Statistics for Social Sciences
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Course Introduction
Statistics for Social Sciences introduces students to the fundamental concepts and techniques of statistical analysis as they pertain to social science research. The course covers descriptive statistics, probability distributions, hypothesis testing, and inferential statistics, providing students with the skills to analyze and interpret data relevant to fields such as sociology, psychology, political science, and economics. Through practical examples and hands-on exercises, students learn how to collect data, summarize findings, assess relationships between variables, and draw meaningful conclusions, ultimately preparing them to critically evaluate social science research and conduct their own quantitative studies.
Recommended Textbook
Essentials of Statistics for The Behavioral Sciences 9th Edition by Gravetter
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Chapter 1: Introduction to Statistics
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Sample Questions
Q1) 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
Q2) Statistical techniques are classified into two major categories: descriptive and inferential.Describe the general purpose of each category.
Answer: The purpose of descriptive statistics is to summarize and simplify the organization and presentation of data.The purpose of inferential statistics is to use the limited data from a sample as the basis for making general conclusions about the population.
Q3) What is the value of (X - 2)for the scores 2,3,5?
Answer: A
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Page 3
Chapter 2: Frequency Distributions
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Sample Questions
Q1) For the following distribution of scores,?X = 18.
\[\begin{array} { c c }
X & \mathrm { f } \\
\hline 4 & 1 \\
3 & 2 \\
2 & 3 \\
1 & 2
\end{array}\]
A)True
B)False
Answer: True
Q2) The normal distribution is an example of
A)a histogram showing data from a sample.
B)a polygon showing data from a sample.
C)a bar graph showing data from a population.
D)a smooth curve showing data from a population.
Answer: D
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Chapter 3: Central Tendency
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Sample Questions
Q1) My electric bills for June,July,and August last summer were $75,$75,and $150,respectively.What was the mean amount for the three bills?
A)$75
B)$100
C)$125
D)$150
Answer: B
Q2) For a 100-point exam,a score of X = 65 is definitely above the median.
A)True
B)False Answer: False
Q3) After 5 points are subtracted from every score,the sample mean is found to be M = 24.What was the mean for the original sample?
A)29
B)24
C)19
D)Cannot determine without knowing the number of scores in the sample Answer: A
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Chapter 4: Variability
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Sample Questions
Q1) A sample with a variance of 25 has a standard deviation equal to 5 points.
A)True
B)False
Q2) For a particular population,the largest distance (deviation)between a score and the mean is 11 points.The smallest distance between a score and the mean is 4 points.Therefore,the standard deviation _____.
A)will be less than 4
B)will be between 4 and 11
C)will be greater than 11
D)It is impossible to say anything about the standard deviation.
Q3) A population of scores has µ = 50 and = 5.If every score in the population is multiplied by 3,then what are the new values for the mean and standard deviation?
A)µ = 50 and = 5
B)µ = 50 and = 15
C)µ = 150 and = 5
D)µ = 150 and = 15
Q4) A sample with SS = 40 and a variance of 8 has n = 5 scores.
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) Using z-scores,a population with µ = 37 and = 6 is standardized so that the new mean is µ = 50 and = 10.After the standardization,one individual has a score of X = 55.What was this individual's score in the original distribution?
A)X = 40
B)X = 42
C)X = 43
D)Cannot be determined with the information given
Q2) A score that is 6 points above the mean corresponds to a z-score of z = +0.50.For this population,the standard deviation is = 3.
A)True
B)False
Q3) Last week Tim got a score of X = 54 on a math exam with µ = 60 and = 8.He also got X = 49 on an English exam with µ = 55 and = 3,and he got X = 31 on a psychology exam with µ = 37 and = 4.For which class should Tim expect the best grade?
A)Math
B)English
C)Psychology
D)All 3 grades should be the same.
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Chapter 6: Probability
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Sample Questions
Q1) What is the probability of randomly selecting a z-score less than z = -1.25 from a normal distribution?
A)0.8944
B)0.1056
C)0.3944
D)0.2112
Q2) Which of the following accurately describes the proportions in the tails of a normal distribution?
A)Proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative.
B)Proportions in the right-hand tail are negative, and proportions in the left-hand tail are positive.
C)Proportions in both tails are positive.
D)Proportions in both tails are negative.
Q3) Which of the following is a requirement for a random sample?
A)Every individual has an equal chance of being selected.
B)The probabilities cannot change during a series of selections.
C)There must be sampling with replacement.
D)All of the other 3 choices are correct.
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Page 8
Chapter 7: Probability and Samples: The Distribution of Sample Means
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Q1) If samples are selected from a normal population,the distribution of sample means will also be normal.
A)True
B)False
Q2) If random samples,each with n = 9 scores,are selected from a normal population with µ = 80 and = 18,how much difference,on average,should there be between a sample mean and the population mean?
A)2 points
B)3 points
C)6 points
D)18 points
Q3) If the sample size is doubled,the standard error will be cut in half.
A)True
B)False
Q4) Two samples probably will have different means even if they are both the same size and they are both selected from the same population.
A)True
B)False
Page 9
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Chapter 8: Introduction to Hypothesis Testing
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Sample Questions
Q1) What is the consequence of a Type I error?
A)Concluding that a treatment has an effect when it really does
B)Concluding that a treatment has no effect when it really has no effect
C)Concluding that a treatment has no effect when it really does
D)Concluding that a treatment has an effect when it really has no effect
Q2) The power of a hypothesis test is the probability that the sample mean will be in the critical region even if the treatment has no effect.
A)True
B)False
Q3) A researcher administers a treatment to a sample from a population with a mean of µ = 60.If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect,then the null hypothesis would state that µ 60.
A)True
B)False
Q4) 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
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Chapter 9: Introduction to the t Statistic
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Sample Questions
Q1) What value is estimated with a confidence interval using the t statistic?
A)The value for an unknown sample mean
B)The value for an unknown population mean
C)The difference between two population means
D)The difference between two sample means
Q2) If other factors are held constant,the bigger the sample is,the greater the likelihood of rejecting the null hypothesis.
A)True
B)False
Q3) With = .01,the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ______.
A)t = ±2.602
B)t = ±2.583
C)t = ±2.947
D)t = ±2.921
Q4) In a hypothesis test,a large value for the sample variance increases the likelihood that you will find a significant treatment effect.
A)True
B)False
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Chapter 10: The t Test for Two Independent Samples
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Sample Questions
Q1) A researcher predicts that scores in treatment A will be higher than scores in treatment B.Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?
A)µA = µB
B)µA / µB
C)µA > µB
D)µA < µB
Q2) An independent-measures study uses n = 15 participants in each group to compare two treatment conditions.What is the df value for the t statistic for this study?
A)14
B)15
C)28
D)29
Q3) The homogeneity of variance assumption states that the two population variances are equal.
A)True
B)False
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Chapter 11: The t Test for Two Related Samples
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Q1) For the repeated-measures t statistic,df = _____.
A)n<sub>1</sub> + n<sub>2</sub> - 2
B)(n<sub>1</sub> - 1) + (n<sub>2</sub> - 1)
C)n - 1
D)n<sub>1</sub> + n<sub>2</sub> - 1
Q2) A research study produces a t statistic with df = 14.For this study,which of the following designs would require a total of 30 participants?
A)An independent-measures design
B)A repeated-measures design
C)A matched-subjects design
D)None of the other options would require a total of 30 participants.
Q3) 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
Q4) One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.
A)True
B)False
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Chapter 12: Introduction to Analysis of Variance
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Q1) An ANOVA is used to determine whether any significant difference exists between treatment means,and posttests are used to determine exactly which treatment means are significantly different.
A)True
B)False
Q2) In analysis of variance,what is measured by the MS values?
A)Sample variance
B)Population variance
C)The average distance from one mean to another
D)The total variability for the set of N scores
Q3) An analysis of variances produces df = 29 and dfw th n = 27.For this analysis,how many treatment conditions are being compared?
A)1
B)2
C)3
D)Cannot be determined without additional information
Q4) \(\text { SSwithin }\) measures the size of the sample variances.
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) The following table shows the results of a repeated-measures ANOVA.Based on this table,what is the value for n²,the percentage of variance accounted for by the treatments? \[\begin{array} { l c c c c }
\text { Source } & \text { SS } & \text { df } & \text { MS } & \\
\text { Between } & 22 & 2 & 11 & F = 5.50 \\
\text { Within } & 58 & 21 & & \\
\text { Bet. Sub. } & 30 & 7 & & \\
\text { Error } & 28 & 14 & 2 & \\
\text { Total } & 80 & 23 & & \end{array}\]
A)22/30
B)22/50
C)22/58
D)22/80
Q2) A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.
A)True
B)False
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Chapter 14: Correlation and Regression
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Q1) The regression equation is determined by finding the minimum value for which of the following?
A)?(X - Y)<sup>2</sup>
B)?(Y - ?)
C)?(Y - ?)<sup>2</sup>
D)r²?(Y - ?)<sup>2</sup>
Q2) For a two-tailed hypothesis test evaluating the significance of a correlation,the null hypothesis states that the sample correlation is zero.
A)True
B)False
Q3) A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores.If the researcher tests the significance of the correlation,what value will be obtained for the t statistic?
A)0.6/0.16 = 3.75
B)0.6/0.4 = 1.50
C)0/6/0.8 = 0.77
D)0.6/1.0 = 0.6
Q4) Compute the Pearson correlation for the following data.
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Chapter 15: The Chi-Square Statistic: Tests for Goodness of
Fit and Independence
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Q1) 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.
Q2) The data for a chi-square test consist of ___________.
A)numerical scores
B)non-numerical categories
C)ranks
D)frequencies
Q3) For either chi-square test, f = n.
A)True
B)False
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