Applied Statistics for Social Sciences
Final Exam Questions
Course Introduction
Applied Statistics for Social Sciences introduces students to the fundamental statistical concepts and methods used in social science research. The course covers topics such as data collection and management, descriptive and inferential statistics, hypothesis testing, correlation, regression analysis, and the interpretation of results. Emphasis is placed on the application of statistical techniques to real-world social issues and the use of statistical software for data analysis. By the end of the course, students will be able to critically evaluate research findings, design basic statistical analyses, and effectively communicate statistical information within the context of social sciences.
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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Q1) A recent report concluded that college graduates have higher life-satisfaction scores than individuals who do not receive college degrees.For this study,graduating versus not graduating is an example of a quasi-independent variable.
A)True
B)False
Answer: True
Q2) Which description provides an example of a continuous variable?
A)The gender of each student in a psychology class
B)The number of males in each class offered by the college
C)The amount of time to solve a problem
D)The number of children in a family
Answer: C
Q3) The first step in computing (X + 1)is to sum the scores.
A)True
B)False
Answer: False
Q4) For the following scores, (X + 1)= 9.Scores: 1,3,0,1
A)True
B)False
Answer: True
Page 3
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Chapter 2: Frequency Distributions
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Sample Questions
Q1) What kind of frequency distribution graph shows the frequencies as bars,with no space between adjacent bars?
A)a bar graph
B)a histogram
C)a polygon
D)a pie chart
Answer: B
Q2) Construct a stem and leaf display for the following scores.30,23,58,28,35,67,27,42,46,3551,33,18,33,25,38,48,36,31,39
Answer: \(
\begin{array}{l}
6 \mid 7 \\
5 \mid 18 \\
4 \mid 826 \\
3 \mid 033586159 \\
2 \mid 3857 \\
1 \mid 8
\end{array}
\)
Key: \( 6 \mid 7=67 \)
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Page 4
Chapter 3: Central Tendency
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Sample Questions
Q1) A sample of n = 8 scores has a mean of M = 10.After one score is removed from the sample,the mean for the remaining score is found to be M = 11.What was the score that was removed?
A)X = 3
B)X = 7
C)X = 8
D)X=10
Answer: A
Q2) What is the median for the following set of scores? Scores: 1,2,6,11,17
A)4
B)6
C)8.5
D)8
Answer: B
Q3) A sample of n = 10 scores has a mean of 50.A second sample has n = 5 scores and M = 60.If the two samples are combined,the sample mean for the combined sample will be greater than 55.
A)True
B)False
Answer: False
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Chapter 4: Variability
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Sample Questions
Q1) In a population of N = 10 scores,the smallest score is X = 8 and the largest score is X = 20.Using the concept of real limits,what is the range for this population?
A)11
B)12
C)13
D)20
Q2) A sample of n = 7 scores has SS = 42.The variance for this sample is s<sup>2</sup> = 6.
A)True
B)False
Q3) If sample variance is computed by dividing SS by n,then the average value of the sample variances from all the possible random samples will be ____ the population variance.
A)smaller than B)larger than C)exactly equal to D)unrelated to
Q4) Using the definitional formula,compute SS,variance and the standard deviation for the following sample of scores.Scores: 3,6,1,6,5,3
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Chapter 5: Z-Scores: Location of Scores and Standardized
Distributions
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Sample Questions
Q1) For a sample with M = 50 and s = 12,what is the X value corresponding to z = -0.25?
A)47
B)53
C)46
D)54
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) For a population with = 30,a score of X = 24 corresponds to z = -2.00.The standard deviation for the population is s = 6.
A)True B)False
Q4) In a sample of n = 40 scores,X = 31 corresponds to z = -1.50 and X = 39 corresponds to z = +0.50.The sample mean is M = 36.
A)True B)False
Q5) For a sample with M = 50 and s = 8,z = 1.50 corresponds to X = 65.
A)True B)False
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Chapter 6: Probability
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Sample Questions
Q1) A vertical line is drawn through a normal distribution at z = 1.20.What proportion of the distribution is on the left-hand side of the line?
A)0.8849
B)0.1151
C)0.3849
D)0.7698
Q2) All probabilities can be expressed as decimal values ranging from 0 to 1.00.
A)True
B)False
Q3) For any normal distribution,the proportion located between the mean and z = 1.40 is 0.9192.
A)True
B)False
Q4) 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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Q1) A sample of n = 4 scores has a standard error of 10 points.For the same population,what is the standard error for a sample of n = 16 scores?
A)1
B)2.5
C)5
D)10
Q2) The mean for a sample of n = 9 scores has a standard error of 2 points.This sample was selected from a population with a standard deviation of s = 18.
A)True
B)False
Q3) Samples of size n = 9 are selected from a population with = 80 with = 18.What is the expected value of M,the mean of the distribution of sample means?
A)6
B)18
C)80/3
D)80
Q4) Describe what is measured by the standard error of M.
Q5) Define the distribution of sample means.
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Chapter 8: Introduction to Hypothesis Testing
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Sample Questions
Q1) The null hypothesis is stated in terms of the population,even though the data come from a sample.
A)True
B)False
Q2) A two-tailed hypothesis test is being used to evaluate a treatment effect with = .05.If the sample data produce a z-score of z = 2.24,then what is the correct decision?
A)Reject the null hypothesis and conclude that the treatment has no effect.
B)Reject the null hypothesis and conclude that the treatment has an effect.
C)Fail to reject the null hypothesis and conclude that the treatment has no effect.
D)Fail to reject the null hypothesis and conclude that the treatment has an effect.
Q3) If the sample data are in the critical region with = .05,then the same sample data would still be in the critical region if were changed to .01.
A)True
B)False
Q4) Define the critical region for a hypothesis test,and explain how the critical region is related to the alpha level.
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Page 10
Chapter 9: Introduction to the T Statistic
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Sample Questions
Q1) A sample of n = 4 scores is selected from a population with an unknown mean.The sample has a mean of M = 40 and a variance of s<sup>2</sup> = 16.Which equation correctly describes the 90% confidence interval for ?
A) = 40 ± 2.353(4)
B) = 40 ± 1.638(4)
C) = 40 ± 2.353(2)
D) = 40 ± 1.638(2)
Q2) If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean, ,what value(s)of t should be used?
A)t = 0
B)t = ±2.131
C)t = ±1.753
D)t = ±1.341
Q3) Two samples from same population probably will have different t statistics even if they are the same size and have the same mean.
A)True
B)False
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Chapter 10: The T Test for Two Independent Samples
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Q1) If two separate samples have M<sub>1</sub> = 10 and M<sub>2</sub> = 18 with a pooled variance of 16,then Cohen's d = 0.50.
A)True
B)False
Q2) An independent-measures research study uses a total of 18 participants to compare two treatment conditions.If the results are used to construct a 90% confidence interval for the population mean difference,then the t values will be ±1.746.
A)True
B)False
Q3) If an independent-measures t statistic has df = 20,then there were a total of 18 individuals participating in the research study.
A)True
B)False
Q4) ?Two samples,each with n = 4 scores,have a pooled variance of 32.The estimated standard error for the sample mean difference is \(\sqrt { 8 }\) .
A)True
B)False
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Chapter 11: The T Test for Two Related Samples
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Q1) For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s<sup>2</sup> = 16.What is the value of the sample mean?
A)M<sub>D</sub> = 2
B)M<sub>D</sub> = 4
C)M<sub>D</sub> = 8
D)M<sub>D</sub> = 16
Q2) A research report describing the results from a repeated-measures t test states,"t(22)= 1.71,p > .05." From this report you can conclude that the outcome of the hypothesis test was to ____.
A)reject the null hypothesis with a sample of n = 23 participants
B)fail to reject the null hypothesis with a sample of n = 23 participants
C)reject the null hypothesis with a sample of n = 22 participants
D)fail to reject the null hypothesis with a sample of n = 22 participants
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
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Chapter 12: Introduction to Analysis of Variance
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Sample Questions
Q1) An analysis of variance comparing three treatment conditions produces df<sub>total</sub> = 32.If the samples are all the same size,how many individuals are in each sample?
A)8
B)9
C)10
D)11
Q2) The distribution of F-ratios is negatively skewed.
A)True
B)False
Q3) An analysis of variance produces SS<sub>between</sub> = 40 and MS<sub>between</sub> = 20.In this analysis,how many treatment conditions are being compared?
A)2
B)3
C)4
D)20
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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Q1) Individual differences refer to participant characteristics such as age,personality,and gender that vary from one person to another.
A)True
B)False
Q2) A repeated-measures ANOVA has SS<sub>within treatments</sub> = 26 and SS<sub>between subjects</sub> = 12.For this analysis,what is the value for SS<sub>error</sub>?
A)12
B)14
C)26
D)38
Q3) For a repeated-measures ANOVA,if SS<sub>between subjects</sub> = 40 and SS<sub>within treatments</sub> = 70,then SS<sub>error</sub> = 30.
A)True
B)False
Q4) One advantage of the repeated-measures ANOVA is that it eliminates "individual differences" as a source of variability.Explain why there are no individual differences in the numerator and in the denominator of the F-ratio.
Page 15
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Chapter 14: Two-Factor Analysis of Variance Independent Measures
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Q1) The results of a two-factor analysis of variance produce df = 1,30 for the F-ratio for factor A,and df = 2,30 for the F-ratio for the A x B interaction.Based on this information,how many levels of factor B were compared in the study?
A)one
B)two
C)three
D)four
Q2) A two-factor study compares two different treatment conditions (factor 1)for males and females (factor 2).In this study,the males have an average score of 20 in the first treatment and an average of 25 in the second.The females average 35 in the first treatment and 45 in the second.For this study,there is no interaction.
A)True
B)False
Q3) For a two-factor analysis of variance,the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.
A)True
B)False
Q4) What are the assumptions for the two-factor ANOVA?
Page 16
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Chapter 15: Correlation
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Sample Questions
Q1) If the Pearson correlation is calculated for a sample of n = 20 individuals,what value for df should be used to determine whether or not the correlation is significant?
A)18
B)19
C)20
D)21
Q2) The value obtained for the sum of products,SP,determines the sign (+/)for the correlation.
A)True
B)False
Q3) A researcher measures driving distance from college and weekly expense on gas for a group of commuting college students.What kind of correlation is likely to be obtained for these two variables?
A)a positive correlation
B)a negative correlation
C)a correlation near zero
D)a correlation near one
Q4) Describe what is meant by a negative relationship and a positive relationship between two variables.
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Chapter 16: Introduction to Regression
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Q1) A regression equation has a slope of b = 3,if M<sub>X</sub> = 3 and M<sub>Y</sub> = 10.The Y-intercept for the equation is 1.
A)True
B)False
Q2) For a linear regression calculated for a sample of n = 20 pairs of X and Y values,what is the value for degrees of freedom for the unpredicted portion of the Y-score variance,MS<sub>residual</sub>?
A)1
B)2
C)18
D)19
Q3) The slope determines how much the Y variable changes when X is increased by one point.
A)True
B)False
Q4) The linear regression equation is structured so that when X = M<sub>X</sub>,the predicted value of Y is equal to M<sub>Y</sub>.
A)True
B)False
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Chapter 17: The Chi-Square Statistic: Tests for Goodness of Fit
and Independence
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Q1) The chi-square test for goodness of fit evaluates the distribution for one variable,and the test for independence evaluates the relationship between two variables.
A)True
B)False
Q2) The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.
A)True
B)False
Q3) What happens to the critical value for a chi-square test if the size of the sample is increased?
A)The critical value also increases.
B)The critical value decreases.
C)The critical value depends on the number of categories, not the sample size.
D)The critical value is determined entirely by the alpha level.
Q4) Cohen's w is a measure of effect size that can be used for both the chi-square test for independence and for goodness of fit.
A)True
B)False
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Chapter 18: The Binomial Test
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Q1) For the binomial test,p = q.
A)True
B)False
Q2) For a binomial distribution with p = 1/2 and n = 30,the value of X ranges from 1 to 30.
A)True
B)False
Q3) For a binomial test with p = 1/2 and n = 36,the z-score for X = 21 is z = +1.00.
A)True
B)False
Q4) For a binomial test,if pn = 10 and qn = 90,then n = 100.
A)True
B)False
Q5) The binomial distribution with p = 1/4 has a standard deviation of 3.For this distribution,there are n = 36 scores in the sample.
A)True
B)False
Q6) The sign test can be used as an alternative to the independent-measures t test.
A)True
B)False
Page 20
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