Introduction to Statistics Exam Questions
Course Introduction
Introduction to Statistics offers students a foundational understanding of the principles and methods used to analyze data and draw meaningful conclusions. The course covers essential topics such as descriptive statistics, probability, sampling techniques, hypothesis testing, confidence intervals, and regression analysis. Through practical examples and problem-solving exercises, students learn how to collect data, interpret statistical results, and apply statistical reasoning to real-world situations across various disciplines. This course equips learners with the quantitative skills necessary for informed decision-making and further study in statistics or related fields.
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) 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) A discrete variable must be measured on a nominal or an ordinal scale.
A)True
B)False
Answer: False
Q3) A researcher is curious about the average monthly cell phone bill for high school students in the state of Florida.If this average could be obtained,it would be an example of a ______.
A)sample
B)statistic
C)population
D)parameter
Answer: D
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Page 3
Chapter 2: Frequency Distributions
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Sample Questions
Q1) What is the shape of the distribution for the following set of data? Scores: 1,2,3,3,4,4,4 5,5,5,5,6
A)Symmetrical
B)Positively skewed
C)Negatively skewed
D)Normal
Answer: C
Q2) A frequency distribution graph represents frequencies with vertical bars without space between them.What scale of measurement was used to measure the scores?
A)Nominal
B)Ordinal
C)Nominal or ordinal
D)Interval or ratio
Answer: D
Q3) 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
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Page 4
Chapter 3: Central Tendency
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Sample Questions
Q1) What is the mean for the following sample of scores? Scores: 1,4,5,6
A)16
B)8
C)4.5
D)4
Answer: D
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) A set of N = 8 scores has a mean of µ = 11.If 16 points are added to one of the scores,what is the new value for the population mean?
A)10
B)11
C)12
D)13
Answer: D
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Page 5
Chapter 4: Variability
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Sample Questions
Q1) If a sample of n = 6 scores has X = 30 and X² = 200,then SS = 20.
A)True
B)False
Q2) The value for SS can never be less than zero.
A)True
B)False
Q3) A population of N = 100 scores has µ = 30 and = 4.What is the population variance?
A)2
B)4
C)8
D)16
Q4) If you have a score of X = 66 on an exam with µ = 70,you should expect a better grade if = 10 than if = 5.
A)True
B)False
Q5) 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) Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?
A)When the population mean is much larger than 15
B)When the population standard deviation is much larger than 15
C)When the population mean is much smaller than 15
D)When the population standard deviation is much smaller than 15
Q2) Under what circumstances is a score that is located 5 points above the mean a central value,relatively close to the mean?
A)When the population mean is much less than 5
B)When the population mean is much greater than 5
C)When the population standard deviation is much less than 5
D)When the population standard deviation is much greater than 5
Q3) 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.
Q4) For a population with = 34,a score of X = 31 corresponds to z = -1.00.The standard deviation for the population is = 6.
A)True
B)False
Page 7
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Chapter 6: Probability
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Sample Questions
Q1) A normal distribution has = 20 and = 4.What is the probability of randomly selecting a score greater than 25 from this distribution?
A)0.3944
B)0.1056
C)0.8944
D)0.7888
Q2) The probability of randomly selecting a red marble from a jar that contains 10 red marbles and 20 blue marbles is 1/30.
A)True
B)False
Q3) What is the probability of randomly selecting a z-score greater than z = -0.75 from a normal distribution?
A)0.7734
B)0.2266
C)0.2734
D)0.4532
Q4) The proportion in the tail of a normal distribution can never be more than 0.50.
A)True
B)False
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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 is obtained from a population with = 70 and = 8.If the sample mean corresponds to a z-score of 2.00,what is the value of the sample mean?
A)M = 86
B)M = 78
C)M = 74
D)M = 72
Q2) On average,a sample of n = 16 scores will provide a better estimate of the population mean than you would get with a sample of n = 9 scores from the same population.
A)True
B)False
Q3) A random sample of n = 4 scores is obtained from a normal population with µ = 30 and = 8.What is the probability that the sample mean will be smaller than M = 22?
A)0.00003
B)0.0228
C)0.1587
D)0.3085
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Page 9
Chapter 8: Introduction to Hypothesis Testing
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Sample Questions
Q1) If other factors are held constant,then increasing the sample size will increase the likelihood of rejecting the null hypothesis.
A)True
B)False
Q2) 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
Q3) You complete a hypothesis test using = .05,and based on the evidence from the sample,your decision is to reject the null hypothesis.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 less than 5%.
D)You have made the correct decision.
Q4) The value obtained for Cohen's d is independent of the sample size.
A)True
B)False
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Page 10
Chapter 9: Introduction to the t Statistic
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Sample Questions
Q1) A sample with a mean of M = 40 and a variance of s² = 20 has an estimated standard error of 1 point.How many scores are in the sample?
A)4
B)5
C)20
D)21
Q2) A hypothesis test produces a t statistic of t = 2.20.If the researcher is using a two-tailed test with = .05,how large does the sample have to be in order to reject the null hypothesis?
A)At least n = 11
B)At least n = 12
C)At least n = 13
D)At least n = 14
Q3) If two samples,each with n = 20 scores,are selected from the same population and both have the same mean (M = 53)and the same variance (s² = 12),then they will also have the same t statistic.
A)True
B)False
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Chapter 10: The t Test for Two Independent Samples
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Q1) An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments.What is the df value for the t statistic for this study?
A)7
B)12
C)13
D)14
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) Two samples,each with n = 5 scores,have a pooled variance of 40.What is the estimated standard error for the sample mean difference?
A)4
B)8
C)10
D)20
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Chapter 11: The t Test for Two Related Samples
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Sample Questions
Q1) A sample of difference scores has a mean of MD = 5 with a variance of s² = 100.If effect size is measured using Cohen's d,what is the value of d?
A)5/10
B)5/100
C)25/100
D)Cannot determine without knowing the sample size
Q2) For a repeated-measures study,a small variance for the difference scores indicates that the treatment effect is consistent across participants.
A)True
B)False
Q3) For a repeated-measures study,as the sample mean difference increases,the likelihood of rejecting the null hypothesis also increases.
A)True
B)False
Q4) Repeated-measures designs are particularly well-suited to research studies examining learning or other changes that occur over time.
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 within treatment?
A)2
B)11
C)33
D)35
Q2) Which of the following describes a typical distribution of F-ratios?
A)Symmetrical with a mean of zero
B)Positively skewed with all values greater than or equal to zero
C)Negatively skewed with all values greater than or equal to zero
D)Symmetrical with a mean equal to \(d f _ { \text {between } }\)
Q3) \(\text { SSwithin }\) measures the size of the sample variances.
A)True
B)False
Q4) For an ANOVA,when the null hypothesis is true,the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.
A)True
B)False
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Chapter 13: Repeated-Measures and Two-Factor Analysis of Variance
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Q1) The analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measures ANOVA.
A)True
B)False
Q2) In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the numerator of the F-ratio?
A)They do not exist because the same individuals participate in all treatments.
B)They are measured and subtracted out in the second stage of the analysis.
C)Individual differences contribute to the variance in the numerator.
D)None of the other options accurately describes individual differences in the numerator.
Q3) 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 = 7.
A)True
B)False
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Chapter 14: Correlation and Regression
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Sample Questions
Q1) It is possible for none of the actual (observed)data points to be located on the regression line described by the regression equation.
A)True
B)False
Q2) Which of the following Pearson correlations shows the greatest strength or consistency of relationship?
A)-0.90
B)+0.74
C)+0.85
D)-0.33
Q3) A sample of n = 25 pairs of scores (X and Y values)produces a correlation of r = -0.40.Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.
Q4) A researcher obtains SS = 20,SS = 5,and SP = 7 for a set of n = 25 pairs of scores.The Pearson correlation for these scores is r = 7/10 = 0.70.
A)True
B)False
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Page 16
Chapter 15: The Chi-Square Statistic: Tests for Goodness of
Fit and Independence
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Q1) For a fixed level of significance,how is the critical value for chi-square related to degrees of freedom?
A)The critical value increases as df increases.
B)The critical value decreases as df increases.
C)The critical value increases as sample size increases.
D)The critical value decreases as sample size increases.
Q2) A researcher selects a sample of 100 people to investigate the relationship between gender (male/female)and registering to vote.The sample consists of 40 females,of whom 30 are registered voters,and 60 males,of whom 40 are registered voters.If these data were used for a chi-square test for independence,what is the expected frequency for registered females?
A)12
B)28
C)40
D)42
Q3) What values are specified by the null hypothesis for a chi-square test?
A)Frequencies for a sample
B)Frequencies for a population
C)Proportions for a sample
D)Proportions for a population
Page 17
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