Statistics for Behavioral Sciences
Exam Solutions
Course Introduction
Statistics for Behavioral Sciences provides students with foundational knowledge in statistical methods and their application within psychology, sociology, and related fields. The course covers descriptive statistics, probability theory, hypothesis testing, correlation, regression analysis, and analysis of variance. Emphasis is placed on developing the ability to critically evaluate research findings, interpret data, and utilize statistical software for data analysis. Students will learn how statistical reasoning supports evidence-based conclusions and gain hands-on experience with real-world behavioral science data sets to enhance their analytical skills for future research or professional practice.
Recommended Textbook
Essentials of Statistics for The Behavioral Sciences 9th Edition by Gravetter
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Page 2
Chapter 1: Introduction to Statistics
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Sample Questions
Q1) The relationship between a statistic and a parameter is the same as the relationship between ______.
A)a sample and a population
B)a statistic and a parameter
C)a parameter and a population
D)descriptive statistics and inferential statistics
Answer: A
Q2) Using letter grades (A,B,C,D,and F)to classify student performance on an exam is an example of measurement on a(n)_______ scale of measurement.
A)nominal
B)ordinal
C)interval
D)ratio
Answer: B
Q3) The goal for an experiment is to demonstrate that changes in one variable are responsible for causing changes in a second variable.
A)True
B)False
Answer: True
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Page 3
Chapter 2: Frequency Distributions
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Sample Questions
Q1) After recording the final grade (A,B,C,D,F)for each individual in a class of N = 26 students,the professor would like to display the grade distribution in a frequency distribution graph.What kind of graph should be used?
A)A bar graph
B)A histogram
C)A polygon
D)Either a histogram or a polygon
Answer: A
Q2) In a positively skewed distribution,the scores pile up on the left side of the distribution and taper off to the right.
A)True
B)False
Answer: True
Q3) In a grouped frequency distribution table,one interval is identified as 30-34.This interval has a width of 5 points.
A)True
B)False
Answer: True
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4
Chapter 3: Central Tendency
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Sample Questions
Q1) A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students.However,one of the participants fails to solve the problems so the researcher has an undetermined score.What is the best measure of central tendency for these data?
A)The mean
B)The median
C)The mode
D)Central tendency cannot be determined for these data
Answer: B
Q2) A sample has n = 5 scores: 2,4,5,8,and 11.The median for the sample is 6.5.
A)True
B)False
Answer: False
Q3) For a perfectly symmetrical distribution with µ = 30,what is the mode?
A)30
B)Greater than 30
C)Less than 30
D)Cannot be determined from the information given
Answer: D
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Page 5
Chapter 4: Variability
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Sample Questions
Q1) What is the variance for the following population of scores? Scores: 5,2,5,4
A)6
B)2
C)1.5
D)1.22
Q2) The range is usually considered to be a relatively crude measure of variability.
A)True
B)False
Q3) For a population with µ = 70 and = 5,about 95% of the individuals will have scores between X = 65 and X = 75.
A)True
B)False
Q4) A sample of n = 6 scores has a standard deviation of s = 3.What is the value of SS,the sum of the squared deviations for this sample?
A)54
B)45
C)18
D)15
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Page 6
Chapter 5: z-Scores: Location of Scores and Standardized
Distributions
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Sample Questions
Q1) A population of scores has µ = 44.In this population,a score of X = 40 corresponds to z = -0.50.What is the population standard deviation?
A)2
B)4
C)8
D)-8
Q2) In a distribution with µ = 80 and = 20,a score of X = 95 corresponds to z = 1.50.
A)True
B)False
Q3) For a population with a standard deviation of = 6,what is the z-score corresponding to a score that is 12 points above the mean?
A)z = 1
B)z = 2
C)z = 6
D)z = 12
Q4) Describe what happens to the mean,the standard deviation,and the shape of a distribution when all of the scores are transformed into z-scores.
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Chapter 6: Probability
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Sample Questions
Q1) For a normal distribution,
a.What z-score separates the highest 25% from the rest of the scores?
b.What z-score separates the highest 60% from the rest of the scores?
c.What z-score separates the lowest 30% from the rest of the scores?
d.What z-score separates the lowest 80% from the rest of the scores?
Q2) A normal distribution has = 80 and = 10.What is the probability of randomly selecting a score greater than 90 from this distribution?
A)0.8413
B)0.1587
C)0.3085
D)0.6915
Q3) A normal distribution has a mean of µ = 40 with = 8.If one score is randomly selected from this distribution,what is the probability that the score will be less than X = 34?
A)0.7734
B)0.2266
C)0.2734
D)0.4532
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Chapter 7: Probability and Samples: The Distribution of Sample Means
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Sample Questions
Q1) A random sample of n = 6 scores is selected from a population.Which of the following distributions will definitely be normal?
A)The scores in the sample will definitely form a normal distribution.
B)The scores in the population will definitely form a normal distribution.
C)The distribution of sample means will definitely form a normal distribution.
D)None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.
Q2) A random sample of n = 9 scores is obtained from a normal population with µ = 40 and = 18.What is the probability that the sample mean will be greater than M = 43?
A)0.4325
B)0.3085
C)0.1587
D)0.0228
Q3) Samples of n = 16 are selected from a population.If the distribution of sample means has a standard error of 2 points,then the population has a standard deviation of = 8.
A)True
B)False
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Page 9
Chapter 8: Introduction to Hypothesis Testing
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Sample Questions
Q1) You complete a hypothesis test using = .05,and based on the evidence from the sample,your decision is to fail to reject the null hypothesis.If the treatment actually does have an effect,which of the following is true?
A)You have made a Type I error.
B)You have made a Type II error.
C)You might have made a Type I error, but the probability is only 5% at most.
D)You have made the correct decision.
Q2) In a research report,p < .05 indicates that the probability of a Type I error is less than .05.
A)True
B)False
Q3) A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population that is known to have a mean of = 80.The results will be examined using a one-tailed hypothesis test.Which of the following is the correct statement of the null hypothesis?
A) > 40
B) > 120
C) < 85
D) < 80
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Page 10
Chapter 9: Introduction to the t Statistic
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Sample Questions
Q1) A random sample with n = 20 scores has df = 19.
A)True
B)False
Q2) A sample is selected from a population with µ = 50.After a treatment is administered to the individuals in the sample,the mean is found to be M = 55 and the variance is s² = 64.
a.For a sample of n = 4 scores, conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen's d to measure the size of the treatment effect.Use a two-tailed test with = .05.
b.For a sample of n = 16 scores, conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen's d to measure the size of the treatment effect.Use a two-tailed test with = .05.
c.Describe how increasing the size of the sample affects the likelihood of rejecting the null hypothesis and the measure of effect size.
Q3) A research report states "t(8)= 2.00,p > .05." For this test,r² = 2/10.
A)True
B)False
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Page 11
Chapter 10: The t Test for Two Independent Samples
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Sample Questions
Q1) For an independent-measures study,the width of a confidence interval estimating µ - µ depends on the size of the difference between M and M .
A)True
B)False
Q2) Which combination of factors is most likely to produce a significant value for an independent-measures t statistic?
A)Large samples and large variance
B)Large samples and small variance
C)Small samples and large variance
D)Small samples and small variance
Q3) Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large effect size?
A)A small mean difference and small sample variances
B)A large mean difference and small sample variances
C)A small mean difference and large sample variances
D)A large mean difference and large sample variances
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Chapter 11: The t Test for Two Related Samples
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Sample Questions
Q1) What is the value of the estimated standard error for the following set of D-scores?
Scores: 2,2,10,2
A)3
B) 3
C)4
D)2
Q2) The null hypothesis for a repeated-measures test states:
A)each individual will have a difference score of D = 0.
B)the overall sample will have a mean difference of MD = 0.
C)the entire population will have a mean difference of D = 0.
D)All of the other options are correct.
Q3) In a repeated measures study,the null hypothesis says that the mean for the sample of difference scores is equal to zero.
A)True
B)False
Q4) A set of n = 16 difference scores has a mean of MD = 4 and a variance of s² = 36.Cohen's d for this sample is d = 4/6.
A)True
B)False
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Chapter 12: Introduction to Analysis of Variance
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Sample Questions
Q1) An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df between treatment?
A)2
B)11
C)33
D)35
Q2) A researcher uses an ANOVA to evaluate the mean difference between two treatments and obtains F(1,22)= 4.00.If the researcher had used an independent-measures t test to evaluate the data,what t value would be obtained?
A)t(22) = 2.00
B)t(22) = 16.00
C)t(23) = 2.00
D)t(23) = 16.00
Q3) Posttests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.
A)True
B)False
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Chapter 13: Repeated-Measures and Two-Factor Analysis of Variance
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Sample Questions
Q1) For the following data,what is SS<sub>total</sub>? \[\begin{array}{l}
\text { Treatments }\\
\begin{array} { c c c c c c }
\text { Subject } & \text { I } & \text { II } & \text { III } & \text { P-totals } & \\
\text { A } & 3 & 4 & 5 & 12 & G = 27 \\
\text { B } & 1 & 1 & 4 & 6 & \Sigma X ^ { 2 } = 109 \\
\text { C } & 2 & 1 & 6 & 9 &
\end{array}\\
\begin{array} { c c c }
T = 6 & T = 6 & T = 15
\end{array}\\
S S = 2 \quad S S = 6 \quad S S = 2
\end{array}\]
A)28
B)18
C)10
D)6
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Page 15
Chapter 14: Correlation and Regression
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Sample Questions
Q1) The distance between the Y value in the data and the predicted Y value from the regression equation is known as the residual.What is the value for the sum of the squared residuals?
A) \(S S _ { \text {residual } }\) = r²(SS?)
B) \(S S _ { \text {residual } }\) = (1 - r²)(SS?)
C) \(S S _ { \text {residual } }\) = r²(SS?)
D) \(S S _ { \text {residual } }\) = (1 - r²)(SS?)
Q2) The sign of the correlation (+/-)is generally meaningless for the point-biserial correlation and the phi-coefficient.
A)True
B)False
Q3) For the linear equation Y = 2X - 3,which of the following points will not be on the line?
A)0, -3
B)2, 1
C)3, 0
D)4, 5
Q4) The line defined by the equation Y = -3X + 6 slopes up to the right.
A)True
B)False
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Chapter 15: The Chi-Square Statistic: Tests for Goodness of
Fit and Independence
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Sample Questions
Q1) Under what conditions is Cramér's V used to measure effect size for a chi-square test for independence?
A)When both variables consist of exactly two categories
B)When both variables consist of more than two categories
C)When either of the two variables consists of exactly two categories
D)When either of the two variables consists of more than two categories
Q2) A chi-square test for independence is being used to evaluate the relationship between two variables.If the test has df = 1,what can you conclude about the two variables?
A)One variable consists of 2 categories and the other consists of 3 categories.
B)One variable consists of 2 categories and the other consists of 4 categories.
C)Both variables consist of 2 categories.
D)Both variables consist of 3 categories.
Q3) Which of the following accurately describes the expected frequencies for a chi-square test?
A)They are always whole numbers.
B)They can contain fractions or decimal values.
C)They can contain both positive and negative values.
D)They can contain fractions and negative numbers.
Page 17
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