Psychological Statistics
Exam Answer Key
Course Introduction
Psychological Statistics introduces students to the fundamental concepts and techniques of statistical analysis as applied to psychological research. The course covers descriptive statistics, probability theory, hypothesis testing, correlation, regression, and analysis of variance (ANOVA), with an emphasis on understanding and interpreting data in the behavioral sciences. Students learn practical skills in data collection, organization, and analysis, as well as critical evaluation of statistical results. Through hands-on exercises and real-world examples, the course prepares students to apply statistical reasoning in conducting and evaluating psychological research.
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) After measuring two individuals,a researcher can say that Tom's score is 4 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 first step in computing (X + 1)is to add 1 point to each score.
A)True
B)False
Answer: True
Q3) What is the first step to be performed in the following mathematical expression, X²?
A)Square each score
B)Add the scores
C)Add the squared scores
D)Square the sum of the scores
Answer: A
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Page 3
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)All of these
Answer: B
Q2) A grouped frequency distribution table does not provide enough information to obtain a complete listing of the original set of scores.
A)True
B)False
Answer: True
Q3) Briefly explain what information is available in a regular frequency distribution table that is not available in a grouped table.
Answer: A regular table identifies each individual score.However,in a grouped table,you only know that an individual score is located in a particular interval,but you do not know its exact value.
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Chapter 3: Central Tendency
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Sample Questions
Q1) For the scores in the following frequency distribution table,the mean is M = 3.
\[\begin{array} { l l }
X & f \\
\hline 4 & 1 \\
3 & 4 \\
2 & 2
\end{array}\]
A)True
B)False
Answer: False
Q2) A population with a mean of = 6 has X = 54.How many scores are in the population?
A)N = 9
B)N = 27
C)N = 6×54 = 324
D)Cannot be determined from the information given
Answer: A
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Chapter 4: Variability
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Sample Questions
Q1) What is the value of SS for the following set of scores? Scores: 8,3,1.
A)26
B)29
C)74
D)144
Q2) For a population of scores,the sum of the deviation scores is equal to N.
A)True
B)False
Q3) What is the value of SS for the following set of scores? Scores: 0,1,4,5
A)17
B)18
C)42
D)Cannot answer without knowing whether it is a sample or a population
Q4) 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
Q5) Using the definitional formula,compute SS for the following population and then find the population variance and the standard deviation.Scores: 9,4,0,6,1,4
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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 = 70 and = 8,what is the z-score corresponding to X = 82?
A)+0.25
B)+0.75
C)+1.25
D)+1.50
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 sample with M = 80,a score of X = 88 corresponds to z = 2.00.What is the sample standard deviation?
A)2
B)4
C)8
D)16
Q4) For a sample with a standard deviation of s = 8,a score of X = 42 corresponds to z = -0.25.The mean for the sample is M = 40.
A)True
B)False
7
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Chapter 6: Probability
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Sample Questions
Q1) For a normal distribution,the proportion in the tail beyond z = 0.30 is p = 0.1179.
A)True
B)False
Q2) If one score is randomly selected from a normal distribution with µ = 100 and = 20,the probability of obtaining a score greater than X = 110 is p = 0.6915.
A)True
B)False
Q3) For any normal distribution,exactly 97.50% of the z-score values are less than z = 1.96.
A)True
B)False
Q4) What z-score value separates the highest 10% of the scores in a normal distribution from the lowest 90%?
A)z = 1.28
B)z = 0.25
C)z = -1.28
D)z = -0.25
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Chapter 7: Probability and Samples: The Distribution of Sample Means
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Q1) A sample is selected from a population with µ = 30 and = 10.If the sample mean of M = 34 corresponds to z = +2.00,then the sample size is n = 25.
A)True
B)False
Q2) For a population with µ = 50 and ? = 6,describe the shape,the mean,and the standard deviation for the distribution of sample means for each of the following:
A)Samples of n = 4.
B)Samples of n = 36.
Q3) A sample of n = 9 scores is selected from a population with µ = 40 and = 18.If the sample mean corresponds to z = -1.00,then the sample mean is M = 31.
A)True
B)False
Q4) Under what circumstances will the distribution of sample means be normal?
A)It is always normal
B)Only if the population distribution is normal
C)Only if the sample size is greater than 30
D)If the population is normal or if the sample size is greater than 30
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Chapter 8: Introduction to Hypothesis Testing
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Q1) Which of the following correctly describes the effect of increasing the alpha level (for example,from .01 to .05)?
A)Increase the likelihood of rejecting H0 and increase the risk of a Type I error
B)Decrease the likelihood of rejecting H0 and increase the risk of a Type I error
C)Increase the likelihood of rejecting H0 and decrease the risk of a Type I error
D)Decrease the likelihood of rejecting H0 and decrease the risk of a Type I error
Q2) 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.
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Chapter 9: Introduction to the t Statistic
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Sample Questions
Q1) A sample of n = 16 scores with a sample variance of s² = 64 has an estimated standard error of 4 points.
A)True
B)False
Q2) 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.
Q3) Under what circumstances can a very small treatment effect be statistically significant?
A)If the sample size big and the sample variance is small
B)If the sample size and the sample variance are both big
C)If the sample size is small and the sample variance is big
D)If the sample size and the sample variance are both small
Q4) If other factors are held constant,as the sample variance increases,the estimated standard error also increases.
A)True
B)False
Q5) A research report states "t(8)= 2.00,p > .05." For this test,r² = 2/10.
A)True
B)False
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Chapter 10: The t Test for Two Independent Samples
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Q1) A researcher predicts that scores in treatment A will be higher than scores in treatment B.If the mean for the 10 participants in treatment A is 4 points higher than the mean for the 10 participants in treatment B and the data produce t = 2.095,what decision should be made?
A)With = .05, reject H0 for both a one-tailed and a two-tailed test
B)With = .05, fail to reject H0 for both a one-tailed and a two-tailed test
C)With = .05, reject H0 for a one-tailed test but fail to reject for a two-tailed test
D)With = .05, reject H0 for a two-tailed test but fail to reject for a one-tailed test
Q2) For the independent-measures t statistic,what is the effect of increasing the difference between sample means?
A)Increase the likelihood of rejecting H0 and increase measures of effect size
B)Increase the likelihood of rejecting H0 and decrease measures of effect size
C)Decrease the likelihood of rejecting H0 and increase measures of effect size
D)Decrease the likelihood of rejecting H0 and decrease measures of effect size
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12
Chapter 11: The t Test for Two Related Samples
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Q1) In general,what is the effect of an increase in the variance for the sample of difference scores?
A)An increase in the standard error and an increase in the value of t
B)An increase in the standard error and a decrease in the value of t
C)A decrease in the standard error and an increase in the value of t
D)A decrease in the standard error and a decrease in the value of t
Q2) If the sample size is held constant,which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?
A)MD = 5 with s2 = 5 for the difference scores
B)MD = 5 with s2 = 10 for the difference scores
C)MD = 3 with s2 = 10 for the difference scores
D)MD = 3 with s2 = 20 for the difference scores
Q3) A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment.What is the value of df for the repeated-measures t statistic?
A)18
B)19
C)38
D)39
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Page 13
Chapter 12: Introduction to Analysis of Variance
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Sample Questions
Q1) On average,what value is expected for the F-ratio if the null hypothesis is true?
A)0
B)1.00
C)k - 1
D)N - k
Q2) The larger the differences among the sample means,the larger the numerator of the F-ratio will be.
A)True
B)False
Q3) \(S S _ { \text {between } }\) measures the size of the mean differences from one treatment to another.
A)True
B)False
Q4) 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
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Chapter 13: Repeated-Measures and Two-Factor Analysis of Variance
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Q1) The result of a repeated-measures ANOVA stated that F(3,21)= 4.57,p < .05.The study used a sample of n = 7 participants.
A)True
B)False
Q2) For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,what are the degrees of freedom for the repeated-measures F-ratio?
A)2, 6
B)2, 9
C)2, 11
D)3, 11
Q3) The F-ratio for a repeated-measures ANOVA has df = 2,16.The research study compared 3 treatments with a sample of n = 8 participants.
A)True
B)False
Q4) A repeated-measures study has n = 8 participants and k = 3 treatments.For this study,df = 21.
A)True
B)False
15
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Chapter 14: Correlation and Regression
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Sample Questions
Q1) A set of n = 5 pairs of X and Y scores has X = 15, Y = 5,and XY = 10.For these data,what is the value of SP?
A)-5
B)5
C)10
D)25
Q2) What is the value of SP for the following set of data? \[\begin{array} { l l }
\mathrm { X } & \mathrm { Y } \\
\hline 4 & 3 \\
1 & 2 \\
1 & 5 \\
2 & 6
\end{array}\]
A)-1
B)-5 4
C)5 1
D)None of the other 3 choices is correct.
Q3) 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) In the observed frequencies for a chi-square test for independence,how often is each participant counted?
A)Just once
B)Once in each row
C)Once in each column
D)Once in each row and once in each column
Q2) 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
Q3) 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
Q4) One characteristic of nonparametric tests is that they make few,if any,assumptions about the populations being investigated.
A)True
B)False
Page 17
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