Statistics for the Behavioral Sciences
Exam Solutions
Course Introduction
Statistics for the Behavioral Sciences introduces students to fundamental statistical methods and concepts essential for analyzing data in psychology, sociology, and related fields. The course covers descriptive statistics, probability theory, hypothesis testing, correlation, regression, analysis of variance (ANOVA), and non-parametric techniques. Emphasis is placed on understanding the application and interpretation of statistical tools, using statistical software for data analysis, and critically evaluating research findings. By the end of the course, students will be able to select appropriate statistical tests, conduct analyses, and interpret results in the context of behavioral science research.
Recommended Textbook
Statistics for The Behavioral Sciences 10th Edition by Frederick J Gravetter
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Chapter 1: Introduction to Statistics
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Sample Questions
Q1) After measuring two individuals,a researcher can say that Tom's score is four points higher than Bill's.The measurements must come from a(n)____ scale.
A)nominal
B)ordinal
C)interval
D)interval or ratio
Answer: D
Q2) 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
Q3) What is the value of (X - 2 )2 for the following scores? Scores: 2,3,5
A)8
B)10
C)16
D)36
Answer: B
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Chapter 2: Frequency Distributions
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Sample Questions
Q1) For the distribution in the following table,what is the 90<sup>th</sup> percentile??
\[\begin{array} { l c }
X & c \% \\
30 - 34 & 100 \% \\
25 - 29 & 90 \% \\
20 - 24 & 60 \% \\
15 - 19 & 20 \% \\ \hline \end{array}\]
A)X = 24.5?
B)?X = 25
C)?X = 29
D)?X = 29.5
Answer: D
Q2) A group of quiz scores ranges from 3 to 10,but no student had a score of X = 5.If the scores are put in a frequency distribution table,X = 5 would not be listed in the X column. A)True
B)False
Answer: False
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Chapter 3: Central Tendency
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Sample Questions
Q1) A sample of n = 7 scores has a mean of M = 5.After one new score is added to the sample the new mean is calculated to be M = 6.The new score was X = 13.
A)True
B)False
Answer: True
Q2) A sample of n = 5 scores has a mean of M = 12.What is X for this sample?
A)12/5 = 2.40
B)5/12 = 0.417
C)5(12) = 60
D)5<sup>2</sup>=25
Answer: C
Q3) A sample has n = 7 scores with a mean of M = 7.If one individual with a score of X = 1 is removed from the sample,the new mean will be M = 8. A)True
B)False
Answer: True
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Chapter 4: Variability
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Sample Questions
Q1) In a population with a mean of = 40 and a standard deviation of = 8,a score of X = 46 would be an extreme value,far out in the tail of the distribution.
A)True
B)False
Q2) For a sample of n = 16 scores,how many scores are used to calculate the sample variance?
A)2
B)8
C)15
D)16
Q3) For each of the following samples: Sample #1: 1,0,3,6Sample #2: 1,3,5,4,7
a. Compute the mean.
b. Determine whether it would be better to use the computational or the definitional formula for SS.
c. Compute the SS.
Q4) Multiplying every score in a sample by 3 will not change the value of the standard deviation.
A)True
B)False
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Chapter 5: Z-Scores: Location of Scores and Standardized
Distributions
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Sample Questions
Q1) For a population with µ = 80 and = 10,what is the z-score corresponding to X = 95?
A)+0.25
B)+0.50
C)+0.75
D)+1.50
Q2) For a population with µ = 48 and = 8,find the X value that corresponds to each of the following z-scores: -0.25,-1.50,0.50,2.00.
Q3) A population with µ = 85 and s = 12 is transformed into z-scores.After the transformation,what is the standard deviation for the population of z-scores?
A)s = 12
B)s = 1.00
C)s = 0
D)s = 4.
Q4) A population of scores with µ = 73 and s = 20 is standardized to create a new population with µ = 50 and s = 10.What is the new value for each of the following scores from the original population?Scores: 63,65,77,83
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Chapter 6: Probability
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Sample Questions
Q1) John drives to work each morning and the trip takes an average of µ = 38 minutes.The distribution of driving times is approximately normal with a standard deviation of = 5 minutes.For a randomly selected morning,what is the probability that John's drive to work will take less than 35 minutes?
A)0.6554
B)0.3446
C)0.7257
D)0.2743
Q2) For the normal approximation to the binomial distribution with n = 100 and p = 1/5,the probability of selecting a score greater than or equal to 25 is p = 0.1056.
A)True
B)False
Q3) A normal distribution has a mean of µ = 24 with = 3.What is the minimum score needed to be in the top 14% of the distribution?
A)X = 20.76
B)X = 27.24
C)X = 25.08
D)X = 24.42
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Chapter 7: Probability and Samples: the Distribution of Sample Means
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Sample Questions
Q1) A sample of n = 9 scores has a standard error of 6.What is the standard deviation of the population from which the sample was obtained?
A)54
B)18
C)6
D)2
Q2) The sampling error is the natural discrepancy,or amount of error,between a sample statistic and its corresponding population parameter.
A)True
B)False
Q3) Define the distribution of sample means.
Q4) The mean for a sample of n = 4 scores has a standard error <sub>M</sub> = 5 points.This sample was selected from a population with a standard deviation of = 20. A)True
B)False
Q5) Describe what is measured by the standard error of M.
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Chapter 8: Introduction to Hypothesis Testing
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Sample Questions
Q1) The alpha level determines the risk of a Type I error.
A)True
B)False
Q2) A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If a hypothesis test is used to evaluate the effect of the treatment,which combination of factors is most likely to result in rejecting the null hypothesis?
A)A sample mean near 80 with = .05
B)A sample mean near 80 with = .01
C)A sample mean much different than 80 with = .05
D)A sample mean much different than 80 with = .01
Q3) A significant treatment effect does not necessarily indicate a large treatment effect.
A)True
B)False
Q4) If the research prediction is that the treatment will decrease scores,then the critical region for a directional test will be in the left-hand tail.
A)True
B)False
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Chapter 9: Introduction to the T Statistic
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Sample Questions
Q1) If other factors are held constant,what is the effect of increasing the sample variance?
A)It will increase the estimated standard error and increase the likelihood of rejecting H<sub>0</sub>.
B)It will increase the estimated standard error and decrease the likelihood of rejecting H<sub>0</sub>.
C)It will decrease the estimated standard error and increase the likelihood of rejecting H<sub>0</sub>.
D)It will decrease the estimated standard error and decrease the likelihood of rejecting H<sub>0</sub>.
Q2) A sample of n = 25 scores has a mean of M = 40 and a variance of s<sup>2</sup> = 100.What is the estimated standard error for the sample mean?? A)4?
B)?2
C)? \(\sqrt { 2 }\)
D)?1
Q3) A sample of n = 16 scores has a mean of M = 58 with SS = 960.Use the sample to construct the 90% confidence interval for µ.
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Chapter 10: The T Test for Two Independent Samples
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Sample Questions
Q1) The independent-measures t statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions.
A)True
B)False
Q2) An independent-measures study produces t(21)= 3.00,p < .01.For this study,if effect size is measured with r<sup>2</sup>,then r<sup>2</sup> = 9/30.
A)True
B)False
Q3) A researcher reports t(22)= 5.30,p < .01 for an independent-measures experiment.How many individuals participated in the entire experiment?
A)20
B)21
C)23
D)24
Q4) Describe the data that are collected for an independent-measures t test and the hypotheses that the test evaluates.
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Chapter 11: The T Test for Two Related Samples
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Sample Questions
Q1) If other factors are held constant,which set of data is most likely to produce a significant value for the repeated-measures t statistic?
A)n = 15 and SS = 10 for the difference scores
B)n = 15 and SS = 100 for the difference scores
C)n = 30 and SS = 10 for the difference scores
D)n = 30 and SS = 100 for the difference scores
Q2) A related-sample design consists of scores in one set that are directly related,one-to-one,with the scores in the second set.
A)True
B)False
Q3) Although the original data for a repeated-measures study consist of two scores for each participant,the calculation of the mean and variance are done with only one score for each participant.
A)True
B)False
Q4) For a repeated-measures design,df = n<sub>1</sub> + n<sub>2</sub> - 2 for the t statistic.
A)True
B)False
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Chapter 12: Introduction to Analysis of Variance
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Sample Questions
Q1) In an analysis of variance,what is measured by the MS values?
A)sample variances
B)population variance
C)the average distance from one mean to another
D)the total variability for the set of N scores
Q2) An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.For this study,the three samples have SS<sub>1</sub> = 10,SS<sub>2</sub> = 20,and SS<sub>3</sub> = 15.What value would be obtained for MS<sub>within</sub>?
A)45/14
B)45/12
C)10/2
D)10/3
Q3) For an analysis of variance comparing four treatment means with a separate sample of n = 8 participants in each treatment,the F-ratio will have df = 3,31.
A)True
B)False
Q4) Describe the circumstances in which post tests are used and explain why these tests are necessary.
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Chapter 13: Repeated-Measures Analysis of Variance
Anova
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Sample Questions
Q1) A repeated-measures ANOVA produces SS<sub>between treatments</sub> = 30 and MS<sub>between treatments</sub> = 10.In this analysis,how many treatment conditions are being compared?
A)3
B)4
C)5
D)20
Q2) A repeated-measures study uses a sample of n = 8 participants to evaluate the mean differences between two treatment conditions.The analysis of variance for this study will have df<sub>error</sub> = 7.
A)True
B)False
Q3) Based on the results of a repeated-measures ANOVA,a researcher reports F(4,20)= 2.57,p > .05.For this ANOVA,the null hypothesis was rejected.
A)True
B)False
Q4) Explain why MS<sub>within</sub> is not an appropriate error term (denominator)for the repeated-measures F-ratio.
Page 15
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Chapter 14: Two-Factor Analysis of Variance Independent Measures
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Sample Questions
Q1) A two-factor,independent-measures research study is evaluated using an analysis of variance.The F-ratio for factor A has df = 1,40 and the F-ratio for factor B has df = 3,40.Based on this information,what are the df values for the A x B interaction?
A)df = 2, 40
B)df = 3, 40
C)df = 4, 40
D)df = 7, 40
Q2) If a two-factor analysis of variance produces a statistically significant interaction between the two factors A and B,then what can you conclude about the main effects for A and B?
A)Either the main effect for factor A or the main effect for factor B is also significant.
B)Both the main effect for factor A and the main effect for factor B are significant.
C)Neither the main effect for factor A nor the main effect for factor B is significant.
D)The significance of the main effects is not related to the significance of the interaction.
Q3) What are the assumptions for the two-factor ANOVA?
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Page 16
Chapter 15: Correlation
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Sample Questions
Q1) Which of the following best describes the Pearson correlation for these data??
\[\begin{array} { l l }
\mathrm { X } & \mathrm { Y } \\
2 & 5 \\
5 & 1 \\
3 & 4 \\
4 & 2 \\
\hline
\end{array}\]
A)?It is positive.
B)?It is negative.
C)?It is close to zero.
D)?It is equal to zero.
Q2) Whenever a correlation is computed from scores that do not represent the full range of possible values,one is working with a restricted range and caution should be used when interpreting the correlation.
A)True
B)False
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Chapter 16: Introduction to Regression
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Sample Questions
Q1) A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores.For the analysis of regression testing the significance of the equation,what are the df values for the F-ratio?
A)df = 1, 11
B)df = 1, 12
C)df = 2, 10
D)df = 2, 11
Q2) For linear regression,the value of SS<sub>residual</sub> can be computed directly by (Y - )<sup>2</sup>.
A)True
B)False
Q3) The Pearson correlation between X<sub>1</sub> and Y is r = 0.40 and SS<sub>Y</sub> = 100.When a second variable,X<sub>2</sub>,is added to the regression equation,we obtain R<sup>2</sup> = 0.25.How much additional variability is contributed by adding the second variable as a predictor compared to using X<sub>1</sub> alone?
A)9 points
B)15 points
C)25 points
D)40 points
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Chapter 17: The Chi-Square Statistic: Tests for Goodness of Fit
and Independence
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Q1) For a chi-square test,the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.
A)True
B)False
Q2) Which of the following accurately describes the chi-square test for goodness of fit?
A)It is similar to a single-sample t test because it uses one sample to test a hypothesis about one population.
B)It is similar to a correlation because it uses one sample to evaluate the relationship between two variables.
C)It is similar to an independent-measures t test because it uses separate samples to evaluate the difference between separate populations.
D)It is similar to both a correlation and an independent-measures t test because it can be used to evaluate a relationship between variables or a difference between populations.
Q3) For a chi-square test,the observed frequencies are obtained from the sample.
A)True
B)False
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Chapter 18: The Binomial Test
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Sample Questions
Q1) If a coin is balanced so that p(Heads)= p(Tails)= 1/2,then which of the following outcomes is least likely to occur?
A)9 Heads in 12 tosses (75% Heads)
B)12 Heads in 16 tosses (75% Heads)
C)30 Heads in 40 tosses (75% Heads)
D)75 Heads in 100 tosses (75% Heads)
Q2) For a binomial distribution with p = 1/2 and = 3,the mean is µ = 18.
A)True
B)False
Q3) For a binomial distribution with p = 1/2 and n = 30,the value of X ranges from 1 to 30.
A)True
B)False
Q4) The null hypothesis specifies a value of p for the population.What is the corresponding statistic for the sample?
A)X
B)X/n
C)z
D)pn
Q5) State the four-step procedure used in a binomial hypothesis test.
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