38. A population has a normal distribution with a mean of 51.4 and a standard deviation of 8.4. Assuming n N  0.05 , the probability, rounded to four decimal places, that the sample mean of a sample of size 18 elements selected from this populations will be more than 51.15 is: Ans: 0.5502 Difficulty level: medium Objective: Compute the probability of x-bar being in an interval, assuming a normal population.

39. A population has a normal distribution with a mean of 79.6 and a standard deviation of 13.3. Assuming n N  0.05 , the probability, rounded to four decimal places, that the sample mean of a sample of size 18 elements selected from this populations will be less than 80.1 is: Ans: 0.5634 Difficulty level: medium Objective: Compute the probability of x-bar being in an interval, assuming a normal population.

40. The number of hours spent per week on household chores by all adults has a mean of 28.1 hours and a standard deviation of 6.0 hours. The probability, rounded to four decimal places, that the mean number of hours spent per week on household chores by a sample of 53 adults will be more than 26.75 is: Ans: 0.9493 Difficulty level: medium Objective: Apply the Central Limit Theorem to compute the probability of x-bar being in an interval, given n ? 30.

41. The time spent commuting from home to work for all employees of a very large company has a normal distribution with a mean of 43.4 minutes and a standard deviation of 12.1 minutes. The probability, rounded to four decimal places, that the mean time spent commuting from home to work by a sample of 21 employees will be between 43.26 and 49.35 minutes is: Ans: 0.5090 Difficulty level: medium Objective: Compute the probability of x-bar being in an interval, assuming a normal population.

42. If you divide the number of elements in a population with a specific characteristic by the total number of elements in the population, the dividend is the population: A) mean B) proportion C) distribution D) sampling distribution Ans: B Difficulty level: low Objective: Identify and compute population and sample proportions.

Page 7

Chapter 7

43. If you divide the number of elements in a sample with a specific characteristic by the total number of elements in the sample, the dividend is the: A) sample mean C) sample distribution B) sample proportion D) sampling distribution Ans: B Difficulty level: low Objective: Identify and compute population and sample proportions.

44. The mean of the sampling distribution of the sample proportion is equal to the population: A) mean B) mean divided by n C) proportion D) proportion divided by n Ans: C Difficulty level: low Objective: Demonstrate an understanding of the relationship between population and sample proportions and relative frequency.

45. The standard deviation of the sampling distribution of the sample proportion is equal to: A) the population standard deviation divided by the square root of n B) the population standard deviation divided by n C) the square root of pq / n pq / n D) Ans: C Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of p-hat.

46. In the case of proportion, the sample size is large if: A) n is greater than or equal to 30 C) n is less than 30 B) np and nq are both less than 5 D) np and nq are both greater than 5 Ans: D Difficulty level: low Objective: Determine the shape of the sampling distribution of p-hat.

47. The sampling distribution of the sample proportion is approximately normal if: A) n is greater than or equal to 30 C) np and nq are both greater than 5 B) np and nq are both greater than 10 D) np and nq are both less than 5 Ans: C Difficulty level: low Objective: Determine the shape of the sampling distribution of p-hat.

48. A company has 411 employees and 104 of them are college graduates. The proportion of employees of this company who are college graduates, rounded to three decimal places, is: Ans: 0.253 Difficulty level: low Objective: Identify and compute population and sample proportions.

49. A class of 61 students has 15 seniors. The proportion of students in this class who are seniors, rounded to three decimal places, is: Ans: 0.246 Difficulty level: low Objective: Identify and compute population and sample proportions.

Page 8

Chapter 7

50. In a sample of 859 adults, 437 are in favor of banning all advertisements relating to alcohol. The proportion of these adults who are in favor of banning all advertisements relating to alcohol, rounded to three decimal places, is: Ans: 0.509 Difficulty level: low Objective: Identify and compute population and sample proportions.

Use the following to answer questions 51-52: Forty percent of all students at a large university live on campus. Suppose you extract a sample of 115 students from this university. The sample proportion is the proportion of students in this sample who live on campus.

51. The mean of the sampling distribution of this sample proportion is: Ans: 0.4 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of p-hat.

52. The standard deviation of the sampling distribution of this sample proportion, rounded to four decimal places, is: Ans: 0.0457 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of p-hat.

Use the following to answer questions 53-54: Thirty-five percent of all adults read at least one newspaper daily. Suppose you select a sample of 486 adults. The sample proportion is the proportion of adults in this sample who read at least one newspaper daily.

53. The mean of the sampling distribution of this sample proportion is: Ans: 0.35 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of p-hat.

54. The standard deviation of the sampling distribution of this sample proportion, rounded to four decimal places, is: Ans: 0.0216 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of p-hat.

Page 9

Chapter 7

55. Suppose the proportion of elements of a population that possess a certain characteristic is 0.62. Assuming n N  0.05 , the probability that the sample proportion for a sample of 120 elements drawn from this population is between .62 and .67, rounded to four decimal places, is approximately: Ans: 0.3704 Difficulty level: medium Objective: Compute the probability of p-hat being in an interval.

56. Suppose the proportion of elements of a population that possess a certain characteristic is 0.34. Assuming n N  0.05 , the probability that the sample proportion for a sample of 472 elements drawn from this population is more than .33, rounded to four decimal places, is approximately: Ans: 0.6767 Difficulty level: medium Objective: Compute the probability of p-hat being in an interval.

Use the following to answer questions 57-58: Suppose that 6.5% or all persons are allergic to penicillin . A sample of 561 persons is selected.

57. The probability that less than 8% of persons in the sample of will be allergic to penicillin, rounded to four decimal places, is approximately: Ans: 0.9252 Difficulty level: medium Objective: Compute the probability of p-hat being in an interval.

58. The probability that 7.5% to 9% of persons in a the sample will be allergic to penicillin, rounded to four decimal places, is approximately: Ans: 0.1602 Difficulty level: medium Objective: Compute the probability of p-hat being in an interval.

Use the following to answer questions 59-60: A study shows 18.0% of all adult males did not visit their physicians' offices last year. A sample of 623 adult males is selected.

59. The probability that more than 18% of adult males in the sample did not visit their physicians' offices last year, rounded to four decimal places, is approximately: Ans: 0.5000 Difficulty level: medium Objective: Compute the probability of p-hat being in an interval.

Page 10

Chapter 7

60. The probability that less than 22.5% of adult males in the sample did not visit their physicians' offices last year, rounded to four decimal places, is approximately: Ans: 0.9983 Difficulty level: medium Objective: Compute the probability of p-hat being in an interval.

61. The following table shows the population probability distribution of x, the random variable representing the price per ticket, in dollars, for 20 upcoming concerts at a certain community's civic center.

Price per Ticket ($) 45 48 50 53 55

P(x) 0.20 0.20 0.15 ?

0.25

How many of the 20 concerts will cost $53 per ticket?

Ans: 4 Difficulty level: low Objective: Use the sampling distribution of p-hat to find the probability of an event in the context of an application.

62. A population consists of five elements: 5, 6, 8, 10, and 13. You choose a random sample of three elements from this population (without replacement). Which of the following is not a possible value of the sample mean?

A) 6.33 B) 8.00 C) 9.33 D) 10.67 Ans: D Difficulty level: medium Objective: Determine the mean of x-bar.

63. You select 15 people at random from a population of 10,000 and ask them how many movies they have rented in the past month. Their responses are: 4

0

6

0

8

3

7

6

5

0

1

4

2

9

5

You know that the mean number of movies rented in the past month by the population is 5.0. Assuming that you made no non-sampling errors, what is the sampling error for the mean?

Ans: –1 Difficulty level: medium Objective: Compute a sampling error.

Page 11

Chapter 7

64. Suppose you are analyzing four different brands of soda. The sodium content, in milligrams, of one can of each of these brands has a distribution with a mean of 45.2 mg and a standard deviation of 8.8600 mg. You take a random sample of 2 cans from a large supply of cans including all four brands of soda. Let x be the mean of this sample. What are the mean and standard deviation of the sampling distribution of x ?

Part A: The mean is 45.20 (rounded to two decimal places) Part B: The standard deviation is 6.2650 (rounded to four decimal places) Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of x-bar from a normal population.

65. The number of hot dogs sold per game at one concession stand at a baseball park is normally distributed with  = 23,750 and  = 106. You select 13 games at random, and the mean number of hot dogs sold, x , is denoted. What is the standard deviation of x , rounded to three decimal places?

Ans: 29.399 Difficulty level: low Objective: Determine the standard deviation of x-bar.

66. For a sample from a normal distribution with standard deviation  , the standard deviation of the sampling distribution of the sample mean is  /3. What is the size of the sample?

Ans: 9 Difficulty level: medium Objective: Determine the standard deviation of x-bar.

67. All 1,035 members at a country club take part in a contest to see who can drive a golf ball the farthest. Each member takes three swings, and his/her best drive is entered into the contest. The distances of the drives entered into the contest have a mean of 188.3 yards and a standard deviation of 16.2 yards. You select a sample of 43 drives, what is the probability, rounded to four decimal places, that the mean of the sample exceeds 192 yards?

Ans: 0.0671 Difficulty level: medium Objective: Compute the probability of x-bar being in an interval, assuming a normal population.

68. There are 2,000 bicycles in a community. The owners of 1,250 of these bicycles also own locks for the bikes. A sample of 184 bicycles is chosen, and it just so happens that the proportion of bicycles in the sample that have locks is the same as that for the entire community. How many of the bicycles in the sample have locks?

Ans: 115 Difficulty level: medium Objective: Identify and compute population and sample proportions.

Page 12

Chapter 7

69. You ask 2,500 actors in the Screen Actors Guild (SAG) if they have ever appeared in a production of Shakespeare's King Lear. 1,225 of them say "yes", while the others say "no". The value p is the proportion of the actors who have appeared in King Lear. You next draw a random sample of 11 actors from the SAG. What are the mean and standard deviation of the sample proportion? Round the mean to two decimal places and the standard deviation to four decimal places.

Part A: The mean is 0.49 (rounded to two decimal places) Part B: The standard deviation is 0.1507 (rounded to four decimal places) Difficulty level: low Objective: Construct the sampling distribution of p-hat.

70. A company has 15,000 employees and 10,800 of them have completed a particular training course. Management decides to choose a random sample from all employees.

What is the minimum number of employees that must be in the sample in order to use the Central Limit Theorem to approximate the distribution of the proportion in the sample who have taken the training course?

Ans: 18 Difficulty level: medium Objective: Construct the sampling distribution of p-hat.

71. Extensive data suggest that the number of overtime hours paid by a large company per month can be modeled as distribution with mean 3.5 and standard deviation 1.4.

If P1 is the probability that the mean of a sample of size 55 lies in the interval (2.9, 4.1) and P2 is the probability that the mean of a sample of size 110 lies in the interval (2.9, 4.1), then A) P1 = P2 B) P1 > P2 C) P1 < P2 D) P1 = 2P2 Ans: C Difficulty Level: Medium Difficulty level: medium Objective: Compute the probability of x-bar being in an interval, assuming a normal population.

Page 13

Chapter 7

72. Suppose the number of books consulted by a student last weekend has distribution

x 0 1 2

Probability 0.20 0.60 0.20

Let X1 and X2 be independent and each have the same distribution as the population.

Determine the missing elements in the table for the sampling distribution of X = ( X1 + X 2 ) / 2 . x Probability 0.0 0.0400 0.5 1.0 1.5 2.0 0.0400 Ans:

x 0.0 0.5 1.0 1.5 2.0

Probability 0.0400 0.2400 0.4400 0.2400 0.0400

Difficulty Level: Medium Difficulty level: medium Objective: Demonstrate an understanding of the relationship between the sampling distribution and the population distribution.

73. A continuous random variable x has a normal distribution with a mean of 51 and a standard deviation of 26. The sampling distribution of the sample mean for a sample of 16 elements has what mean and standard deviation?

Ans: Mean of the distribution of the sampling mean = 51 Standard deviation of the distribution of the sampling mean = 6.5 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of x-bar from a normal population.

Page 14

Chapter 7

74. A continuous random variable x has a right-skewed distribution with a mean of 72 and a standard deviation of 36. The sampling distribution of the sample mean for a sample of 100 elements has what mean and standard deviation?

Ans: Mean of the distribution of the sampling mean = 72 Standard deviation of the distribution of the sampling mean = 3.6 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of x-bar from a normal population.

75. A continuous random variable x has a left-skewed distribution with a mean of 101 and a standard deviation of 72. The sampling distribution of the sample mean for a sample of 64 elements has what mean and standard deviation?

Ans: Mean of the distribution of the sampling mean = 101 Standard deviation of the distribution of the sampling mean = 9 Difficulty level: low Objective: Compute the mean, standard deviation, and sampling distribution of x-bar from a normal population.

76. A continuous random variable x has a normal distribution with a mean of 65 and a standard deviation of 21. In the sampling distribution of the sample mean for a sample of 25 elements, what is the z-score for a sample mean of 68.36?

Ans: 0.8 Difficulty level: low Objective: Compute the z-value for a value of x-bar.

Page 15

1. Estimation is a procedure by which we assign a numerical value or numerical values to the: A) population parameter based on the information collected from a sample B) sample statistic based on the information collected from a sample C) population parameter based on the information collected from a population D) sample statistic based on the information collected from a population Ans: A Difficulty level: low Objective: Describe estimation.

2. The values assigned to a population parameter based on the value(s) of a sample statistic are: A) the probabilities C) a sampling distribution B) the probability distribution D) estimate(s) Ans: D Difficulty level: low Objective: Describe estimation.

3. The sample statistic used to estimate a population parameter is a(n): A) random variable B) qualitative variable C) estimator D) parameter Ans: C Difficulty level: low Objective: Define a point estimate of a population parameter.

4. The single value of a sample statistic that we assign to the population parameter is a: A) single estimate B) unique estimate C) point estimate D) singular estimate Ans: C Difficulty level: low Objective: Define a point estimate of a population parameter.

5. The confidence level of an interval estimate is denoted by: A)  B) (1 −  ) 100% C)  D) (1 −  ) 100% Ans: B Difficulty level: low Objective: Define interval estimation of a population parameter.

6. For most distributions, we can use the normal distribution to make a confidence interval for a population mean provided that the population standard deviation  is known and the sample size is: A) greater than 30 C) greater than or equal to 30 B) less than 25 D) greater than 100 Ans: C Difficulty level: low Objective: Compute a point estimate of the population mean.

7. The margin of error for the population mean, assuming  is known, is: A) z multiplied by the population standard deviation B) z multiplied by t C) z multiplied by the standard deviation of the sample mean D) z multiplied by the sample mean Ans: C Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n < 30, assuming a normal population.

Page 1

Chapter 8

8. The z value for a 90% confidence interval for the population mean with  known is: A) 2.05 B) 1.645 C) 2.17 D) 1.60 Ans: B Difficulty level: low Objective: Compute a point estimate of the population mean.

9. The z value for a 85% confidence interval for the population mean with  known is: A) 1.96 B) 2.33 C) 1.44 D) 2.58 Ans: C Difficulty level: low Objective: Compute a point estimate of the population mean.

10. The width of a confidence interval depends on the size of the: A) population mean B) margin of error C) sample mean D) none of these Ans: B Difficulty level: medium Objective: Explain the relationships among the width, sample size, and confidence level of a confidence interval.

11. You can decrease the width of a confidence interval by: A) lowering the confidence level or decreasing the sample size B) increasing the confidence level or decreasing the sample size C) lowering the confidence level or increasing the sample size D) increasing the confidence level or increasing the sample size Ans: C Difficulty level: medium Objective: Explain the relationships among the width, sample size, and confidence level of a confidence interval.

12. To decrease the width of a confidence interval, we should always prefer to: A) lower the confidence level C) increase the sample size B) increase the confidence level D) decrease the sample size Ans: C Difficulty level: medium Objective: Explain the relationships among the width, sample size, and confidence level of a confidence interval.

13. A sample of size 97 from a population having standard deviation  = 7 produced a mean of 47. The 99% confidence interval for the population mean (rounded to two decimal places) is: Part A: The lower limit is 45.17 Part B: The upper limit is 48.83 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n >= 30.

14. A sample of size 65 from a population having standard deviation  = 55 produced a mean of 234.00. The 95% confidence interval for the population mean (rounded to two decimal places) is: Part A: The lower limit is 220.63 Part B: The upper limit is 247.37 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n >= 30.

Page 2

Chapter 8

15. A random sample of 82 customers, who visited a department store, spent an average of $71 at this store. Suppose the standard deviation of expenditures at this store is  = $19.

The 98% confidence interval for the population mean (rounded to two decimal places) is: Part A: The lower limit is $66.11 Part B: The upper limit is $75.89 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n >= 30.

16. The mean IQ score of a sample of 61 students selected from a high school is 87. Suppose the standard deviation of IQ's at this school is  = 8.4. The 99% confidence interval for the population mean (rounded to two decimal places) is: Part A: The lower limit is 84.23 Part B: The upper limit is 89.77 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n >= 30.

17. The mean federal income tax paid last year by a random sample of 45 persons selected from a city was $4,242. Suppose the standard deviation of tax paid in this city is  = $991. The 95% confidence interval for the population mean (rounded to two decimal places) is: Part A: The lower limit is $3,952.45 Part B: The upper limit is $4,531.55 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n ? 30.

18. We use the t distribution to make a confidence interval for the population mean if the population from which the sample is drawn is (approximately) normally distributed, the population standard deviation is unknown, and the sample size is at least: A) 30 B) 100 C) 50 D) 2 Ans: D Difficulty level: low Objective: Distinguish between a t-distribution and a normal distribution.

19. Which of the following conditions is required to use the t distribution to make a confidence interval for the population mean?

A) The population from which the sample is drawn is (approximately) normally distributed.

B) The sample size is at least 30.

C) The population from which the sample is drawn has a t distribution.

D) The population standard deviation is known.

Ans: A Difficulty level: low Objective: Distinguish between a t-distribution and a normal distribution.

Page 3

Chapter 8

20. When making a confidence interval for the population mean using the t procedures, the degrees of freedom for the t distribution are: A) n B) n - 2 C) n + 1 D) n - 1 Ans: D Difficulty level: low Objective: Distinguish between a t-distribution and a normal distribution.

21. The value of t for 19 degrees of freedom and a 98% confidence interval is: A) 2.861 B) 2.539 C) -2.539 D) 1.328 Ans: B Difficulty level: low Objective: Read the t-distribution table.

22. The value of t for 19 degrees of freedom and a 90% confidence interval is: A) 1.729 B) -1.729 C) 2.539 D) -2.539 Ans: A Difficulty level: low Objective: Read the t-distribution table.

23. A sample of 20 elements produced a mean of 91.4 and a standard deviation of 11.16.

Assuming that the population has a normal distribution, the 90% confidence interval for the population mean is: Part A: the lower limit is 87.09 (rounded to two decimal places) Part B: the upper limit is 95.71 (rounded to two decimal places) Difficulty level: medium Objective: Construct a confidence interval for mu when sigma is unknown and n < 30.

24. A sample of 25 elements produced a mean of 123.4 and a standard deviation of 18.32.

Assuming that the population has a normal distribution, the 90% confidence interval for the population mean, rounded to two decimal places, is: Part A: the lower limit is 117.13 Part B: the upper limit is 129.67 Difficulty level: medium Objective: Construct a confidence interval for mu when sigma is unknown and n < 30.

25. A random sample of 23 tourists who visited Hawaii this summer spent an average of $1,456.0 on this trip with a standard deviation of $263.00. Assuming that the money spent by all tourists who visit Hawaii has an approximate normal distribution, the 95% confidence interval for the average amount of money spent by all tourists who visit Hawaii, rounded to two decimal places, is: Part A: The lower limit is $1,342.26 Part B: The upper limit is $1,569.74 Difficulty level: medium Objective: Construct a confidence interval for mu when sigma is unknown and n < 30.

Page 4

Chapter 8

26. A random sample of 12 life insurance policy holders showed that the mean value of their life insurance policies is $210,000 with a standard deviation of $44,600. Assuming that the values of life insurance policies for all such policy holders are approximately normally distributed, the 99% confidence interval for the mean value of all life insurance policies, rounded to two decimal places, is: Part A: the lower limit is $170,010.53 Part B: the upper limit is $249,989.47 Difficulty level: medium Objective: Construct a confidence interval for mu when sigma is unknown and n < 30.

27. A random sample of 8 houses selected from a city showed that the mean size of these houses is 1,881.0 square feet with a standard deviation of 328.00 square feet. Assuming that the sizes of all houses in this city have an approximate normal distribution, the 90% confidence interval for the mean size of all houses in this city, rounded to two decimal places, is: Part A: the lower limit is 1,661.25 Part B: the upper limit is 2,100.75 Difficulty level: medium Objective: Construct a confidence interval for mu when sigma is unknown and n < 30.

28. A random sample of 450 produced a sample proportion of 0.71. The 95% confidence interval for the population proportion, rounded to four decimal places, is: Part A: the lower endpoint is 0.6681 Part B: the upper endpoint is 0.7519 Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

29. A random sample of 188 produced a sample proportion of 0.40. The 98% confidence interval for the population proportion, rounded to four decimal places, is: Part A: the lower endpoint is 0.3168 Part B: the upper endpoint is 0.4832 Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

30. A random sample of 1,100 adults showed that 32% of them are smokers. Based on this sample, the 90% confidence interval for the proportion of all adults who are smokers, rounded to four decimal places, is: Part A: the lower endpoint is 0.2968 Part B: the upper endpoint is 0.3432 Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

Page 5

Chapter 8

31. In a random sample of 562 items produced by a machine, the quality control staff found 6.6% to be defective. Based on this sample, the 95% confidence interval for the proportion of defective items in all items produced by this machine, rounded to four decimal places, is: Part A: the lower endpoint is 0.0455 Part B: the upper endpoint is 0.0865 Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

32. A random sample of 983 families selected from a large city showed that 17.5% of them make $100,000 or more per year. Based on this sample, the 99% confidence interval for the proportion of all families living in this city who make $100,000 or more per year, rounded to four decimal places, is: Part A: the lower endpoint is 0.1437 Part B: the upper endpoint is 0.2063 Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

33. A random sample of 765 persons showed that 13.5% do not have any health insurance.

Based on this sample, the 95% confidence interval for the proportion of all persons who do not have any health insurance, rounded to four decimal places, is: Part A: the lower endpoint is 0.1108 Part B: the upper endpoint is 0.1592 Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

34. A researcher wants to make a 99% confidence interval for a population mean. She wants the margin of error to be within 4.6 of the population mean. The population standard deviation is 18.22. The sample size that will yield a margin of error within 4.6 of the population mean is: Ans: 105 Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level.

35. A researcher wants to make a 95% confidence interval for a population mean. She wants the margin of error to be within 1.9 of the population mean. The population standard deviation is 11.07. The sample size that will yield a margin of error within 1.9 of the population mean is: Ans: 131 Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level.

Page 6

Chapter 8

36. A researcher wants to estimate the mean age of all Business Week readers at a 99% confidence level. She wants the margin of error to be within 3.1 years of the population mean. The standard deviation of ages of all Business Week readers is 10.04 years. The sample size that will yield a margin of error within 3.1 of the population mean is: Ans: 70 Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level.

37. A company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level. The margin of error is to be within 0.025 ounces of the population mean. The population standard deviation is 0.096 ounces.

The sample size that will yield a margin of error within 0.025 ounces of the population mean is: Ans: 57 Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level.

38. A researcher wants to make a 99% confidence interval for a population proportion. A preliminary sample produced the sample proportion of 0.680. The sample size that would limit the margin of error to be within 0.024 of the population proportion is: Ans: 2,515 Difficulty level: medium Objective: Determine the sample size for a given estimation of p, given preliminary sample results.

39. A researcher wants to make a 99% confidence interval for a population proportion. The most conservative estimate of the sample size that would limit the margin of error to be within 0.033 of the population proportion is: Ans: 1,529 Difficulty level: medium Objective: Determine the sample size for a given estimation of p.

40. A company wants to estimate, at a 95% confidence level, the proportion of all families who own its product. A preliminary sample showed that 30.0% of the families in this sample own this company's product. The sample size that would limit the margin of error to be within 0.045 of the population proportion is: Ans: 399 Difficulty level: medium Objective: Determine the sample size for a given estimation of p, given preliminary sample results.

41. A company wants to estimate, at a 95% confidence level, the proportion of all families who own its product. The most conservative estimate of the sample size that would limit the margin of error to be within 0.046 of the population proportion is: Ans: 454 Difficulty level: medium Objective: Determine the sample size for a given estimation of p.

Page 7

Chapter 8

42. The Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all households that receive welfare. The most conservative estimate of the sample size that would limit the margin of error to be within 0.030 of the population proportion is: Ans: 757 Difficulty level: medium Objective: Determine the sample size for a given estimation of p.

43. The Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all households that receive welfare. A preliminary sample showed that 18.5% of households in this sample receive welfare. The sample size that would limit the margin of error to be within 0.036 of the population proportion is: Ans: 317 Difficulty level: medium Objective: Determine the sample size for a given estimation of p, given preliminary sample results.

44. Which of the following is not part of the procedure for estimating the value of a population parameter?

A) Selecting a sample B) Collecting the required information from the members of the sample C) Calculating the value of the sample statistic D) Calculating the exact value of the corresponding population parameter Ans: D Difficulty level: low Objective: Describe estimation.

45. You are estimating the mean waiting time in line at a particular fast-food restaurant. You ask 30 customers, at varying times of the day, how long they waited in line before placing their order. You then take the average of these values and use this average to estimate the mean waiting time for all customers. The average of the 30 values is an example of a(n): A) Chebyshev estimate C) interval estimate B) point estimate D) confidence estimate Ans: B Difficulty level: low Objective: Define a point estimate of a population parameter.

46. A scientist is estimating the mean lifetime of a newly-discovered insect. From a sample of 88 insects, she finds a sample mean of 49.2 days. Suppose that the population standard deviation of all lifetimes is 2.500 days. What are the boundaries for a 90% confidence interval for the mean lifetime of the insect, rounded to two decimal places?

Part A: The lower limit is 48.76 Part B: The upper limit is 49.64 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n ? 30.

Page 8

Chapter 8

47. The Eks Survey Company employs 2000 people to conduct telephone surveys. Because many people don't like to answer such surveys, many "hang-ups" (whereby the person hangs up without completing the survey) occur. The owner of Eks wants to determine the mean number of "hang-ups" per employee on a particular day, using 95% confidence. He samples 50 employees, and finds that the mean number of "hang-ups" on that day was 41.0. Suppose that the standard deviation of the number of "hang-ups" for all employees is 21.8 What is the value of the margin of error? (round to four decimal places) Ans:  6.0427 Difficulty level: medium Objective: Develop a confidence interval for mu when sigma is known and n ? 30.

48. We are using the mean of a sample as a point estimate for the mean of a normal distribution with a standard deviation of 5. The margin of error, with 95% confidence, for this estimate is 0.860. What is the sample size?

Ans: 130 Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level. n −1 . If the standard deviation is equal to n−3 1.1055, what is the value of the t critical value for a 90% confidence interval?

Ans: 1.782 Difficulty level: medium Objective: Read the t-distribution table.

49. A t distribution has a standard deviation of

50. Which of the following is not an acceptable condition for using the t distribution to make a confidence interval for  ?

A) The population from which the sample is drawn is right-skewed B) The population from which the sample is drawn is normal C) The population standard deviation is unknown D) The population distribution has a mean of zero Ans: A Difficulty level: low Objective: Distinguish between a t-distribution and a normal distribution.

51. Each employee of a large company is encouraged to contribute, through payroll deduction, to an international charity. Annual contributions per employee follow (approximately) a normal distribution. You take a random sample of 25 employees and find that the sample mean annual contribution per employee is $501 with a standard deviation of $17.00. What are the boundaries for a 99% confidence interval for the population mean, rounded to two decimal places?

Part A: The lower limit is $491.49 Part B: The upper limit is $510.51 Difficulty level: medium Objective: Construct a confidence interval for mu when sigma is unknown and n < 30.

Page 9

Chapter 8

52. In a 1997 poll of 261 male, married, upper-level managers conducted by Joy Schneer and Frieda Reitman for Fortune magazine, 31% of the men stated that their wives worked either full-time or part-time (Fortune, March 17, 1997). What are the boundaries for a 99% confidence interval for p, the proportion of all male, married, upper-level managers whose wives work?

Part A: The lower limit is 0.2361 (rounded to four decimal places) Part B: The upper limit is 0.3839 (rounded to four decimal places) Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

53. An advisor to the mayor of a large city wants to estimate, within 2.450 minutes, the mean travel time to work for all employees who work within the city limits. He knows that the standard deviation of all travel times is 11.35 minutes. He also wants to achieve a 95% confidence interval. He will poll a random sample of city employees. How many employees should he poll?

Ans: 83 Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level.

54. Determine the sample size n that is required for estimating the population mean. The population standard deviation  and the desired margin of error are specified.  = 150 94% margin of error 3 A) 8,836 B) 8,836 C) 8,835 D) 8,837 Ans: B Difficulty Level: Medium Difficulty level: medium Objective: Determine the sample size to estimate mu with a given confidence level.

55. An employee of the College Board analyzed the mathematics section of the SAT for 97 students and finds x = 30.2 and s = 13.0. She reports that a 97% confidence interval for the mean number of correct answers is (27.336, 33.064). Does the interval (27.336, 33.064) cover the true mean?

Which of the following alternatives is the best answer for the above question?

A) Yes, (27.336, 33.064) covers the true mean.

B) No, (27.336, 33.064) does not cover the true mean.

C) We will never know whether (27.336, 33.064) covers the true mean.

D) The true mean will never be in (27.336, 33.064).

Ans: C Difficulty Level: Medium Difficulty level: medium Objective: Explain the relationships among the width, sample size, and confidence level of a confidence interval.

Page 10

Chapter 8

56. Out of a sample of 639 gasoline purchases at a self-service gas station, 544 were made with a credit or debit card. Obtain the predeterminated margin of error. Round your answer to three decimal places.

Ans: 0.014 Difficulty Level: Medium Difficulty level: medium Objective: Construct a confidence interval for the population proportion using a large sample.

57. In a random sample of 53 items produced by a machine, the quality control staff found 5 of them to be defective. Calculate the point estimate of the population proportion of defective items. Round to 4 decimal places.

Ans: 0.0943 Difficulty level: medium Objective: Compute a point estimate of the population proportion using a large sample.

58. A random sample of 354 persons showed that 306 do not have health insurance.

Calculate the point estimate of the population proportion of persons who do not have health insurance. Round to 4 decimal places.

Ans: 0.8644 Difficulty level: medium Objective: Compute a point estimate of the population proportion using a large sample.

59. The correct formula for the limits of a confidence interval is: A) x − z, x + z

(

B) C) D)

)

( z − margin of error, z + margin of error )

( x − margin of error, x + margin of error ) ( x  -margin of error, x  margin of error )

Ans: C Difficulty level: low Objective: Use the notions of point estimate and margin of error to develop the notion of a confidence interval.

60. True or False. The statement: "The 90% confidence interval for the mean is (29.83 , 50.1)." can be interpreted to mean that the probability that the mean lies in the range (29.83 , 50.1) is 90%.

Ans: False Difficulty level: low Objective: Distinguish between correct and incorrect interpretations of a confidence interval.

Page 11

1. The null hypothesis is a claim about a: A) parameter, where the claim is assumed to be false until it is declared true B) parameter, where the claim is assumed to be true until it is declared false C) statistic, where the claim is assumed to be false until it is declared true D) statistic, where the claim is assumed to be true until it is declared false Ans: B Difficulty level: medium Objective: Define null and alternative hypotheses, giving an example in an applied setting.

2. The alternative hypothesis is a claim about a: A) parameter, where the claim is assumed to be true until it is declared false B) parameter, where the claim is assumed to be true if the null hypothesis is declared false C) statistic, where the claim is assumed to be true if the null hypothesis is declared false D) statistic, where the claim is assumed to be false until it is declared true Ans: B Difficulty level: medium Objective: Define null and alternative hypotheses, giving an example in an applied setting.

3. In a one-tailed hypothesis test, a critical point is a point that divides the area under the sampling distribution of a: A) statistic into one rejection region and one nonrejection region B) parameter into one rejection region and one nonrejection region C) statistic into one rejection region and two nonrejection regions D) parameter into two rejection regions and one nonrejection region Ans: A Difficulty level: low Objective: Explain the differences between a one-tailed and a two-tailed test.

4. In a two-tailed hypothesis test, the two critical points are the points that divide the area under the sampling distribution of a: A) statistic into two rejection regions and one nonrejection region B) parameter into one rejection region and one nonrejection region C) statistic into one rejection region and two nonrejection regions D) parameter into two rejection regions and one nonrejection region Ans: A Difficulty level: low Objective: Explain the differences between a one-tailed and a two-tailed test.

5. In a hypothesis test, a Type I error occurs when: A) a false null hypothesis is rejected C) a false null hypothesis is not rejected B) a true null hypothesis is not rejected D) a true null hypothesis is rejected Ans: D Difficulty level: medium Objective: Distinguish between Type I and Type II errors in a hypothesis test.

Page 1

Chapter 9

6. In a hypothesis test, a Type II error occurs when: A) a false null hypothesis is rejected C) a false null hypothesis is not rejected B) a true null hypothesis is not rejected D) a true null hypothesis is rejected Ans: C Difficulty level: medium Objective: Distinguish between Type I and Type II errors in a hypothesis test.

7. In a hypothesis test, the probability of committing a Type I error is called the: A) confidence level B) confidence interval C) significance level D) beta error Ans: C Difficulty level: low Objective: Distinguish between Type I and Type II errors in a hypothesis test.

8. A one-tailed hypothesis test contains: A) one rejection region and two nonrejection regions B) two rejection regions and one nonrejection region C) two rejection regions and two nonrejection regions D) one rejection region and one nonrejection region Ans: D Difficulty level: low Objective: Distinguish between Type I and Type II errors in a hypothesis test.

9. A two-tailed hypothesis test contains: A) one rejection region and two nonrejection regions B) two rejection regions and one nonrejection region C) two rejection regions and two nonrejection regions D) one rejection region and one nonrejection region Ans: B Difficulty level: low Objective: Distinguish between Type I and Type II errors in a hypothesis test.

10. In a left-tailed hypothesis test, the sign in the alternative hypothesis is: A) not equal to (  ) C) less than (  ) B)

greater than (  )

Ans: C Difficulty level: low region of a hypothesis test.

D)

less than or equal to (  )

Objective: Identify and interpret the rejection

11. In a right-tailed hypothesis test, the sign in the alternative hypothesis is: A) not equal to (  ) C) less than (  ) B)

greater than (  )

Ans: B Difficulty level: low region of a hypothesis test.

D)

less than or equal to (  )

Objective: Identify and interpret the rejection

Page 2

Chapter 9

12. In a two-tailed hypothesis test, the sign in the alternative hypothesis is: A) not equal to (  ) C) less than (  ) B)

greater than (  )

Ans: A Difficulty level: low region of a hypothesis test.

D)

less than or equal to (  )

Objective: Identify and interpret the rejection

13. A researcher wants to test if the mean price of houses in an area is greater than $145,000.

The alternative hypothesis for this example will be that the population mean is: A) equal to $145,000 C) greater than or equal to $145,000 B) not equal to $145,000 D) greater than $145,000 Ans: D Difficulty level: low Objective: Define null and alternative hypotheses, giving an example in an applied setting.

14. A researcher wants to test if the mean price of houses in an area is greater than $175,000.

The null hypothesis for this example will be that the population mean is: A) less than or equal to $175,000 C) greater than or equal to $175,000 B) not equal to $175,000 D) greater than $175,000 Ans: A Difficulty level: low Objective: Define null and alternative hypotheses, giving an example in an applied setting.

15. A researcher wants to test if the mean annual salary of all lawyers in a city is different than $110,000. The alternative hypothesis for this example will be that the population mean is: A) equal to $110,000 C) not equal to $110,000 B) less than to $110,000 D) greater than $110,000 Ans: C Difficulty level: low Objective: Define null and alternative hypotheses, giving an example in an applied setting.

16. A researcher wants to test if the mean annual salary of all lawyers in a city is different than $110,000. The null hypothesis for this example will be that the population mean is: A) equal to $110,000 C) not equal to $110,000 B) less than to $110,000 D) greater than $110,000 Ans: A Difficulty level: low Objective: Define null and alternative hypotheses, giving an example in an applied setting.

17. A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: A) equal to 30 minutes C) less than or equal to 30 minutes B) not equal to 30 minutes D) less than 30 minutes Ans: D Difficulty level: low Objective: Define null and alternative hypotheses, giving an example in an applied setting.

Page 3

Chapter 9

18. A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The null hypothesis for this example will be that the population mean is: A) greater than or equal to 30 minutes C) less than or equal to 30 minutes B) not equal to 30 minutes D) less than 30 minutes Ans: A Difficulty level: low Objective: Define null and alternative hypotheses, giving an example in an applied setting.

19. The p-value is the: A) largest significance level at which the null hypothesis can be rejected B) largest significance level at which the alternative hypothesis can be rejected C) smallest significance level at which the null hypothesis can be rejected D) smallest significance level at which the alternative hypothesis can be rejected Ans: C Difficulty level: medium Objective: Explain the difference between the p-value approach and the critical value approach to hypothesis testing.

20. For a one-tailed test, the p-value is: A) the area under the curve between the mean and the observed value of the sample statistic B) twice the area under the curve between the mean and the observed value of the sample statistic C) the area under the curve to the same side of the value of the sample statistic as is specified in the alternative hypothesis D) twice the area under the curve to the same side of the value of the sample statistic as is specified in the alternative hypothesis Ans: C Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

21. For a two-tailed test, the p-value is: A) the area under the curve between the mean and the observed value of the sample statistic B) twice the area under the curve between the mean and the observed value of the sample statistic C) the area in the tail under the curve on the side which the sample statistic lies D) twice the area in the tail under the curve on the side which the sample statistic lies Ans: D Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

Page 4

Chapter 9

22. The following four steps must be taken to perform a hypothesis test using the p-value approach: 1.

2.

3.

4.

Calculate the p-value.

Select the distribution to use.

Make a decision.

State the null and alternative hypotheses and determine the significance level.

The correct order for performing these steps is: A) 4, 1, 2, 3 B) 2, 3, 1, 4 C) 4, 2, 1, 3 D) 3, 2, 1, 4 Ans: C Difficulty level: medium Objective: Explain the difference between the p-value approach and the critical value approach to hypothesis testing.

23. A two-tailed hypothesis test using the normal distribution reveals that the area under the sampling distribution curve of the mean and located to the right of the sample mean equals 0.032. Consequently, the p-value for this test equals: Ans: 0.064 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

24. The following five steps must be taken to perform a hypothesis test using the critical-value approach: 1.

2.

3.

4.

5.

Calculate the value of the test statistic.

Select the distribution to use.

Make a decision.

Determine the rejection and nonrejection regions.

State the null and alternative hypotheses and determine the significance level.

The correct order for performing these steps is: A) 4, 1, 2, 3, 5 B) 5, 2, 4, 1, 3 C) 5, 4, 2, 1, 3 D) 5, 1, 2, 3, 4 Ans: B Difficulty level: medium Objective: Explain the difference between the p-value approach and the critical value approach to hypothesis testing.

25. Suppose that the batting average for all major league baseball players after each team completes 100 games through the season is 0.248 and the standard deviation is 0.034.

The null hypothesis is that American League infielders average the same as all other major league players. A sample of 46 players taken from the American League reveals a mean batting average of 0.255. What is the value of the test statistic, z (rounded to two decimal places)?

Ans: 1.40 Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

Page 5

Chapter 9

26. In a hypothesis test with hypotheses H 0 :  = 60 and H1 :   60 , a random sample of 37 elements selected from the population produced a mean of 62.5. Assuming that  = 5.2 and the population is normally distributed, what is the approximate p-value for this test? (round your answer to four decimal places) Ans: 0.0035 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

27. In a hypothesis test with hypotheses H 0 :   37 and H1 :   37 , a random sample of 59 elements selected from the population produced a mean of 35.8. Assuming that  = 9.9, what is the approximate p-value for this test? (round your answer to four decimal places) Ans: 0.1759 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

28. In a hypothesis test with hypotheses H 0 :   125 and H1 :   125 , a random sample of 131 elements selected from the population produced a mean of 131.6. Assuming that  = 18.8, what is the approximate p-value for this test? (round your answer to four decimal places) Ans: 0.0000 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

29. In a hypothesis test with hypotheses H 0 :  = 75 and H1 :   75 , a random sample of 38 elements selected from the population produced a mean of 74.4. Assuming that  = 8.9 and the population is normally distributed, what is the approximate p-value for this test? (round your answer to four decimal places) Ans: 0.6777 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

30. In a hypothesis test with hypotheses H 0 :   140 and H1 :   140 , a random sample of 100 elements selected from the population produced a mean of 137.0. Assuming that  = 28.1, what is the approximate p-value for this test? (round your answer to four decimal places) Ans: 0.1428 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

Page 6

Chapter 9

31. In a hypothesis test with hypotheses H 0 :   90 and H1 :   90 , a random sample of 61 elements selected from the population produced a mean of 90.7. Assuming that  = 29.8, what is the approximate p-value for this test? (round your answer to four decimal places) Ans: 0.4272 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

Use the following to answer questions 32-35: In a hypothesis test with hypotheses H 0 :   80 and H1 :   80 , a random sample of 99 elements selected from the population produced a mean of 75.3. Assume that  = 24.6, and that the test is to be made at the 5% significance level.

32. What is the critical value of z?

A) 1.88 B) 2.17 C) -1.88 D) -2.17 Ans: C Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

33. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –1.901 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

34. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0287 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

35. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

Use the following to answer questions 36-39: In a hypothesis test with hypotheses H 0 :   45 and H1 :   45 , a random sample of 67 elements selected from the population produced a mean of 46.0. Assume that  = 6.9, and that the test is to be made at the 2.5% significance level.

36. What is the critical value of z?

A) -1.96 B) 1.65 C) 1.96 D) -1.65 Ans: C Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Page 7

Chapter 9

37. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 1.186 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

38. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.1178 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

39. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Use the following to answer questions 40-43: In a hypothesis test with hypotheses H 0 :  = 24 and H1 :   24 , a random sample of 38 elements selected from the population produced a mean of 26.0. Assume that  = 4.4, and that the test is to be made at the 5% significance level.

40. What are the critical values of z?

A) -2.07 and 2.07 C) -1.645 and 1.645 B) -1.96 and 1.96 D) -2.33 and 2.33 Ans: B Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

41. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 2.802 Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

42. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0051 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

43. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

Page 8

Chapter 9

Use the following to answer questions 44-47: In a hypothesis test with hypotheses H 0 :   136 and H1 :   136 , a random sample of 68 elements selected from the population produced a mean of 133.4. Assume that  = 21.4, and that the test is to be made at the 3% significance level.

44. What is the critical value of z?

A) 1.96 B) -1.96 C) -1.645 D) 1.645 Ans: C Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

45. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –1.002 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

46. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.1582 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

47. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Use the following to answer questions 48-51: In a hypothesis test with hypotheses H 0 :   50 and H1 :   50 , a random sample of 113 elements selected from the population produced a mean of 52.3. Assume that  = 22.0, and that the test is to be made at the 2% significance level.

48. What is the critical value of z?

A) 2.17 B) 1.88 C) -1.28 D) -1.88 Ans: B Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

49. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 1.111 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Page 9

Chapter 9

50. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.1332 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

51. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Use the following to answer questions 52-55: In a hypothesis test with hypotheses H 0 :  = 90 and H1 :   90 , a random sample of 103 elements selected from the population produced a mean of 94.3. Assume that  = 22.1, and that the test is to be made at the 5% significance level.

52. What are the critical values of z?

A) -1.645 and 1.645 C) -2.33 and 2.33 B) -2.05 and 2.05 D) -2.58 and 2.58 Ans: C Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

53. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 1.975 Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

54. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0483 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

55. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

Page 10

Chapter 9

Use the following to answer questions 56-59: A researcher wants to test if the mean price of houses in an area is greater than $145,000. A random sample of 35 houses selected from the area produces a mean price of $149,700. Assume that  = $13,100, and that the test is to be made at the 1% significance level.

56. What is the critical value of z?

A) 1.88 B) 2.17 C) 1.96 D) 2.58 Ans: A Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

57. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 2.123 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

58. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0169 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

59. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Use the following to answer questions 60-63: A researcher wants to test if the mean annual salary of all lawyers in a city is different from $110,000. A random sample of 53 lawyers selected from the city reveals a mean annual salary of $114,000. Assume that  = $17,000, and that the test is to be made at the 1% significance level.

60. What are the critical values of z?

A) -1.96 and 1.96 B) -2.58 and 2.58 C) -2.33 and 2.33 D) -2.05 and 2.05 Ans: B Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

61. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 1.713 Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

Page 11

Chapter 9

62. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0867 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

63. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a two-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

Use the following to answer questions 64-67: A researcher wants to test if the elementary school children spend less than 30 minutes per day on homework. A random sample of 64 children from the school shows that they spend an average of 24.5 minutes per day on homework. Assume that  = 15.3 minutes, and that the test is to be made at the 1% significance level.

64. What is the critical value of z?

A) -2.06 B) -2.33 C) -2.58 D) -1.96 Ans: B Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

65. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –2.876 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

66. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0020 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.

67. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (normal population with given sigma) using the p-value approach.; Perform a one-tailed hypothesis test for mu (sigma known, n < 30) using the critical-value approach.

Page 12

Chapter 9

68. We use the t distribution to perform a hypothesis test about the population mean when: A) the population from which the sample is drawn is approximately normal and the population standard deviation is known B) the population from which the sample is drawn is not approximately normal and the population standard deviation is known C) the population from which the sample is drawn is approximately normal and the population standard deviation is unknown D) the population from which the sample is drawn is not approximately normal and the population standard deviation is unknown Ans: C Difficulty level: low Objective: Perform a hypothesis test for the population mean when the population standard deviation is unknown.

69. Which of the following conditions is not required to use the t distribution to perform a hypothesis test about a population mean?

A) The population from which the sample is drawn is approximately normal B) The population from which the sample is drawn has a t distribution C) The population standard deviation is unknown D) The sample does not have any extreme outliers Ans: B Difficulty level: medium Objective: Perform a hypothesis test for the population mean when the population standard deviation is unknown.

Use the following to answer questions 70-73: In a hypothesis test with hypotheses H 0 :   54 and H1 :   54 , a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4.

The test is to be made at the 10% significance level. Assume the population is normally distributed.

70. What is the critical value of t?

A) 1.318 B) 1.28 C) -1.319 D) 1.319 Ans: D Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

71. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 1.682 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

72. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0531 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

Page 13

Chapter 9

73. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.; Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

Use the following to answer questions 74-77: In a hypothesis test with hypotheses H 0 :  = 90 and H1 :   90 , a random sample of 16 elements selected from the population produced a mean of 91.9 and a standard deviation of 4.9.

The test is to be made at the 2% significance level. Assume the population is normally distributed.

74. What are the critical values of t?

A) -2.33 and 2.33 C) -2.131 and 2.131 B) -2.602 and 2.602 D) -2.583 and 2.583 Ans: B Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the critical-value approach.

75. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 1.551 Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the critical-value approach.

76. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.1417 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the p-value approach.

77. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the critical-value approach.; Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the p-value approach.

Use the following to answer questions 78-81: In a hypothesis test with hypotheses H 0 :   74 and H1 :   74 , a random sample of 20 elements selected from the population produced a mean of 67.8 and a standard deviation of 11.9.

The significance level is 5%. Assume the population is normally distributed.

Page 14

Chapter 9

78. What is the critical value of t?

A) -1.645 B) -1.725 C) -1.729 D) -2.093 Ans: C Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

79. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –2.330 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

80. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0155 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

81. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.; Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

Use the following to answer questions 82-86: A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours. A sample of 25 light bulbs manufactured by this company gave a mean life of 1,097 hours and a standard deviation of 133 hours. A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours. The significance level is 5%. Assume the population is normally distributed.

82. What is the critical value of t?

A) -1.704 B) -1.711 C) -2.797 D) -2.787 Ans: B Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

83. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –1.992 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

84. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0289 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

Page 15

Chapter 9

85. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.; Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

86. Does the data provide evidence to contradict the company's claim about the average lifetime of their light bulbs? (State your answer as "no" or "yes", but don't include the quotation marks.)

Ans: yes Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.; Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

Use the following to answer questions 87-90: In a hypothesis test with hypotheses H 0 : p  .39 and H1 : p  .39 , a random sample of size 481 produced a sample proportion of 0.4350. The test is to be made at the 5% significance level.

87. What is the critical value of z?

A) 1.96 B) 1.645 C) 2.12 D) 2.72 Ans: B Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

88. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 2.023 Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

89. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0215 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

90. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.; Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

Page 16

Chapter 9

Use the following to answer questions 91-94: In a hypothesis test with hypotheses H 0 : p  0.76 and H1 : p  0.76 , a random sample of size 974 produced a sample proportion of 0.7380. The test is to be made at the 5% significance level.

91. What is the critical value of z?

A) -2.05 B) -2.33 C) -1.96 D) -1.65 Ans: D Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

92. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –1.608 Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

93. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0540 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

94. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.; Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

Use the following to answer questions 95-98: In a hypothesis test with hypotheses H 0 : p = 0.26 and H1 : p  0.26 , a random sample of size 809 produced a sample proportion of 0.2400. The test is to be made at the 5% significance level.

95. What are the critical values of z?

A) -2.58 and 2.58 C) -1.96 and 1.96 B) -1.645 and 1.645 D) -1.72 and 1.72 Ans: C Difficulty level: low Objective: Perform a two-tailed hypothesis test for the population proportion using the critical-value approach.

96. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –1.297 Difficulty level: low Objective: Perform a two-tailed hypothesis test for the population proportion using the critical-value approach.

Page 17

Chapter 9

97. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.1947 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for the population proportion using the p-value approach.

98. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a two-tailed hypothesis test for the population proportion using the critical-value approach.; Perform a two-tailed hypothesis test for the population proportion using the p-value approach.

Use the following to answer questions 99-102: In a hypothesis test with hypotheses H 0 : p  0.58 and H1 : p  0.58 , a random sample of size 1,165 produced a sample proportion of 0.6160. The test is to be made at the 2.5% significance level.

99. What is the critical value of z?

A) 1.65 B) 2.33 C) 1.96 D) 2.58 Ans: C Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

100. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 2.490 Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

101. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0064 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

102. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.; Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

Use the following to answer questions 103-106: In a hypothesis test with hypotheses H 0 : p  0.31 and H1 : p  0.31 , a random sample of size 530 produced a sample proportion of 0.2755. The test is to be made at the 2% significance level.

Page 18

Chapter 9

103. What is the critical value of z?

A) -2.33 B) -2.05 C) -1.645 D) -1.714 Ans: B Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

104. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –1.717 Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.

105. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0430 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

106. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: fail to reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for the population proportion using the critical-value approach.; Perform a one-tailed hypothesis test for the population proportion using the p-value approach.

107. Which of the following statements describes a Type II error in hypothesis testing?

A) A court declares a defendant guilty, when he is actually innocent.

B) A scientist, trying to support a theory about the number of different species of animals in a particular country, declares the null hypothesis to be "there are 715 different species" when there are actually more than 800.

C) A statistician determines, through hypothesis testing, that the mean number of televisions per household in a certain community is 1.4, when it is actually greater than 1.4.

D) Through hypothesis testing, we find the alternative hypothesis to be true when it is actually false.

Ans: C Difficulty level: high Objective: Distinguish between Type I and Type II errors in a hypothesis test.

108. The power of a hypothesis test is .96. Which of the following statements is true about this test?

A) The probability of a Type II error is .04.

B) The probability of a Type I error is .04.

C) The probability of a Type II error is .96.

D) The probability of a Type I error is .96.

Ans: A Difficulty level: medium Objective: Distinguish between Type I and Type II errors in a hypothesis test.

Page 19

Chapter 9

109. A study conducted in 2000 found that the mean number of children under 18 per household in a certain community was 1.7. A statistician is trying to determine whether this number has changed in the last 6 years. Which of the following sets of hypotheses is correct for this test?

A) C) H 0 :   1.7; H1 :   1.7 H 0 :  = 1.7; H1 :   1.7 B) D) H 0 :   1.7; H1 :   1.7 H 0 :   1.7; H1 :   1.7 Ans: C Difficulty level: medium Objective: Perform a hypothesis test for the population mean when the population standard deviation is unknown.

Use the following to answer questions 110-113: The director of a radio broadcast company wants to determine whether the mean length of commercials on his station is equal to 24 seconds. A sample of 41 commercials had a mean life of 26.90 seconds and a standard deviation of 7.88 seconds. The significance level is 5%.

110. What are the critical values of t?

A) -1.714 and 1.714 C) -2.010 and 2.010 B) -1.684 and 1.684 D) -2.021 and 2.021 Ans: D Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the critical-value approach.

111. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 2.356 Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the critical-value approach.

112. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0234 Difficulty level: medium Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the p-value approach.

113. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the critical-value approach.; Perform a two-tailed hypothesis test for mu (normal population, sigma unknown) using the p-value approach.

Use the following to answer questions 114-118: Thousands of people nationwide are to take part in a Spring Clean-Up day along highways near their hometowns. The goal is to have individuals collect an average of 50 pounds (or more) of garbage. In a random sample of 36 people, an average of 46.3 pounds was collected, with a standard deviation of 9.2 pounds. The significance level is 2%.

Page 20

Chapter 9

114. What is the critical value of t?

A) -1.803 B) -1.988 C) -2.133 D) -2.438 Ans: C Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

115. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –2.413 Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.

116. What is the p-value for this hypothesis test, rounded to four decimal places?

Ans: 0.0106 Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

117. Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject", but don't include the quotation marks.)

Ans: reject Difficulty level: low Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.; Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

118. Does the data provide evidence to suggest that the goal is not being met? (State your answer as "no" or "yes", but don't include the quotation marks.)

Ans: yes Difficulty level: medium Objective: Perform a one-tailed hypothesis test for mu (sigma known, n ? 30) using the critical-value approach.; Perform a one-tailed hypothesis test for mu (sigma unknown, n ? 30) using the p-value approach.

119. If the significance level of a hypothesis test is 5% we will reject the null hypothesis is the p-value is A) greater than 0.95 C) less than 0.05 B) less than 0.025 D) greater than 0.025 Ans: C Difficulty level: low Objective: Explain the difference between the p-value approach and the critical value approach to hypothesis testing.

120. When  is unknown and the sample size is larger than 76, use: A) a t test.

B) a test for proportions.

C) a z test.

D) cannot perform a test.

Ans: C Difficulty level: low Objective: Perform a hypothesis test for mu when sigma is unknown and n > 76.

Page 21

1. Two samples drawn from two populations are independent if: A) the selection of one sample from a population is not related to the selection of the second sample from the same population B) the selection of one sample from one population does not affect the selection of the second sample from the second population C) the selection of one sample from a population is related to the selection of the second sample from the same population D) two samples selected from the same population have no relation Ans: B Difficulty level: low Objective: Distinguish between independent and dependent samples.

2. Two samples drawn from two populations are dependent if: A) the selection of one sample from a population is not related to the selection of the second sample from the same population B) the selection of one sample from one population is not related to the selection of the second sample from the second population C) for each data value collected from one sample there corresponds another data value collected from the second sample and both data values are collected from the same source D) two samples selected from the same population have no relation Ans: C Difficulty level: low Objective: Distinguish between independent and dependent samples.

Use the following to answer questions 3-4: The mean G.P.A (grade point average) of all male students at a college is 2.75 and the mean G.P.A of all female students at the same college is 2.98. The standard deviations of the G.P.As are 0.36 for the males and 0.30 for the females. Suppose we take one sample of 48 male students and another sample of 41 female students from this college. Assume the populations are normally distributed.

3. What is the mean, rounded to two decimal places, of the sampling distribution of the difference between the mean G.P.As for males and females?

Ans: –0.23 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

4. What is the standard deviation of the sampling distribution of the difference between the mean G.P.As for males and females, rounded to four decimal places?

Ans: 0.0700 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

Page 1

Chapter 10

Use the following to answer questions 5-6: The mean weekly earnings of all female workers in a state is $710 and the mean weekly earnings of all male workers in the same state is $760. The standard deviations of the weekly earnings are $86 for the females and $106 for the males. Suppose we take one sample of 316 female workers and another sample of 329 male workers from this state.

5. What is the mean of the sampling distribution of the difference between the mean weekly earnings for females and males?

Ans: $–50 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

6. What is the standard deviation of the sampling distribution of the difference between the mean weekly earnings for females and males, rounded to two decimal places?

Ans: $7.59 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

Use the following to answer questions 7-8: The mean job-related stress score for all corporate managers is 8.40 and the mean job-related stress score for all college professors is 5.95. The standard deviations of the job-related stress scores are 0.66 for the corporate managers and 0.82 for the college professors. Suppose we take one sample of 225 corporate managers and another sample of 167 college professors.

7. What is the mean, rounded to two decimal places, of the sampling distribution of the difference between the mean stress scores for corporate managers and college professors?

Ans: 2.45 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

8. What is the standard deviation of the sampling distribution of the difference between the mean stress scores for corporate managers and college professors, rounded to four decimal places?

Ans: 0.0772 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

Page 2

Chapter 10

Use the following to answer questions 9-13: A sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males.

The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males.

9. Derive the corresponding 95% confidence interval, rounded to two decimal places, for the difference between the mean weekly earnings for all female and male workers in this state.

Part A: The lower limit is $–65.01 Part B: The upper limit is $–3.25 Difficulty level: medium Objective: Construct a confidence interval for the difference of two population means when SIGMA1 and SIGMA2 are known and samples are large.

10. The significance level for the test is 1%. What is the critical value of z?

A) -2.58 B) -1.96 C) -2.33 D) -2.17 Ans: C Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

11. What is the value of the test statistic, rounded to three decimal places?

Ans: –2.167 Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

12. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0151 Difficulty level: medium Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

13. Do you reject or fail to reject the null hypothesis at the 1% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: fail to reject Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

Page 3

Chapter 10

Use the following to answer questions 14-18: A sample of 31 male students and another sample of 33 female students from the same college produced mean G.P.As of 2.66 for the males and 2.89 for the females. Suppose that the standard deviations of the G.P.As are 0.71 for the males and 0.63 for the females. The null hypothesis is that the mean G.P.A's are the same for males and females, while the alternative hypothesis is that the mean G.P.A for males is less than the mean G.P.A for females.

14. Derive the corresponding 99% confidence interval for the difference between the mean G.P.As for all male and female students at this college, rounded to three decimal places.

Part A: The lower limit is –0.664 Part B: The upper limit is 0.204 Difficulty level: medium Objective: Construct a confidence interval for the difference of two population means when SIGMA1 and SIGMA2 are known and samples are large.

15. The significance level for the test is 2.5%. What is the critical value of z?

A) -2.58 B) -1.96 C) -2.33 D) -1.65 Ans: B Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

16. What is the value of the test statistic, rounded to three decimal places?

Ans: –1.367 Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

17. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0857 Difficulty level: medium Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

18. Do you reject or fail to reject the null hypothesis at the 2.5% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: fail to reject Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

Page 4

Chapter 10

Use the following to answer questions 19-23: A sample of 126 corporate managers and another sample of 168 college professors produced mean job-related stress scores of 7.35 for the managers and 6.86 for the professors. Suppose that the standard deviations of the stress scores are 1.12 for the managers and 1.82 for the professors.

The null hypothesis is that the mean stress scores are the same for corporate managers and college professors, while the alternative hypothesis is that the mean stress score for managers is different from the mean stress score for professors.

19. Derive the corresponding 90% confidence interval for the difference between the mean stress scores for all corporate managers and college professors, rounded to three decimal places.

Part A: The lower limit is 0.206 Part B: The upper limit is 0.774 Difficulty level: medium Objective: Construct a confidence interval for the difference of two population means when SIGMA1 and SIGMA2 are known and samples are large.

20. The significance level for the test is 1%. What are the critical values of z?

A) -2.58 and 2.58 B) -1.96 and 1.96 C) -2.33 and 2.33 D) -3.09 and 3.09 Ans: A Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

21. What is the value of the test statistic, rounded to three decimal places?

Ans: 2.845 Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

22. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0044 Difficulty level: medium Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

23. Do you reject or fail to reject the null hypothesis at the 1% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test for the difference of two population means when SIGMA1 and SIGMA2 are known and the samples are large.

Page 5

Chapter 10

Use the following to answer questions 24-30: A sample of 20 from a population produced a mean of 66.0 and a standard deviation of 10.0. A sample of 25 from another population produced a mean of 58.6 and a standard deviation of 13.0.

Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.

The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the two population means are different. The significance level is 5%.

24. What is the pooled standard deviation of the two samples, rounded to three decimal places?

Ans: 11.769 Difficulty level: medium Objective: Compute the pooled standard deviation for two samples.

25. What is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places?

Ans: 3.531 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

26. Derive the corresponding 95% confidence interval for the difference between the means of these two populations, rounded to three decimal places.

Part A: The lower limit is 0.279 Part B: The upper limit is 14.521 Difficulty level: medium Objective: Construct a confidence interval for the difference of two populations means when SIGMA1 and SIGMA2 are unknown but equal.

27. What are the critical values of t for the hypothesis test?

A) -2.014 and 2.014 C) -1.681 and 1.681 B) -2.017 and 2.017 D) -1.679 and 1.679 Ans: B Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

28. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 2.096 Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

29. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0420 Difficulty level: medium Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

Page 6

Chapter 10

30. Do you reject or fail to reject the null hypothesis at the 5% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

Use the following to answer questions 31-37: A sample of 16 from a population produced a mean of 86.9 and a standard deviation of 14.3. A sample of 18 from another population produced a mean of 75.4 and a standard deviation of 15.9.

Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.

The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is greater than the mean of the second population. The significance level is 1%.

31. What is the pooled standard deviation of the two samples, rounded to three decimal places?

Ans: 15.171 Difficulty level: medium Objective: Compute the pooled standard deviation for two samples.

32. What is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places?

Ans: 5.213 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

33. Derive the corresponding 99% confidence interval for the difference between the means of these two populations, rounded to three decimal places.

Part A: The lower limit is –2.772 Part B: The upper limit is 25.772 Difficulty level: medium Objective: Construct a confidence interval for the difference of two populations means when SIGMA1 and SIGMA2 are unknown but equal.

34. What is the critical value of t for the hypothesis test?

A) 2.738 B) 2.449 C) 2.441 D) 2.733 Ans: B Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

Page 7

Chapter 10

35. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 2.206 Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

36. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0173 Difficulty level: medium Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

37. Do you reject or fail to reject the null hypothesis at the 1% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: fail to reject Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

Use the following to answer questions 38-44: A sample of 27 from a population produced a mean of 75.8 and a standard deviation of 8.3. A sample of 22 from another population produced a mean of 80.0 and a standard deviation of 6.3.

Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.

The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is less than the mean of the second population. The significance level is 2.5%.

38. What is the pooled standard deviation of the two samples, rounded to three decimal places?

Ans: 7.473 Difficulty level: medium Objective: Compute the pooled standard deviation for two samples.

39. What is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places?

Ans: 2.146 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution of the difference of two sample means.

Page 8

Chapter 10

40. Derive the corresponding 90% confidence interval for the difference between the means of these two populations, rounded to three decimal places.

Part A: The lower limit is –7.801 Part B: The upper limit is –0.599 Difficulty level: medium Objective: Construct a confidence interval for the difference of two populations means when SIGMA1 and SIGMA2 are unknown but equal.

41. What is the critical value of t for the hypothesis test?

A) -2.012 B) -2.009 C) -2.685 D) -1.678 Ans: A Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

42. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –1.957 Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

43. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0282 Difficulty level: medium Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

44. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: fail to reject Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown but equal.

Use the following to answer questions 45-51: A sample of 14 from a population produced a mean of 55.1 and a standard deviation of 7. A sample of 20 from another population produced a mean of 50.1 and a standard deviation of 10.

Assume that the two populations are normally distributed and the standard deviations of the two populations are not equal.

The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the two population means are different. The significance level is 10%.

45. What is the number of degrees of freedom of the t distribution to make a confidence interval for the difference between the two population means?

Ans: 31 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

Page 9

Chapter 10

46. What is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places?

Ans: 2.915 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

47. Derive the corresponding 90% confidence interval for the difference between the means of these two populations, rounded to three decimal places.

Part A: The lower limit is 0.055 Part B: The upper limit is 9.945 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

48. What are the critical values of t for the hypothesis test?

A) -2.040 and 2.040 C) -2.026 and 2.026 B) -1.696 and 1.696 D) -2.045 and 2.045 Ans: B Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

49. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 1.715 Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

50. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0963 Difficulty level: medium Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

51. Do you reject or fail to reject the null hypothesis at the 10% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

Use the following to answer questions 52-58: A sample of 12 from a population produced a mean of 84.4 and a standard deviation of 16. A sample of 16 from another population produced a mean of 71.9 and a standard deviation of 14.

Assume that the two populations are normally distributed and the standard deviations of the two populations are not equal.

The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is greater than the mean of the second population. The significance level is 2.5%.

Page 10

Chapter 10

52. What is the number of degrees of freedom of the t distribution to make a confidence interval for the difference between the two population means?

Ans: 21 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

53. What is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places?

Ans: 5.795 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

54. Derive the corresponding 99% confidence interval for the difference between the means of these two populations, rounded to three decimal places.

Part A: The lower limit is –3.906 Part B: The upper limit is 28.906 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

55. What is the critical value of t for the hypothesis test?

A) 2.319 B) 2.311 C) 1.997 D) 2.080 Ans: D Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

56. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 2.157 Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

57. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0214 Difficulty level: medium Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

58. Do you reject or fail to reject the null hypothesis at the 2.5% significance level? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

Page 11

Chapter 10

Use the following to answer questions 59-65: A sample of 16 from a population produced a mean of 30.9 and a standard deviation of 4. A sample of 18 from another population produced a mean of 33.1 and a standard deviation of 3.

Assume that the two populations are normally distributed and the standard deviations of the two populations are not equal.

The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is less than the mean of the second population. The significance level is 1%.

59. What is the number of degrees of freedom of the t distribution to make a confidence interval for the difference between the two population means?

Ans: 27 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

60. What is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places?

Ans: 1.225 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

61. Derive the corresponding 95% confidence interval for the difference between the means of these two populations, rounded to three decimal places.

Part A: The lower limit is –4.713 Part B: The upper limit is 0.313 Difficulty level: medium Objective: Construct a confidence interval for the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

62. What is the critical value of t for the hypothesis test?

A) -2.473 B) -2.080 C) -2.211 D) -2.425 Ans: A Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.\ 63. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –1.796 Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

64. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0418 Difficulty level: medium Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

Page 12

Chapter 10

65. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: fail to reject Difficulty level: low Objective: Perform a hypothesis test of the difference of population means when SIGMA1 and SIGMA2 are unknown and unequal.

66. Two paired or matched samples would imply that: A) data are collected on one variable from the elements of two independent samples B) two data values are collected from the same source (elements) for two dependent samples C) two data values are collected from the same source (elements) for two independent samples D) data are collected on two variables from the elements of two independent samples Ans: B Difficulty level: low Objective: Define the paired difference for two samples.

67. For two paired samples with sample size of n, the degrees of freedom are: A) 2n - 1 B) 2n - 2 C) n - 1 D) n - 2 Ans: C Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.Determine the mean, standard deviation, and sampling distribution of d-bar.

Use the following to answer questions 68-75: Five persons, who were suffering from depression, attended 10 one-hour counseling sessions.

The following table gives the depression scores (on a scale of 1 to 10) of these five persons before and after attending the counseling sessions. Note that a higher score means that a person has a worse case of depression.

Before 7.5 6.4 7.1 9.7 7.8

After 4.3 5.1 6.2 6.9 7.2

Let the paired difference be the score before minus the score after attending the counseling sessions. The null hypothesis is that the mean of the population paired differences is equal to zero (i.e., attending the counseling sessions does not change the depression score). The alternative hypothesis is that the mean of the population paired differences is not equal to zero (i.e., attending the counseling sessions does change the depression score). The significance level is 5%.

Page 13

Chapter 10

68. What is the mean of the sample paired differences, rounded to two decimal places?

Ans: 1.76 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.

69. What is the standard deviation of the paired differences, rounded to three decimal places?

Ans: 1.167 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.

70. What is the standard deviation of the mean of the sample paired differences, rounded to three decimal places?

Ans: 0.522 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.

71. Calculate the 95% confidence interval for the mean of the population paired differences that corresponds to these data, rounded to two decimal places.

Part A: The lower limit is 0.31 Part B: The upper limit is 3.21 Difficulty level: medium Objective: Construct a confidence interval for MU_d-bar using paired samples with SIGMA_d-bar unknown and normal population.

72. What are the critical values of t for the hypothesis test?

A) -2.776 and 2.776 C) -2.132 and 2.132 B) -2.571 and 2.571 D) -2.015 and 2.015 Ans: A Difficulty level: low Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

73. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 3.371 Difficulty level: low Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

74. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0280 Difficulty level: medium Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

75. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

Page 14

Chapter 10

Use the following to answer questions 76-83: A city recently launched a neighborhood watch program to control crime. The following table gives the number of crimes reported in six neighborhoods during the six months before and six months after the city launched the neighborhood watch program.

Before 57 73 53 73 79 39

After 41 65 28 73 61 32

Let the paired difference be the number of crimes before minus the number of crimes after the city launched the neighborhood watch program. The null hypothesis is that the mean of the population paired differences is equal to zero (i.e., the neighborhood watch program does not affect the number of crimes). The alternative hypothesis is that the mean of the population paired differences is greater than zero (i.e., the neighborhood watch program decreases the number of crimes). The significance level is 1%.

76. What is the mean of the sample paired differences, rounded to two decimal places?

Ans: 12.33 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.

77. What is the standard deviation of the paired differences, rounded to three decimal places?

Ans: 9.004 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.

78. What is the standard deviation of the mean of the sample paired differences, rounded to three decimal places?

Ans: 3.676 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of d-bar.

79. Calculate the 99% confidence interval for the mean of the population paired differences that corresponds to these data, rounded to two decimal places.

Part A: The lower limit is –2.49 Part B: The upper limit is 27.15 Difficulty level: medium Objective: Construct a confidence interval for MU_d-bar using paired samples with SIGMA_d-bar unknown and normal population.

Page 15

Chapter 10

80. What are the critical values of t for the hypothesis test?

A) 3.143 B) 3.365 C) 3.747 D) 4.032 Ans: B Difficulty level: low Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

81. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 3.355 Difficulty level: low Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

82. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0142 Difficulty level: medium Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

83. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: fail to reject Difficulty level: low Objective: Perform a hypothesis test for MU_d-bar using paired samples with SIGMA_d-bar unknown, small samples, and normal population.

Use the following to answer questions 84-85: The proportion of elements in a population that possess a certain characteristic is 0.66. The proportion of elements in another population that possess the same characteristic is 0.77. You select samples of 189 and 356 elements, respectively, from the first and second populations.

84. What is the mean of the sampling distribution of the difference between the two sample proportions, rounded to two decimal places?

Ans: –0.11 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution for the difference of sample proportions.

85. What is the standard deviation of the sampling distribution of the difference between the two sample proportions, rounded to four decimal places?

Ans: 0.0410 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution for the difference of sample proportions.

Use the following to answer questions 86-87: The proportion of elements in a population that possess a certain characteristic is 0.44. The proportion of elements in another population that possess the same characteristic is 0.46. You select samples of 988 and 867 elements, respectively, from the first and second populations.

Page 16

Chapter 10

86. What is the mean of the sampling distribution of the difference between the two sample proportions, reported to two decimal places?

Ans: –0.02 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution for the difference of sample proportions.

87. What is the standard deviation of the sampling distribution of the difference between the two sample proportions, rounded to four decimal places?

Ans: 0.0231 Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution for the difference of sample proportions.

Use the following to answer questions 88-93: A sample of 482 school teachers, who are married, showed that 209 of them hold a second job to supplement their incomes. Another sample of 408 school teachers, who are single, showed that 135 of them hold a second job to supplement their incomes. The null hypothesis is that the proportions of married and single school teachers who hold a second job to supplement their incomes are not different. The alternative hypothesis is that the proportions of married and single school teachers who hold a second job to supplement their incomes are different. The significance level is 5%.

88. What is the 95% confidence interval for the difference between the proportions of married and single school teachers who hold a second job to supplement their income, rounded to four decimal places?

Part A: The lower limit is 0.0392 Part B: The upper limit is 0.1663 Difficulty level: medium Objective: Construct a confidence interval for the difference of population proportions for large, independent samples.

89. What are the critical values of z for the hypothesis test?

A) -2.33 and 2.33 B) -1.65 and 1.65 C) -2.17 and 2.17 D) -1.96 and 1.96 Ans: D Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

90. What is the value of the pooled sample proportion, rounded to four decimal places?

Ans: 0.3865 Difficulty level: medium Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

91. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 3.136 Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

Page 17

Chapter 10

92. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0017 Difficulty level: medium Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

93. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

Use the following to answer questions 94-99: According to a Louis Harris survey, 500 in a sample of 983 female drivers reported that they never speed, while 538 in a sample of 1218 male drivers report that they never speed. The null hypothesis is that the proportions of all female and male drivers who never speed are the same.

The alternative hypothesis is that the proportion of female drivers who never speed is higher than the proportion of male drivers who never speed. The significance level is 1%.

94. What is the 99% confidence interval for the difference between the proportions of female and male drivers who state that they never speed, rounded to four decimal places?

Part A: The lower limit is 0.0118 Part B: The upper limit is 0.1221 Difficulty level: medium Objective: Construct a confidence interval for the difference of population proportions for large, independent samples.

95. What is the critical value of z for the hypothesis test?

A) 2.33 B) 2.05 C) 2.17 D) 2.58 Ans: A Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

96. What is the value of the pooled sample proportion, rounded to four decimal places?

Ans: 0.4716 Difficulty level: medium Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

97. What is the value of the test statistic, z, rounded to three decimal places?

Ans: 3.128 Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

98. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0009 Difficulty level: medium Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

Page 18

Chapter 10

99. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

Use the following to answer questions 100-105: In a survey regarding job satisfaction, 574 in a sample of 934 female job-holders stated that they are satisfied with their jobs, while 500 in a sample of 755 male job-holders stated that they are satisfied with their jobs. The null hypothesis is that the proportions of all female and male job-holders who are satisfied with their jobs are the same. The alternative hypothesis is that the proportion of female job-holders who are satisfied with their jobs is lower than the proportion of male job-holders stated who are satisfied with their jobs. The significance level is 2.5%.

100. What is the 97% confidence interval for the difference between the proportions of all female and all male job-holders who will say that they are satisfied with their job, rounded to four decimal places?

Part A: The lower limit is –0.0986 Part B: The upper limit is 0.0032 Difficulty level: medium Objective: Construct a confidence interval for the difference of population proportions for large, independent samples.

101. What is the critical value of z for the hypothesis test?

A) -1.96 B) -2.17 C) -2.33 D) -2.05 Ans: A Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

102. What is the value of the pooled sample proportion, rounded to four decimal places?

Ans: 0.6359 Difficulty level: medium Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

103. What is the value of the test statistic, z, rounded to three decimal places?

Ans: –2.025 Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

104. What is the p-value for this test, rounded to four decimal places?

Ans: 0.0214 Difficulty level: medium Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

Page 19

Chapter 10

105. Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.

Ans: reject Difficulty level: low Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

106. Calculate the observed value from these two samples. Round your answer to the nearest tenth.

Sample from population 1: 2 2 3 4 2 2 8 Sample from population 2: 8 4 2 3 8 1 Ans: 6.8 Difficulty Level: Medium Difficulty level: medium Objective: Determine the mean, standard deviation, and sampling distribution for the difference of sample proportions.

107. Suppose the following information comes from random samples from normal populations with means and , respectively. n1 = 13

x = 30

s1 = 3.3

n2 = 17

y = 29

s2 = 3

Using the data given, obtain a 95% confidence interval for the difference in means.

Round your answer to three decimal places.

Ans: (–1.363, 3.363) Difficulty Level: Difficult Difficulty level: high Objective: Construct a confidence interval for the difference of population proportions for large, independent samples.

Page 20

Chapter 10

108. Consider the following statistics associated with a productivity index. n1 = 11 n2 = 19

Group 1 x = 2.514 s1 = 0.773 Group 2 y = 2.963 s2 = 0.525

Do these data strongly indicate that the mean index for group 1 is lower than that for group 2? Test at level  = 0.05 . Answer "Reject null hypothesis" or "Not reject null hypothesis".

Ans: Reject the null hypothesis Difficulty Level: Difficult Difficulty level: high Objective: Perform a hypothesis test for the difference of population proportions for large, independent samples.

Page 21

1. The parameter(s) of the chi-square distribution is/are: A) the sample size B) degrees of freedom C) n and x D) n, x, and p Ans: B Difficulty level: low Objective: Compare chi-square distributions with different numbers of degrees of freedom.Compare chi-square distributions with different numbers of degrees of freedom.

2. For a chi-square distribution curve with 3 or more degrees of freedom, the peak occurs at the point: A) x = 10 C) x = degrees of freedom minus 2 B) x = degrees of freedom minus 1 D) n - x Ans: C Difficulty level: low Objective: Compare chi-square distributions with different numbers of degrees of freedom.

3. A chi-square distribution assumes: A) negative values only C) nonnegative values only B) positive values only D) all values Ans: C Difficulty level: low Objective: Compare chi-square distributions with different numbers of degrees of freedom.

4. For small degrees of freedom, the chi-square distribution is: A) symmetric B) skewed to the right C) skewed to the left D) rectangular Ans: B Difficulty level: low Objective: Compare chi-square distributions with different numbers of degrees of freedom.

5. For very large degrees of freedom, the chi-square distribution becomes: A) symmetric B) skewed to the right C) skewed to the left D) rectangular Ans: A Difficulty level: low Objective: Compare chi-square distributions with different numbers of degrees of freedom.

6. What is the chi-square value for 14 degrees of freedom and a .05 area in the right tail?

A) 21.604 B) 26.119 C) 23.685 D) 29.141 Ans: C Difficulty level: low Objective: Use the chi-square table to compute a right-tail or left-tail area.

7. What is the chi-square value for 9 degrees of freedom and a .01 area in the left tail?

A) 21.666 B) -21.666 C) 2.088 D) -2.088 Ans: C Difficulty level: low Objective: Use the chi-square table to compute a right-tail or left-tail area.

8. What is the chi-square value for 19 degrees of freedom and a 0.025 area in the right tail?

A) 30.144 B) 32.852 C) 8.907 D) 10.117 Ans: B Difficulty level: low Objective: Use the chi-square table to compute a right-tail or left-tail area.

Page 1

Chapter 11

9. What is the chi-square value for 12 degrees of freedom and a 0.10 area in the left tail?

A) 6.304 B) -6.304 C) 18.549 D) -18.549 Ans: A Difficulty level: low Objective: Use the chi-square table to compute a right-tail or left-tail area.

10. Which of the following is not a characteristic of a multinomial experiment?

A) It consists of two identical trials.

B) Each trial results in one of the k possible outcomes where k is a number greater than 2.

C) The trials are independent.

D) The probabilities of various outcomes remain constant for each trial.

Ans: A Difficulty level: low Objective: Identify characteristics of a multinomial experiment.

11. Which of the following is not a characteristic of a multinomial experiment?

A) It consists of n identical trials.

B) Each trial results in one of two possible outcomes.

C) The trials are independent.

D) The probabilities of various outcomes remain constant for each trial.

Ans: B Difficulty level: low Objective: Identify characteristics of a multinomial experiment.

12. Which of the following is not a characteristic of a multinomial experiment?

A) It consists of n identical trials.

B) Each trial results in one of the k possible outcomes where k is a number greater than 2.

C) The trials are dependent.

D) The probabilities of various outcomes remain constant for each trial.

Ans: C Difficulty level: low Objective: Identify characteristics of a multinomial experiment.

13. Which of the following is not a characteristic of a multinomial experiment?

A) It consists of n identical trials.

B) Each trial results in one of the k possible outcomes where k is a number greater than 2.

C) The trials are independent.

D) The probabilities of various outcomes are different for each trial.

Ans: D Difficulty level: low Objective: Identify characteristics of a multinomial experiment.

Page 2

Chapter 11

14. For a goodness-of-fit test, the frequencies obtained from the performance of an experiment are the: A) expected frequencies C) objective frequencies B) subjective frequencies D) observed frequencies Ans: D Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

15. For a goodness-of-fit test, the frequencies that we would obtain if the null hypothesis is true are the: A) expected frequencies C) objective frequencies B) subjective frequencies D) observed frequencies Ans: A Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

16. For a goodness-of-fit test with the number of categories equal to k and sample size equal to n, the degrees of freedom are: A) k - 2 B) n - k C) k - n D) k - 1 Ans: D Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

17. For a goodness-of-fit test, when n is the sample size and p is the probability of a category occurring, we calculate the expected frequency for a category by: A) E = np B) E = xp C) E = nx D) E = nkp Ans: A Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

18. For a goodness-of-fit test, the sample size should be large enough so that the: A) observed frequency for each category is at least 10 B) expected frequency for each category is at least 10 C) observed frequency for each category is at least 5 D) expected frequency for each category is at least 5 Ans: D Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

19. A goodness-of-fit test: A) is always a right-tailed test B) is always a left-tailed test C) is always a two-tailed test D) can be a right-tailed, left-tailed, or a two-tailed test Ans: A Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

Page 3

Chapter 11

Use the following to answer questions 20-24: The table below lists the observed frequencies for all four categories for an experiment.

Category 1 2 3 4

Observed Frequency 12 18 14 16

20. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the expected frequency for the second category?

Ans: 15 Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

21. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. The expected frequencies for the four categories are: Part A: Category 1: 15 Part B: Category 2: 15 Part C: Category 3: 15 Part D: Category 4: 15 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

22. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What are the degrees of freedom for this test?

Ans: 3 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

23. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. The significance level is 1%. What is the critical value of chi-square?

A) 13.277 B) 11.345 C) 12.838 D) 14.860 Ans: B Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

Page 4

Chapter 11

24. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the value of the test statistic, rounded to three decimal places?

Ans: 1.333 Difficulty level: medium Objective: Perform a goodness-of-fit test for equality of proportions across categories.

Use the following to answer questions 25-29: The table below lists the observed frequencies for all four categories for an experiment.

Category 1 2 3 4

Observed Frequency 23 5 41 11

25. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category, 30% belong to the second category, 20% belong to the third category, and 10% belong to the fourth category. What is the expected frequency for the fourth category?

Ans: 8 Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

26. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category, 30% belong to the second category, 20% belong to the third category, and 10% belong to the fourth category. The expected frequencies for the four categories are: Part A: Category 1: 32 Part B: Category 2: 24 Part C: Category 3: 16 Part D: Category 4: 8 Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

27. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category, 30% belong to the second category, 20% belong to the third category, and 10% belong to the fourth category. What are the degrees of freedom for this test?

Ans: 3 Difficulty level: low Objective: Determine observed and expected frequencies in an experiment.

Page 5

Chapter 11

28. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category, 30% belong to the second category, 20% belong to the third category, and 10% belong to the fourth category. The significance level is 10%. What is the critical value of chi-square?

A) 9.488 B) 7.815 C) 7.779 D) 6.251 Ans: D Difficulty level: low Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

29. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the value of the test statistic, rounded to three decimal places?

Ans: 57.760 Difficulty level: medium Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

Use the following to answer questions 30-34: The table below lists the observed frequencies for all four categories for an experiment.

Category 1 2 3 4 5

Observed Frequency 39 13 15 19 14

30. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same. What is the expected frequency for the fourth category?

Ans: 20 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

31. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same. The expected frequencies for the five categories are: Part A: Category 1: 20 Part B: Category 2: 20 Part C: Category 3: 20 Part D: Category 4: 20 Part E: Category 5: 20 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

Page 6

Chapter 11

32. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same. What are the degrees of freedom for this test?

Ans: 4 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

33. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same. The significance level is 5%. What is the critical value of chi-square?

A) 11.070 B) 12.833 C) 11.143 D) 9.488 Ans: D Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

34. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same. What is the value of the test statistic, rounded to three decimal places?

Ans: 23.600 Difficulty level: medium Objective: Perform a goodness-of-fit test for equality of proportions across categories.

Use the following to answer questions 35-39: You ask 100 persons what color of car they like the most. The table below lists the observed frequencies for such a survey.

Color Observed Frequency Black 22 Blue 29 Red 14 White 5 Other 30

35. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars, 25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.

What is the expected frequency for red cars?

Ans: 20 Difficulty level: low Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

Page 7

Chapter 11

36. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars, 25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.

The expected frequencies for the various colors are: Part A: Black: 10 Part B: Blue: 25 Part C: Red: 20 Part D: White: 10 Part E: Other: 35 Difficulty level: low Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

37. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars, 25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.

What are the degrees of freedom for this test?

Ans: 4 Difficulty level: low Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

38. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars, 25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.

The significance level is 2.5%. What is the critical value of chi-square?

A) 9.488 B) 11.143 C) 12.833 D) 11.070 Ans: B Difficulty level: low Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

39. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars, 25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.

What is the value of the test statistic, rounded to three decimal places?

Ans: 20.054 Difficulty level: medium Objective: Perform a goodness-of-fit test to determine if the results of an experiment conform to a prescribed distribution.

Use the following to answer questions 40-44: The table below lists the number of crimes reported at a police station on each day of the week for the past three months.

Day of the Week Number of Crimes Monday 21 Tuesday 10 Wednesday 13 Thursday 16 Friday 25 Saturday 29 Sunday 26

Page 8

Chapter 11

40. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week. What is the expected number of crimes reported on a Thursday?

Ans: 20 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

41. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week. The expected frequencies for each of the seven days are: Part A: Monday: 20 Part B: Tuesday: 20 Part C: Wednesday: 20 Part D: Thursday: 20 Part E: Friday: 20 Part F: Saturday: 20 Part G: Sunday: 20 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

42. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week. What are the degrees of freedom for this test?

Ans: 6 Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

43. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week. The significance level is 10%.

What is the critical value of chi-square?

A) 12.017 B) 14.067 C) 10.645 D) 12.592 Ans: C Difficulty level: low Objective: Perform a goodness-of-fit test for equality of proportions across categories.

44. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week. What is the value of the test statistic?

Ans: 15.4 Difficulty level: medium Objective: Perform a goodness-of-fit test for equality of proportions across categories.

Page 9

Chapter 11

45. For a chi-square test of independence, what are the degrees of freedom?

A) sample size minus one B) sample size minus two C) (R-1)(C-1) where R is the number of rows and C is the number of columns in the contingency table D) (n-1)(k-1) where n is the sample size and k is the number of categories Ans: C Difficulty level: low Objective: Define contingency tables.

46. For a chi-square test of homogeneity, what are the degrees of freedom?

A) sample size minus one B) sample size minus two C) (R-1)(C-1) where R is the number of rows and C is the number of columns in the contingency table D) (n-1)(k-1) where n is the sample size and k is the number of categories Ans: C Difficulty level: low Objective: Define contingency tables.

47. A chi-square test of independence: A) is always a right-tailed test B) is always a left-tailed test C) is always a two-tailed test D) can be a right-tailed, a left-tailed, or a two-tailed test Ans: A Difficulty level: low Objective: Define contingency tables.

48. A chi-square test of homogeneity: A) is always a right-tailed test B) is always a left-tailed test C) is always a two-tailed test D) can be a right-tailed, a left-tailed, or a two-tailed test Ans: A Difficulty level: low Objective: Perform a test of homogeneity.

49. A chi-square test of independence is about the independence of: A) two means B) two proportions C) two characteristics presented in a contingency table D) means of several populations Ans: C Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

50. A chi-square test of homogeneity is about: A) testing the null hypothesis that two samples are homogeneous B) testing the null hypothesis that two proportions are homogeneous C) the independence of two characteristics presented in a contingency table D) testing the null hypothesis that the proportions of elements with certain characteristics in two or more different populations are the same Ans: D Difficulty level: low Objective: Perform a test of homogeneity.

Page 10

Chapter 11

51. For a chi-square test of independence, a contingency table with 2 rows and 2 columns has how many degrees of freedom?

Ans: 1 Difficulty level: low Objective: Define contingency tables.

52. For a chi-square test of independence, a contingency table with 7 rows and 8 columns has how many degrees of freedom?

Ans: 42 Difficulty level: low Objective: Define contingency tables.

53. For a chi-square test of homogeneity, a contingency table with 5 rows and 6 columns has how many degrees of freedom?

Ans: 20 Difficulty level: low Objective: Define contingency tables.

54. For a chi-square test of homogeneity, a contingency table with 7 rows and 9 columns has how many degrees of freedom?

Ans: 48 Difficulty level: low Objective: Define contingency tables.

Use the following to answer questions 55-61: You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes. The table below gives a two-way classification for these students.

Gender Female Male

On Time 35 43

Late 9 13

55. For a chi-square test of independence for this contingency table, what is the number of degrees of freedom?

Ans: 1 Difficulty level: low Objective: Define contingency tables.

56. For a chi-square test of independence for this contingency table, what are the observed frequencies for the first row?

Part A: Column 1: 35 Part B: Column 2: 9 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

Page 11

Chapter 11

57. For a chi-square test of independence for this contingency table, what are the expected frequencies for the first row, rounded to two decimal places?

Part A: Column 1: 34.32 Part B: Column 2: 9.68 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

58. For a chi-square test of independence for this contingency table, what are the observed frequencies for the second column?

Part A: Row 1: 9 Part B: Row 2: 13 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

59. For a chi-square test of independence for this contingency table, what are the expected frequencies for the second column, rounded to two decimal places?

Part A: Row 1: 9.68 Part B: Row 2: 12.32 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

60. To perform a chi-square test of independence for this contingency table at the 1% significance level, what is the critical value of chi-square?

A) 7.879 B) 6.635 C) 10.597 D) 9.210 Ans: B Difficulty level: low Objective: Perform a test of independence involving a 2 x 2 table.

61. To perform a chi-square test of independence for this contingency table, what is the value of the chi-square test statistic (rounded to three decimal places)?

Ans: 0.109 Difficulty level: medium Objective: Perform a test of independence involving a 2 x 2 table.

Use the following to answer questions 62-68: You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.

The table below gives a two-way classification for these adults.

Gender Female Male

Satisfied 192 240

Page 12

Not Satisfied 94 74

Chapter 11

62. For a chi-square test of independence for this contingency table, what is the number of degrees of freedom?

Ans: 1 Difficulty level: low Objective: Define contingency tables.

63. For a chi-square test of independence for this contingency table, what are the observed frequencies for the second row?

Part A: Column 1: 240 Part B: Column 2: 74 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

64. For a chi-square test of independence for this contingency table, what are the expected frequencies for the second row, rounded to two decimal places?

Part A: Column 1: 226.08 Part B: Column 2: 87.92 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

65. For a chi-square test of independence for this contingency table, what are the observed frequencies for the first column?

Part A: Row 1: 192 Part B: Row 2: 240 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

66. For a chi-square test of independence for this contingency table, what are the expected frequencies for the first column, rounded to two decimal places?

Part A: Row 1: 205.92 Part B: Row 2: 226.08 Difficulty level: low Objective: Calculate the expected frequencies for a test of independence.

67. To perform a chi-square test of independence for this contingency table at the 5% significance level, what is the critical value of chi-square?

A) 5.991 B) 7.378 C) 3.841 D) 5.024 Ans: C Difficulty level: low Objective: Perform a test of independence involving a 2 x 2 table.

68. To perform a chi-square test of independence for this contingency table, what is the value of the chi-square test statistic (rounded to three decimal places)?

Ans: 6.422 Difficulty level: medium Objective: Perform a test of independence involving a 2 x 2 table.

Page 13

Chapter 11

Use the following to answer questions 69-75: A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II. The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

Drug I II

Cured 60 59

Not Cured 10 21

69. For a chi-square test of homogeneity for this contingency table, what is the number of degrees of freedom?

Ans: 1 Difficulty level: low Objective: Perform a test of homogeneity.

70. For a chi-square test of homogeneity for this contingency table, what are the observed frequencies for the first row?

Part A: Column 1: 60 Part B: Column 2: 10 Difficulty level: low Objective: Perform a test of homogeneity.

71. For a chi-square test of homogeneity for this contingency table, what are the expected frequencies for the first row, rounded to two decimal places?

Part A: Column 1: 55.53 Part B: Column 2: 14.47 Difficulty level: low Objective: Perform a test of homogeneity.

72. For a chi-square test of homogeneity for this contingency table, what are the observed frequencies for the second column?

Part A: Row 1: 10 Part B: Row 2: 21 Difficulty level: low Objective: Perform a test of homogeneity.

73. For a chi-square test of homogeneity for this contingency table, what are the expected frequencies for the second column, rounded to two decimal places?

Part A: Row 1: 14.47 Part B: Row 2: 16.53 Difficulty level: low Objective: Perform a test of homogeneity.

74. To perform a chi-square test of homogeneity for this contingency table at the 10% significance level, what is the critical value of chi-square?

A) 5.991 B) 4.605 C) 3.841 D) 2.706 Ans: D Difficulty level: low Objective: Perform a test of homogeneity.

Page 14

Chapter 11

75. To perform a chi-square test of homogeneity for this contingency table, what is the value of the chi-square test statistic (rounded to three decimal places)?

Ans: 3.259 Difficulty level: medium Objective: Perform a test of homogeneity.

Use the following to answer questions 76-77: A random sample of 25 elements selected from a population produced a variance equal to 3.937.

Assume that the population is normally distributed.

76. Based on this sample, the 95% confidence interval for the population variance, rounded to three decimal places, is: Part A: lower limit: 2.400 Part B: upper limit: 7.619 Difficulty level: medium Objective: Construct a confidence interval for population variance.

77. Based on this sample, the 95% confidence interval for the population standard deviation, rounded to three decimal places, is: Part A: lower limit: 1.549 Part B: upper limit: 2.760 Difficulty level: medium Objective: Construct a confidence interval for population variance.

Use the following to answer questions 78-79: A random sample of 16 elements selected from a population produced a variance equal to 7.954.

Assume that the population is normally distributed.

78. Based on this sample, the 99% confidence interval for the population variance, rounded to three decimal places, is: Part A: lower limit: 3.637 Part B: upper limit: 25.931 Difficulty level: medium Objective: Construct a confidence interval for population variance.

79. Based on this sample, the 99% confidence interval for the population standard deviation, rounded to three decimal places, is: Part A: lower limit: 1.907 Part B: upper limit: 5.092 Difficulty level: medium Objective: Construct a confidence interval for population variance.

Page 15

Chapter 11

Use the following to answer questions 80-81: A random sample of 20 elements selected from a population produced a variance equal to 11.072. Assume that the population is normally distributed.

80. Based on this sample, the 90% confidence interval for the population variance, rounded to three decimal places, is: Part A: lower limit: 6.979 Part B: upper limit: 20.794 Difficulty level: medium Objective: Construct a confidence interval for population variance.

81. Based on this sample, the 90% confidence interval for the population standard deviation, rounded to three decimal places, is: Part A: lower limit: 2.642 Part B: upper limit: 4.560 Difficulty level: medium Objective: Construct a confidence interval for population variance.

Use the following to answer questions 82-83: A random sample of 29 workers selected from a large company produced a variance of their weekly earnings equal to 8124. Assume that the population is normally distributed.

82. Based on this sample, the 95% confidence interval for the variance of the weekly earnings of all of this company's employees, rounded to three decimal places, is: Part A: lower limit: 5,116.214 Part B: upper limit: 14,859.681 Difficulty level: medium Objective: Construct a confidence interval for population variance.

83. Based on this sample, the 95% confidence interval for the standard deviation of the weekly earnings of all of this company's employees, rounded to the nearest cent, is: Part A: lower limit: $71.53 Part B: upper limit: $121.90 Difficulty level: medium Objective: Construct a confidence interval for population variance.

Use the following to answer questions 84-85: A random sample of 25 elements selected from a population produced a variance equal to 4.959.

The null hypothesis is that the population variance is less than or equal to 3.90 and the alternative hypothesis is that the population variance is greater than 3.90. Assume that the population is normally distributed. The significance level is 1%.

Page 16

Chapter 11

84. The critical value of chi-square is: A) 42.980 B) 45.559 C) 41.638 D) 44.181 Ans: A Difficulty level: low Objective: Perform a hypothesis test for population variance.

85. The value of the chi-square test statistic is, rounded to three decimal places: Ans: 30.517 Difficulty level: medium Objective: Perform a hypothesis test for population variance.

Use the following to answer questions 86-87: A random sample of 20 elements selected from a population produced a variance equal to 9.606.

The null hypothesis is that the population variance is equal to 10.05 and the alternative hypothesis is that the population variance is not equal to 10.05. Assume that the population is normally distributed. The significance level is 5%.

86. The critical values of chi-square are: A) 10.117 and 30.144 C) 7.633 and 36.191 B) 8.231 and 31.526 D) 8.907 and 32.852 Ans: D Difficulty level: low Objective: Perform a hypothesis test for population variance.

87. The value of the chi-square test statistic is, rounded to three decimal places: Ans: 18.161 Difficulty level: medium Objective: Perform a hypothesis test for population variance.

Use the following to answer questions 88-89: A random sample of 28 elements selected from a population produced a variance equal to 16.682. The null hypothesis is that the population variance is greater than or equal to 18.70 and the alternative hypothesis is that the population variance is less than 18.70. Assume that the population is normally distributed. The significance level is 2.5%.

88. The critical value of chi-square is: A) 14.573 B) 43.195 C) 41.923 D) 13.844 Ans: A Difficulty level: low Objective: Perform a hypothesis test for population variance.

89. The value of the chi-square test statistic is, rounded to three decimal places: Ans: 24.086 Difficulty level: medium Objective: Perform a hypothesis test for population variance.

Page 17

Chapter 11

Use the following to answer questions 90-91: The variance of the prices of all college textbooks was 81.30 last year. A recent sample of 20 college textbooks produced a variance of their prices equal to 164.649. The null hypothesis is that the current variance of the prices of all college textbooks is equal to 81.30 and the alternative hypothesis is that the current variance of the prices of all college textbooks is greater than 81.30.

Assume that the prices of college textbooks are normally distributed. The significance level is 1%.

90. The critical value of chi-square is: A) 36.191 B) 38.582 C) 39.997 D) 37.566 Ans: A Difficulty level: low Objective: Perform a hypothesis test for population variance.

91. The value of the chi-square test statistic is, rounded to three decimal places: Ans: 38.479 Difficulty level: medium Objective: Perform a hypothesis test for population variance.

Use the following to answer questions 92-93: A researcher claims that the variance of the heights of all female college basketball players is 4.80 square inches. A random sample of 28 female college basketball players produced a variance of their heights equal to 11.122 square inches. The null hypothesis is that the variance of the heights of all female college basketball players is equal to 4.80 square inches and the alternative hypothesis is that the variance of the heights of all female college basketball players is not equal to 4.80. Assume that the population is normally distributed. The significance level is 5%.

92. The critical values of chi-square are: A) 13.844 and 41.923 C) 15.308 and 44.461 B) 14.573 and 43.195 D) 12.879 and 40.113 Ans: B Difficulty level: low Objective: Perform a hypothesis test for population variance.

93. The value of the chi-square test statistic is, rounded to three decimal places: Ans: 62.561 Difficulty level: medium Objective: Perform a hypothesis test for population variance.

Page 18

Chapter 11

94. Jean, an expert on dental hygiene, hypothesizes that the dental hygiene of students at the Westwood Elementary School is similar to that of students at Easton Elementary. In order to test her hypothesis, she collects information about children at each school from dentists in the area, recording the number of cavities that each child has had in the past year. Her findings appear in the following table.

Tooth Decay Level No Cavities One Cavity Two Cavities Three or more Cavities

Westwood School 10 8 14 6

Easton School 9 12 6 8

The null hypothesis is that the proportions of students with no cavities, one cavity, two cavities, and three or more cavities are relatively the same between schools. What is the value of the test statistic, rounded to three decimal places, that Jean will use?

Ans: 4.222 Difficulty level: medium Objective: Perform a test of independence involving a 2 x 3 table.

95. Using the table for the chi-square distributions, find the lower 10% point when d.f. = 17.

Ans: 10.09 Difficulty Level: Easy Difficulty level: low Objective: Perform a test of independence involving a 2 x 3 table.

96. Find the probability of  2  36.42 when d.f. = 24.

Ans: 0.05 Difficulty Level: Easy Difficulty level: low to compute a right-tail or left-tail area.

Objective: Use the chi-square table

97. Find the probability of  2 1.73 when d.f. = 9.

A) 0.005 B) 0.1 C) 0.01 D) 0.025 Ans: A Difficulty Level: Easy Difficulty level: low chi-square table to compute a right-tail or left-tail area.

98. Find the probability of 7.63   2  32.85 when d.f. = 19.

Ans: 0.89 Difficulty Level: Medium Difficulty level: medium chi-square table to compute a right-tail or left-tail area.

Page 19

Objective: Use the

Objective: Use the

1. To use an F distribution, the random variable must be: A) a discrete random variable B) a continuous random variable C) a qualitative random variable D) either a discrete or a continuous random variable Ans: B Difficulty level: low Objective: Compare F distributions with different numbers of degrees of freedom.

2. The shape of the F distribution curve is: A) skewed to the left B) skewed to the right C) symmetric D) rectangular Ans: B Difficulty level: low Objective: Compare F distributions with different numbers of degrees of freedom.

3. Which of the following is not a characteristic of an F distribution?

A) The F distribution is continuous and skewed to the right.

B) The F distribution has two numbers of degrees of freedom: degrees of freedom for the numerator and for the denominator.

C) The F distribution has two parameters: the mean and the standard deviation.

D) The units of an F distribution are always nonnegative.

Ans: C Difficulty level: low Objective: Compare F distributions with different numbers of degrees of freedom.

4. The units of an F distribution: A) are always negative B) are always positive Ans: C Difficulty level: low numbers of degrees of freedom.

C) are always nonnegative D) can be negative, zero, or positive Objective: Compare F distributions with different

5. The parameters of the F distribution are: A) the mean and the standard deviation B) the sample size minus one and F C) the degrees of freedom for the numerator and the degrees of freedom for the denominator D) F and n, where n is the sample size Ans: C Difficulty level: low Objective: Compare F distributions with different numbers of degrees of freedom.

6. The F value for 9 degrees of freedom for the numerator, 12 degrees of freedom for the denominator, and a .01 area in the right tail is: A) 2.80 B) 5.11 C) 4.74 D) 4.39 Ans: D Difficulty level: low Objective: Use the F distribution table for a right-tail area.

Page 1

Chapter 12

7. The F value for 25 degrees of freedom for the numerator, 14 degrees of freedom for the denominator, and a .05 area in the right tail is: A) 2.78 B) 2.34 C) 3.19 D) 1.87 Ans: B Difficulty level: low Objective: Use the F distribution table for a right-tail area.

8. We can use the analysis of variance procedure to test hypotheses about: A) the mean of one population C) two or more population proportions B) the proportion of one population D) two or more population means Ans: D Difficulty level: low Objective: Explain the assumptions of one-way ANOVA. 9. Which of the following assumptions is not required to use ANOVA? A) The populations from which the samples are drawn are (approximately) normally distributed.

B) The populations from which the samples are drawn have the same variance.

C) All samples are of the same size.

D) The samples drawn from different populations are random and independent.

Ans: C Difficulty level: low Objective: Explain the assumptions of one-way ANOVA. 10. In a one-way ANOVA, we analyze only one: A) mean B) population C) sample D) variable Ans: D Difficulty level: medium Objective: Explain the assumptions of one-way ANOVA. 11. A one-way ANOVA test: A) is a left-tailed test B) is a right-tailed test C) is a two-tailed test D) can be a two-tailed, a right-tailed, or a left-tailed test Ans: B Difficulty level: low Objective: Explain the assumptions of one-way ANOVA. 12. To make tests of hypotheses about more than two population means, we use the: A) t distribution C) chi-square distribution B) normal distribution D) analysis of variance procedure Ans: D Difficulty level: low Objective: Explain the assumptions of one-way ANOVA.

Page 2

Chapter 12

Use the following to answer questions 13-22: The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.

Sample I 15 15 28 19 12

Sample II 14 9 18 10 19

Sample III 21 16 24 13 19

By using ANOVA, we wish to test the null hypothesis that the means of the three corresponding populations are equal. The significance level is 1%.

13. The value of  x is: Ans: 252 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a one-way

14. The value of  x 2 is: Ans: 4,604 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a one-way

15. The value of SSB, rounded to two decimal places, is: Ans: 60.40 Difficulty level: medium Objective: Compute the value of the test statistic for a one-way ANOVA test.

16. The value of SSW is: Ans: 310 Difficulty level: medium one-way ANOVA test.

17. The value of MSB is: Ans: 30.2 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a

Objective: Compute the value of the test statistic for a one-way

18. The value of MSW, rounded to three decimal places, is: Ans: 25.833 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

Page 3

Chapter 12

19. The degrees of freedom for the numerator of the F distribution are: Ans: 2 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

20. The degrees of freedom for the denominator of the F distribution are: Ans: 12 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

21. The critical value of F is: A) 4.81 B) 2.76 C) 6.93 Ans: C Difficulty level: low equal sample sizes.

D) 99.42 Objective: Perform a one-way ANOVA test with

22. The value of the test statistic F, rounded to three decimal places, is: Ans: 1.169 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

Use the following to answer questions 23-32: The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.

Sample I 5 7 11 9 6 13

Sample II 8 14 20 20 13

Sample III 19 11 8 11 4

Sample IV 16 12 19 8 7 16

By using ANOVA, we wish to test the null hypothesis that the means of the four corresponding populations are equal. The significance level is 5%.

23. The value of  x is: Ans: 257 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a one-way

Page 4

Chapter 12

24. The value of  x 2 is: Ans: 3,523 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a one-way

25. The value of SSB, rounded to three decimal places, is: Ans: 132.073 Difficulty level: medium Objective: Compute the value of the test statistic for a one-way ANOVA test.

26. The value of SSW is: Ans: 388.7 Difficulty level: medium one-way ANOVA test.

Objective: Compute the value of the test statistic for a

27. The value of MSB, rounded to three decimal places, is: Ans: 44.024 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

28. The value of MSW, rounded to three decimal places, is: Ans: 21.594 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

29. The degrees of freedom for the numerator of the F distribution are: Ans: 3 Difficulty level: low Objective: Perform a one-way ANOVA test with unequal sample sizes.

30. The degrees of freedom for the denominator of the F distribution are: Ans: 18 Difficulty level: low Objective: Perform a one-way ANOVA test with unequal sample sizes.

31. The critical value of F is: A) 5.48 B) 3.16 C) 7.15 Ans: B Difficulty level: low unequal sample sizes.

D) 1.84 Objective: Perform a one-way ANOVA test with

32. The value of the test statistic F, rounded to three decimal places, is: Ans: 2.039 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

Page 5

Chapter 12

Use the following to answer questions 33-42: A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same. Fifteen overweight persons were selected at random, then randomly divided into three groups of five, and each group was assigned one of the diets. The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.

Diet A 7 8 6 6 8

Diet B 4 3 6 4 7

Diet C 15 12 17 15 11

By using ANOVA, we wish to test the null hypothesis that the mean weight loss is the same for the three diets. The significance level is 2.5%.

33. The value of  x is: Ans: 129 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a one-way

34. The value of  x 2 is: Ans: 1,379 Difficulty level: low ANOVA test.

35. The value of SSB is: Ans: 230.8 Difficulty level: medium one-way ANOVA test.

36. The value of SSW is: Ans: 38.8 Difficulty level: medium one-way ANOVA test.

37. The value of MSB is: Ans: 115.4 Difficulty level: low ANOVA test.

Objective: Compute the value of the test statistic for a one-way

Objective: Compute the value of the test statistic for a

Objective: Compute the value of the test statistic for a

Objective: Compute the value of the test statistic for a one-way

Page 6

Chapter 12

38. The value of MSW, rounded to three decimal places, is: Ans: 3.233 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

39. The degrees of freedom for the numerator of the F distribution are: Ans: 2 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

40. The degrees of freedom for the denominator of the F distribution are: Ans: 12 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

41. The critical value of F is: A) 4.75 B) 3.18 C) 5.10 Ans: C Difficulty level: low equal sample sizes.

D) 9.57 Objective: Perform a one-way ANOVA test with

42. The value of the test statistic F, rounded to three decimal places, is: Ans: 35.691 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

43. Which of the following is not a characteristic of the F distribution?

A) It has two numbers of degrees of freedom: df for the numerator, and df for the denominator, and these two numbers may or may not be equal to each other.

B) It is symmetric.

C) It is continuous.

D) All units are nonnegative.

Ans: B Difficulty level: low Objective: Compare F distributions with different numbers of degrees of freedom.

Page 7

Chapter 12

Use the following to answer questions 44-48: A market research company randomly divides 12 stores from a large grocery chain into three groups of four stores each in order to compare the effect on mean sales of three different types of displays. The company uses display type 1 in four of the stores, display type 2 in four others, and display type 3 in the remaining four stores. Then it records the amount of sales (in $1,000's) during a one month period at each of the twelve stores. The table shown below reports the sales information.

Display Type I 109 116 135 115

Display Type II 135 137 123 120

Display Type III 160 150 147 128

By using ANOVA, we wish to test the null hypothesis that the means of the three corresponding populations are equal. The significance level is 1%.

44. The value of SSB is: Ans: 1,550 Difficulty level: medium one-way ANOVA test.

Objective: Compute the value of the test statistic for a

45. The value of SSW, rounded to two decimal places, is: Ans: 1134.25 Difficulty level: medium Objective: Compute the value of the test statistic for a one-way ANOVA test.

46. The degrees of freedom for the numerator of the F distribution are: Ans: 2 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

47. The degrees of freedom for the denominator of the F distribution are: Ans: 9 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

48. The value of the test statistic F, rounded to three decimal places, is: Ans: 6.149 Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

Page 8

Chapter 12

Use the following to answer questions 49-53: The marketing manager for a software company is trying to decide whether to market her company's newest product by mail, on television, or through the Internet. She selects 20 communities in which to test-market the product, advertising through one of the three media in each community. The following table shows the amount of sales, in hundreds of dollars, for each community: Mail 6 8 10 7 9 5 4

TV 9 12 8 14 4 7

Internet 16 11 10 8 9 14 12

Sales are normally distributed and the standard deviations are equal for all three methods of advertising. You are to test the hypothesis that the means are the same for all three treatments using the ANOVA method.

49. The value of SSB, rounded to four decimal places, is: Ans: 68.8357 Difficulty level: medium Objective: Compute the value of the test statistic for a one-way ANOVA test.

50. What is the variance within samples, rounded to four decimal places?

Ans: 8.2185 Difficulty level: medium Objective: Compute the value of the test statistic for a one-way ANOVA test.

51. The degrees of freedom for the numerator of the F distribution are: Ans: 2 Difficulty level: low Objective: Perform a one-way ANOVA test with unequal sample sizes.

52. The degrees of freedom for the denominator of the F distribution are: Ans: 17 Difficulty level: low Objective: Perform a one-way ANOVA test with unequal sample sizes.

53. The value of the test statistic F, rounded to three decimal places, is: Ans: 4.188 Difficulty level: low Objective: Perform a one-way ANOVA test with unequal sample sizes.

Page 9

Chapter 12

54. Using ANOVA, you test the hypothesis that the means of 3 treatments are the same. You calculate the MSW as 16.6. The value of the test statistic F is 2.1. What is the between samples sum of squares, rounded to two decimal places?

Ans: 69.72 Difficulty level: medium Objective: Perform a one-way ANOVA test with unequal sample sizes.

Use the following to answer questions 55-61: Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon. The null hypothesis for this test is H 0 : 1 = 2 = 3 = 4 = 5 .

Source of Variation Between Within Total

Degrees of Freedom

Sum of Squares 33.9 68.3

Mean Square

F

29

55. How many data points were used in this analysis?

Ans: 30 Difficulty level: low Objective: Explain the assumptions of one-way ANOVA. 56. How many degrees of freedom are there for the between groups variation?

Ans: 4 Difficulty level: medium Objective: Compute the value of the test statistic for a one-way ANOVA test.

57. How many degrees of freedom are there for the within groups variation?

Ans: 25 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

58. What is the value of the total sum of squares? Round your answer to one decimal place.

Ans: 102.2 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

59. What is the value of the mean square between groups? Round your answer to three decimal places.

Ans: 8.475 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

Page 10

Chapter 12

60. What is the value of the mean square within groups? Round your answer to three decimal places.

Ans: 2.732 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

61. What is the value of the test statistic F? Round your answer to three decimal places.

Ans: 3.102 Difficulty level: low Objective: Compute the value of the test statistic for a one-way ANOVA test.

62. Find the critical value of F for d.f = (7, 2) and the area in the right tail = 0.025.

A) 39.36 B) 99.36 C) 19.35 D) 1.96 Ans: A Difficulty Level: Easy Difficulty level: low Objective: Perform a one-way ANOVA test with equal sample sizes.

Page 11

1. A simple regression model contains: A) two independent variables B) two dependent variables C) one independent and one dependent variable D) more than one independent variable Ans: C Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

2. A linear regression: A) gives a relationship between two variables that can be described by a line B) gives a relationship between two variables that cannot be described by a line C) gives a relationship between three variables that can be described by a line D) contains only two variables Ans: A Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

3. In a regression model, the y-intercept is the: A) point where the y-axis intersects the x-axis B) point where the regression line intersects the y-axis C) point where the x-axis intersects the y-axis D) value of y when x is equal to 1 Ans: B Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

4. In a regression model, the slope represents the: A) point where the y-axis intersects the x-axis B) change in y due to a one unit change in x C) point where the x-axis intersects the y-axis D) change in the independent variable due to a one unit change in the dependent variable Ans: B Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

5. In the equation y = 12 + 6 x , y is the: A) independent variable C) dependent variable B) slope of the line D) y-intercept Ans: C Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

6. In the equation y = 12 + 6 x , x is the: A) independent variable C) dependent variable B) slope of the line D) y-intercept Ans: A Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

Page 1

Chapter 13

7. In the equation y = 2 + 3x , 2 is the: A) independent variable B) slope of the line Ans: D Difficulty level: low model and its equation.

C) dependent variable D) y-intercept Objective: Interpret a simple linear regression

8. In the equation y = 3 + 6 x , 6 is the: A) independent variable B) slope of the line Ans: B Difficulty level: low model and its equation.

C) dependent variable D) y-intercept Objective: Interpret a simple linear regression

9. In the equation y = 120 − 14 x , 120 is the: A) value of y when x is equal to 1 B) point where the line intersects the x-axis C) change in y due to a one-unit change in x D) point where the line intersects the y-axis Ans: D Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

10. In the equation y = 85 − 17 x , −17 is the: A) value of y when x is equal to 1 B) point where the line intersects the x-axis C) change in y due to a one-unit change in x D) change in x due to a one-unit change in y Ans: C Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

11. The model y = A + Bx is a: A) probabilistic model B) nonlinear model Ans: D Difficulty level: medium model and its equation.

C) stochastic model D) deterministic model Objective: Interpret a simple linear regression

12. The regression model y = A + Bx + e is: A) a probabilistic model C) an exact relationship B) a nonlinear model D) a deterministic model Ans: A Difficulty level: medium Objective: Interpret a simple linear regression model and its equation.

Page 2

Chapter 13

13. In the regression model y = A + Bx + e , A and B are the: A) sample statistics C) population parameters B) random variables D) omitted variables Ans: C Difficulty level: medium Objective: Interpret a simple linear regression model and its equation.

14. In the regression model y = A + Bx + e , e is the: A) slope of the regression line C) y-intercept B) random error term D) missing variable Ans: B Difficulty level: medium Objective: Interpret a simple linear regression model and its equation.

15. In the regression model y = A + Bx + e , x is the: A) dependent variable C) error term B) independent variable D) missing variable Ans: B Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

16. In the regression model y = A + Bx + e , y is the: A) dependent variable C) error term B) independent variable D) missing variable Ans: A Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

17. In a regression model, the random error term is included to capture the effects of the: A) independent variable B) dependent variable C) missing variables and random variation D) deterministic relationship Ans: C Difficulty level: medium Objective: Interpret a simple linear regression model and its equation.

18. In the regression model ŷ = a + bx , a and b are the: A) estimates of the population parameters A and B B) random variables C) population parameters D) omitted variables Ans: A Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

Page 3

Chapter 13

19. In the regression model ŷ = a + bx , a and b are the: A) sample statistics C) population parameters B) random variables D) omitted variables Ans: A Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

20. In the regression model ŷ = a + bx , ŷ is the: A) actual value of y C) value of y when a and b are zero B) predicted value of y D) missing value of y Ans: B Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

21. We construct a scatter diagram by: A) scattering the values of x over the values of y B) scattering the values of y over the values of x C) plotting the paired values of x and y D) plotting the values of the population parameters A and B Ans: C Difficulty level: low Objective: Construct a scatter diagram.

22. The value of y obtained for an element from a survey is the: A) predicted value of y C) actual value of y B) estimated value of y D) residual Ans: C Difficulty level: low Objective: Construct a scatter diagram.

23. The random error for the sample regression model, denoted by e, is equal to the: A) predicted value of y minus the estimated value of y B) estimated value of y minus the predicted value of y C) actual value of y minus the predicted value of y D) actual value of y minus the actual value of x Ans: C Difficulty level: medium Objective: Interpret a simple linear regression model and its equation.

24. For a regression model, the error sum of squares, denoted by SSE, is equal to the sum of the: A) errors B) squares of errors C) squares of y values D) squares of the difference between x and y values Ans: B Difficulty level: low Objective: Interpret a simple linear regression model and its equation.

Page 4

Chapter 13

25. The least squares method minimizes the: A) difference between the y and x values C) sum of the squares of errors B) sum of the errors D) sum of the y values Ans: C Difficulty level: low Objective: Explain the assumptions of the regression model.

26. The value of SS xx : A) is always negative B) is always non-negative Ans: B Difficulty level: low regression model.

C) is always positive D) can be negative, zero, or positive Objective: Explain the assumptions of the

27. The value of SS xy : A) is always negative B) is always non-negative Ans: D Difficulty level: medium regression model.

C) is always positive D) can be negative, zero, or positive Objective: Explain the assumptions of the

28. Given that SS xx = 875 and SS xy = 275, the value of b in the regression of y on x, rounded to two decimal places, is: Ans: 0.31 Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

29. Given that SS xx = 968 and SS xy = –915, the value of b in the regression of y on x, rounded to two decimal places, is: Ans: –0.95 Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

30. For a data set on x and y, the value of SS xx is 979, SS xy is –1,538, the mean of the x values is 88 , and the mean of the y values is 55. The value of a in the regression of y on x, rounded to two decimal places, is: Ans: 193.25 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

31. For a data set on x and y, the value of SS xx is 831, SS xy is 386, the mean of the x values is 9 , and the mean of the y values is 48. The value of a in the regression of y on x, rounded to two decimal places, is: Ans: 43.82 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

Page 5

Chapter 13

Use the following to answer questions 32-34: The table shown below gives six pairs of x and y values. x 16 20 12 10 9 9

y 8 13 9 4 6 4

32. The values of SS xx and SS xy , rounded to three decimal places, are: Part A: SS xx = 99.333 Part B: SS xy = 68.667 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

33. For the regression of y on x, the values of a and b, rounded to two decimal places, are: Part A: a = –1.42 Part B: b = 0.69 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

34. Using the regression of y on x, the predicted value of y for x = 17, rounded to two decimal places, is: Ans: 10.33 Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

Use the following to answer questions 35-37: The table shown below gives seven pairs of x and y values. x 12 9 14 8 10 4 18

y 18 35 12 40 29 33 10

Page 6

Chapter 13

35. The values of SS xx and SS xy , rounded to three decimal places, are: Part A: SS xx = 121.429 Part B: SS xy = –275.429 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

36. For the regression of y on x, the values of a and b, rounded to two decimal places, are: Part A: a = 49.59 Part B: b = –2.27 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

37. Using the regression of y on x, the predicted value of y for x = 14, rounded to two decimal places, is: Ans: 17.83 Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

Use the following to answer questions 38-42: The following table lists the monthly incomes (in hundreds of dollars) and the monthly rents paid (in hundreds of dollars) by a sample of six families.

Monthly Income 24 16 19 31 10 27

Monthly Rent 7.0 4.5 6.5 11.6 4.5 8.5

38. The values of SS xx and SS xy , rounded to three decimal places, are: Part A: SS xx = 294.833 Part B: SS xy = 95.900 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

39. For the regression of y on x, the values of a and b, rounded to two decimal places, are: Part A: a = 0.22 Part B: b = 0.33 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

Page 7

Chapter 13

40. Using the regression of monthly rent paid on monthly income, the predicted value of monthly rent paid by a family with a monthly income of $3,000, rounded to the nearest dollar, is: Ans: $997 Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

41. Suppose we have information on the monthly incomes and the monthly rents paid by a sample of families. In the regression of monthly rent paid on the monthly income for these data, the value of a will represent: A) the point where this regression line will intersect the y-axis B) the point where this regression line will intersect the x-axis C) an increase in the monthly rent paid by a family due to a $100 increase in income D) an increase in the income of a family due to a $100 increase in the monthly rent Ans: A Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

42. Suppose we have information on the monthly incomes and the monthly rents paid by a sample of families. In the regression of monthly rent paid on the monthly income for these data, the value of b will represent: A) the point where this regression line will intersect the y-axis B) the point where this regression line will intersect the x-axis C) an increase in the monthly rent paid by a family due to a $100 increase in income D) an increase in the income of a family due to a $100 increase in the monthly rent Ans: C Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

Use the following to answer questions 43-47: The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses.

Age 27 15 3 35 7 18

Price 165 182 205 161 180 161

Page 8

Chapter 13

43. The values of SS xx and SS xy , rounded to three decimal places, are: Part A: SS xx = 723.500 Part B: SS xy = –852.000 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

44. For the regression of price on age, the estimated values of A and B, rounded to two decimal places, are: Part A: Estimated A = 196.27 Part B: Estimated B = –1.18 Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

45. Using the regression of house value on age, the predicted value of a house that 16 years old, rounded to the nearest dollar, is: Ans: $177,433 Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

46. Suppose we have information on the ages (in years) and the prices of a sample of houses.

In the regression of price on age for these data, the value of a will represent: A) the point where this regression line will intersect the y-axis B) the point where this regression line will intersect the x-axis C) an decrease in the age of a house due to a $1,000 increase in its price D) an decrease in the price of a house due to a one year increase in its age Ans: A Difficulty level: low Objective: Estimate the least squares regression line and interpret its slope and intercept.

47. Suppose we have information on the ages (in years) and the prices of a sample of houses.

In the regression of price on age for these data, the value of b will represent: A) the point where this regression line will intersect the y-axis B) the point where this regression line will intersect the x-axis C) an decrease in the age of a house due to a $1,000 increase in its price D) an decrease in the price of a house due to a one year increase in its age Ans: D Difficulty level: medium Objective: Estimate the least squares regression line and interpret its slope and intercept.

48. An assumption of the regression model is that the random error term has a mean equal to: A) zero for each x C) the value of each x B) one for each x D) zero for each y Ans: A Difficulty level: medium Objective: Explain the assumptions of the regression model.

Page 9

Chapter 13

49. An assumption of the regression model is that the distribution of errors is A) binomial B) rectangular C) normal D) bimodal Ans: C Difficulty level: low Objective: Explain the assumptions of the regression model.

50. The regression model assumes that the spread of points around the regression line is: A) different for all values of x C) similar for all values of y B) different for all values of y D) similar for all values of x Ans: D Difficulty level: medium Objective: Explain the assumptions of the regression model.

51. The degrees of freedom for a simple linear regression of sample size n are: A) n - 1 B) n - 2 C) n - 3 D) 2n - 1 Ans: B Difficulty level: low Objective: Determine the degrees of freedom for a simple linear regression model.

52. The coefficient of determination represents the proportion of: A) SSE (error sum of squares) that the regression model explains B) SSR (regression sum of squares) that the regression model explains C) SST (total sum of squares) that the regression model explains D) SSR (regression sum of squares) that the regression model does not explain Ans: C Difficulty level: medium Objective: Calculate the coefficient of determination.

53. The value of SS yy : A) is always negative B) is always nonnegative Ans: B Difficulty level: low errors.

C) is always positive D) can be negative, positive, or zero Objective: Calculate the standard deviation of

54. The value of the coefficient of determination is always: A) less than 1 C) in the range zero to 1 B) greater than 1 D) between -1 and 1 Ans: C Difficulty level: low Objective: Interpret the meaning of the coefficient of determination.

55. The total sum of squares (SST) is always equal to the: A) regression sum of squares plus the error sum of squares B) regression sum of squares minus the error sum of squares C) error sum of squares minus the regression sum of squares D) regression sum of squares divided by the error sum of squares Ans: A Difficulty level: low Objective: Interpret the meaning of the coefficient of determination.

Page 10

Chapter 13

56. The coefficient of determination is equal to the: A) total sum of squares divided by the regression sum of squares B) error sum of squares divided by the regression sum of squares C) regression sum of squares divided by the total sum of squares D) error sum of squares divided by the total sum of squares Ans: C Difficulty level: medium Objective: Calculate the coefficient of determination.

57. One way to measure the quality of the regression model is to inspect the value of the: A) constant term C) coefficient of determination B) coefficient on x D) mean of x Ans: C Difficulty level: low Objective: Interpret the meaning of the coefficient of determination.

Use the following to answer questions 58-59: For a sample of 22 values of x and y, SS yy = 746, SS xy = 254, and b = 1.36.

58. The standard deviation of errors for the regression of y on x, rounded to three decimal places, is: Ans: 4.475 Difficulty level: medium Objective: Calculate the standard deviation of errors.

59. The coefficient of determination for the regression of y on x, rounded to three decimal places, is: Ans: 0.463 Difficulty level: medium Objective: Calculate the coefficient of determination.

Use the following to answer questions 60-61: For a sample of 19 values of x and y, SS yy = 294, SS xy = 502, and b = 0.27.

60. The standard deviation of errors for the regression of y on x, rounded to three decimal places, is: Ans: 3.053 Difficulty level: medium Objective: Calculate the standard deviation of errors.

61. The coefficient of determination for the regression of y on x, rounded to three decimal places, is: Ans: 0.461 Difficulty level: medium Objective: Calculate the coefficient of determination.

Page 11

Chapter 13

Use the following to answer questions 62-63: For a sample of 17 values of x and y, SS yy = 127, SS xy = –99, and b = –0.91.

62. The standard deviation of errors for the regression of y on x, rounded to three decimal places, is: Ans: 1.569 Difficulty level: medium Objective: Calculate the standard deviation of errors.

63. The coefficient of determination for the regression of y on x, rounded to three decimal places, is: Ans: 0.709 Difficulty level: medium Objective: Calculate the coefficient of determination.

Use the following to answer questions 64-65: The table shown below gives six pairs of x and y values. x 16 20 12 10 9 9

y 8 13 9 4 6 4

64. The standard deviation of errors for the regression of y on x, rounded to three decimal places, is: Ans: 1.722 Difficulty level: medium Objective: Calculate the standard deviation of errors.

65. The coefficient of determination for the regression of y on x, rounded to three decimal places, is: Ans: 0.800 Difficulty level: medium Objective: Calculate the coefficient of determination.

Page 12

Chapter 13

Use the following to answer questions 66-67: The following table lists the monthly incomes (in hundreds of dollars) and the monthly rents paid (in hundreds of dollars) by a sample of six families.

Monthly Income 24 16 19 31 10 27

Monthly Rent 7.0 4.5 6.5 11.6 4.5 8.5

66. The standard deviation of errors for the regression of monthly rent on monthly income, rounded to three decimal places, is: Ans: 1.108 Difficulty level: medium Objective: Calculate the standard deviation of errors.

67. The coefficient of determination for the regression of y on x, rounded to three decimal places, is: Ans: 0.864 Difficulty level: medium Objective: Calculate the coefficient of determination.

Use the following to answer questions 68-69: The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses.

Age 27 15 3 35 7 18

Price 165 182 205 161 180 161

68. The standard deviation of errors for the regression of y on x, rounded to three decimal places, is: Ans: 10.724 Difficulty level: medium Objective: Calculate the standard deviation of errors.

Page 13

Chapter 13

69. The coefficient of determination for the regression of y on x, rounded to three decimal places, is: Ans: 0.686 Difficulty level: medium Objective: Calculate the coefficient of determination.

70. The slope, b, of the regression line: A) is a point estimator of the slope of the population regression line B) possesses no sampling distribution C) will have the same value for all samples taken from the population D) is not affected by the elements taken from the population Ans: A Difficulty level: low Objective: Explain the assumptions of the regression model.

71. For a data set of x and y values, the value of SS xx = 266 and the standard deviation of errors for the regression of y on x is 8.875. The standard deviation of the sampling distribution of b, rounded to three decimal places, is: Ans: 0.544 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of b.

72. For a data set of x and y values, the value of SS xx = 944 and the standard deviation of errors for the regression of y on x is 72.937. The standard deviation of the sampling distribution of b, rounded to three decimal places, is: Ans: 2.374 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of b.

73. For a data set of x and y values, the value of SS xx = 66 and the standard deviation of errors for the regression of y on x is 4.345. The standard deviation of the sampling distribution of b, rounded to three decimal places, is: Ans: 0.535 Difficulty level: low Objective: Determine the mean, standard deviation, and sampling distribution of b.

Use the following to answer questions 74-76: For a data set of 10 values of x and y, the value of SS xx = 86, the standard deviation of errors for the regression of y on x is 3.662, and the value of b is 3.00.

For the purpose of running a hypothesis test, the null hypothesis is that the slope of the population regression line of y on x is zero and the alternative hypothesis is that the slope of this population regression line is different from zero. The significance level is 5%.

Page 14

Chapter 13

74. The 95% confidence interval for the slope, B, of the population regression line is: Part A: the lower limit is 2.09 Part B: the upper limit is 3.91 Difficulty level: medium Objective: Construct a confidence interval for B. 75. What are the critical values of t?

A) -2.306 and 2.306 B) -2.228 and 2.228 Ans: A Difficulty level: low

C) -1.812 and 1.812 D) -1.860 and 1.860 Objective: Perform a hypothesis test about B.

76. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 7.597 Difficulty level: medium Objective: Perform a hypothesis test about B. Use the following to answer questions 77-79: For a data set of 8 values of x and y, the value of SS xx = 180, the standard deviation of errors for the regression of y on x is 9.237, and the value of b is –6.28.

For the purpose of running a hypothesis test, the null hypothesis is that the slope of the population regression line of y on x is zero and the alternative hypothesis is that the slope of this population regression line is less than zero. The significance level is 1%.

77. The 99% confidence interval for the slope, B, of the population regression line is: Part A: the lower limit is –8.83 Part B: the upper limit is –3.73 Difficulty level: medium Objective: Construct a confidence interval for B. 78. What is the critical value of t?

A) -2.896 B) -2.998 C) -3.499 D) -3.143 Ans: D Difficulty level: low Objective: Perform a hypothesis test about B. 79. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –9.121 Difficulty level: medium Objective: Perform a hypothesis test about B. Use the following to answer questions 80-82: For a data set of 15 values of x and y, the value of SS xx = 313, the standard deviation of errors for the regression of y on x is 8.347, and the value of b is 1.78.

For the purpose of running a hypothesis test, the null hypothesis is that the slope of the population regression line of y on x is zero and the alternative hypothesis is that the slope of this population regression line is greater than zero. The significance level is 5%.

Page 15

Chapter 13

80. The 90% confidence interval for the slope, B, of the population regression line is: Part A: the lower limit is 0.94 Part B: the upper limit is 2.62 Difficulty level: medium Objective: Construct a confidence interval for B. 81. What is the critical value of t?

A) 1.753 B) 1.751 C) 1.771 D) 2.131 Ans: C Difficulty level: low Objective: Perform a hypothesis test about B. 82. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 3.773 Difficulty level: medium Objective: Perform a hypothesis test about B. Use the following to answer questions 83-85: The following table lists the monthly incomes (in hundreds of dollars) and the monthly rents paid (in hundreds of dollars) by a sample of six families.

Monthly Income 24 16 19 31 10 27

Monthly Rent 7.0 4.5 6.5 11.6 4.5 8.5

83. The 99% confidence interval for the slope, B, of the population regression line is: Part A: the lower limit is 0.03 Part B: the upper limit is 0.62 Difficulty level: medium Objective: Construct a confidence interval for B. 84. The null hypothesis is that the slope of the population regression line of monthly rent on monthly income is zero and the alternative hypothesis is that the slope of this population regression line is greater than zero. The significance level is 1%. What is the critical value of t?

A) 3.747 B) 3.143 C) 3.365 D) 4.032 Ans: A Difficulty level: low Objective: Perform a hypothesis test about B. 85. The null hypothesis is that the slope of the population regression line of monthly rent on monthly income is zero and the alternative hypothesis is that the slope of this population regression line is greater than zero. The significance level is 1%. What is the value of the test statistic, t, rounded to three decimal places?

Ans: 5.043 Difficulty level: medium Objective: Perform a hypothesis test about B.

Page 16

Chapter 13

Use the following to answer questions 86-88: The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses.

Age 27 15 3 35 7 18

Price 165 182 205 161 180 161

86. The 95% confidence interval for the slope, B, of the population regression line of price on age is: Part A: the lower limit is –2.28 Part B: the upper limit is –0.07 Difficulty level: low Objective: Construct a confidence interval for B. 87. The null hypothesis is that the slope of the population regression line of price on age is zero and the alternative hypothesis is that the slope of this population regression line is less than zero. The significance level is 5%. What is the critical value of t?

A) -2.015 B) -2.132 C) -1.943 D) -2.447 Ans: B Difficulty level: low Objective: Perform a hypothesis test about B. 88. The null hypothesis is that the slope of the population regression line of price on age is zero and the alternative hypothesis is that the slope of this population regression line is less than zero. The significance level is 5%. What is the value of the test statistic, t, rounded to three decimal places?

Ans: –2.954 Difficulty level: medium Objective: Perform a hypothesis test about B. 89. The value of the correlation coefficient is always: A) in the range 0 to 1 C) in the range -1 to 1 B) less than zero D) greater than zero Ans: C Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

Page 17

Chapter 13

90. A perfect positive correlation means: A) the points in a scatter diagram lie on an upward sloping line B) the points in a scatter diagram lie on a downward sloping line C) r is equal to -1 D) r is equal to 0 Ans: A Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

91. A perfect negative correlation means: A) the points in a scatter diagram lie on an upward sloping line B) the points in a scatter diagram lie on a downward sloping line C) r is equal to 1 D) r is equal to 0 Ans: B Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

92. A strong positive correlation means: A) the points in a scatter diagram lie on an upward sloping line B) the points in a scatter diagram lie on a downward sloping line C) r is close to 1 D) r is close to -1 Ans: C Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

93. A strong negative correlation means: A) the points in a scatter diagram lie on an upward sloping line B) the points in a scatter diagram lie on a downward sloping line C) r is close to -1 D) r is close to 1 Ans: C Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

94. A weak positive correlation means: A) the points in a scatter diagram are very close to an upward sloping line B) the points in a scatter diagram are very close to a downward sloping line C) r is positive and close to zero D) r is close to 1 Ans: C Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

Page 18

Chapter 13

95. A weak negative correlation means: A) the points in a scatter diagram are very close to an upward sloping line B) the points in a scatter diagram are very close to a downward sloping line C) r is negative and close to zero D) r is close to -1 Ans: C Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

96. The value of the correlation coefficient is zero if the points in a scatter diagram: A) lie on an upward sloping line C) are scattered all over the diagram B) lie on a downward sloping line D) are close to the regression line Ans: C Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

97. Given that SS xx = 276, SS yy = 183, and SS xy = 153, what is the value of the correlation coefficient, rounded to three decimal places?

Ans: 0.681 Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

98. Given that SS xx = 853, SS yy = 642, and SS xy = 314, what is the value of the correlation coefficient, rounded to three decimal places?

Ans: 0.424 Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

99. Given that SS xx = 241, SS yy = 326, and SS xy = –71, what is the value of the correlation coefficient, rounded to three decimal places?

Ans: –0.253 Difficulty level: low Objective: Compute and interpret the linear correlation coefficient.

Page 19

Chapter 13

Use the following to answer question 100: The following table lists the monthly incomes (in hundreds of dollars) and the monthly rents paid (in hundreds of dollars) by a sample of six families.

Monthly Income 24 16 19 31 10 27

Monthly Rent 7.0 4.5 6.5 11.6 4.5 8.5

100. What is the value of the correlation coefficient?

Ans: 0.930 Difficulty level: medium Objective: Compute and interpret the linear correlation coefficient.

Use the following to answer question 101: The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses.

Age 27 15 3 35 7 18

Price 165 182 205 161 180 161

101. What is the value of the correlation coefficient?

Ans: –0.828 Difficulty level: medium Objective: Compute and interpret the linear correlation coefficient.

Page 20

Chapter 13

Use the following to answer questions 102-103: The following table lists the monthly incomes (in hundreds of dollars) and the monthly rents paid (in hundreds of dollars) by a sample of six families.

Monthly Income 24 16 19 31 10 27

Monthly Rent 7.0 4.5 6.5 11.6 4.5 8.5

102. What is the 99% confidence interval for the mean monthly rent of all families with a monthly income of $2500, rounded to the nearest penny?

Part A: The lower limit is $597.42 Part B: The upper limit is $1,071.95 Difficulty level: high Objective: Construct a confidence interval for the mean value of y.

103. What is the 99% confidence interval for the mean monthly rent of a randomly selected family with a monthly income of $2500, rounded to the nearest penny?

Part A: The lower limit is $272.27 Part B: The upper limit is $1,397.10 Difficulty level: high Objective: Construct a prediction interval for a particular value of y.; Explain the difference between the confidence interval for the mean of y and a prediction interval for a specific value of y.

Use the following to answer questions 104-105: The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses.

Age 27 15 3 35 7 18

Price 165 182 205 161 180 161

Page 21

Chapter 13

104. What is the 90% confidence interval for the average price of all 16-year old homes, rounded to the nearest dollar?

Part A: The lower limit is $168,012 Part B: The upper limit is $186,854 Difficulty level: high Objective: Construct a confidence interval for the mean value of y.

105. What is the 90% confidence interval for the average price of all 16-year old homes, rounded to the nearest dollar?

Part A: The lower limit is $152,705 Part B: The upper limit is $202,161 Difficulty level: high Objective: Construct a prediction interval for a particular value of y.; Explain the difference between the confidence interval for the mean of y and a prediction interval for a specific value of y.

Page 22