Introduction to Statistics Exam Solutions
Course Introduction
Introduction to Statistics offers a comprehensive foundation in the principles and methods of statistical analysis, essential for interpreting data in a variety of disciplines. Students will learn to collect, organize, and summarize data, as well as to perform and interpret basic statistical procedures such as measures of central tendency, variability, probability distributions, hypothesis testing, confidence intervals, and correlation. Emphasis is placed on real-world applications, critical thinking, and the use of statistical software, preparing students to make informed decisions based on data-driven evidence.
Recommended Textbook
Statistics A Tool for Social Research 8th Edition by Joseph F. Healey
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Chapter 1: Introduction
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Sample Questions
Q1) In addition to saying that one case is different from another,the ordinal level of measurement allows us to
A)order categories from high to low.
B)measure the distance between high and low.
C)say that one case is more or less than another.
D)both a and c
Answer: D
Q2) Which of the following questions would generate a continuous variable?
A)How old are you?
B)How many books do you own?
C)How many times have you ever changed a flat tire?
D)How many degrees do you have?
Answer: A
Q3) Without statistics,____ research would be impossible.
A)meaningful
B)important
C)qualitative
D)quantitative
Answer: D
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Page 3
Chapter 2: Basic Descriptive Statistics:
Percentages,
Ratios
and Rates, Tables, Charts and Graphs
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Sample Questions
Q1) The ratio of men to women in a karate class is 3.3:1.If there are 100 women,how many men are there?
A)33
B)66
C)133
D)330
Answer: D
Q2) Forty of every two hundred students attend all of their classes.What percentage of the student body is this?
A)5%
B)50%
C)2%
D)20%
Answer: D
Q3) Proportions and percentages,ratios and rates are all ways of expressing
A)concise distributions of a variable
B)data without leaving out any details
C)relative frequencies
D)raw frequencies
Answer: C
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Chapter 3: Measures of Central Tendency
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Q1) The median represents the score that is A)half of the sum of the other scores.
B)the most common or frequent.
C)in the middle.
D)midway between the highest and lowest scores.
Answer: C
Q2) The most appropriate measure of central tendency for gender would be the A)median.
B)mode.
C)mean.
D)none of the above
Answer: B
Q3) In any distribution,the mean and the median will have the same value when the distribution is A)symmetrical.
B)positively skewed.
C)negatively skewed.
D)all of the above
Answer: A
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Page 5
Chapter 4: Measures of Dispersion
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Sample Questions
Q1) The average deviation (AD)is based on
A)squaring the differences between the score and the mean.
B)ignoring the signs of the differences between the scores and the mean.
C)subtracting each score from the median.
D)subtracting each score from the mode.
Q2) According to the data presented in the text,incomes in the U.S.are
A)falling for the average family.
B)rising for everyone except the very rich.
C)decreasing in dispersion (income inequality is decreasing).
D)increasing in dispersion (income inequality is increasing).
Q3) If the standard deviation of a group of scores is 0,
A)the range would be at a maximum value.
B)there is maximum variation in the scores.
C)there is no variation in the scores.
D)the mean is larger than the median.
Q4) The distances between the scores and the mean are called A)deviations.
B)differences.
C)ranges.
D)summations.
Page 6
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Chapter 5: The Normal Curve
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Sample Questions
Q1) A social researcher has constructed a measure of racial prejudice and obtained a distribution of scores on this measure from a randomly selected sample of public office holders.The scores were normally distributed with a mean of 45 and a standard deviation of 7.What is the probability that a randomly selected case from the sample will have a score less than 38?
A)0.4526
B)0.5018
C)0.5200
D)0.1587
Q2) The area between the mean and a Z score of +1.50 is 43.32%.This score is higher than ____ of the scores in the distribution.
A)43.32%
B)51.50%
C)57.68%
D)93.32%
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Chapter 6: Introduction to Inferential Statistics: Sampling and
the Sampling Distribution
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Sample Questions
Q1) According to the theorems presented in Chapter 6,we can be sure that the sampling distribution is normal if
A)the population is small.
B)the population is normal.
C)the sample is stratified.
D)the sample is normal.
Q2) Both the sample and the population distributions are empirical,which means that they are A)theoretical.
B)real.
C)ordinal.
D)stratifieD.
Q3) A researcher tests a theory about sexism by administering a survey to the 200 students in her sociology classes.This sample is best characterized as a A)cluster sample.
B)stratified random sample.
C)non-probability sample.
D)sampling distribution.
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Chapter 7: Estimation Procedures
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Q1) In a two person race,if the Republican presidential candidate is projected to attract 44%\(\pm\) 3% of the vote,and the Democratic candidate is projected to attract 46%\(\pm\) 3% of the vote,then
A)the Republican is the probable winner.
B)the Democrat is the probable winner.
C)neither candidate will win a majority of votes in the electoral college.
D)the race is "too close to call."
Q2) From a random sample of 300 state university students,you found that the average number of hours of study time each week is 30 with a standard deviation of 5.A point estimate of the average study time for all state university students would be A)5.
B)30.
C)300.
D)15\(\pm\) 1 standard deviation.
Q3) As our confidence in an interval estimate increases,the width of the interval
A)decreases.
B)increases.
C)remains the same.
D)increases or decreases depending on the alpha level.
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Page 9
Chapter 8: Hypothesis Testing I: the One-Sample Case
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Q1) When testing a single sample mean for significance when the population standard deviation is unknown and sample size is 75,the correct sampling distribution is A)the t distribution.
B)the Z distribution.
C)it makes no difference.
D)t for a one-tailed test,Z for a two-tailed test.
Q2) In tests of significance,if the test statistic does NOT fall in the critical region,we
A)conclude that the population distribution is normal.
B)reject the null hypothesis.
C)fail to reject the research hypothesis.
D)conclude that our alpha level was too low.
Q3) As the Critical Region decreases in size,
A)the probability of Type I error increases.
B)the probability of rejecting the null hypothesis increases.
C)alpha increase.
D)the probability of Type II error increases.
Q4) Cite an example of a research situation in which a one-tailed test of significance would be appropriate.
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Page 10
Chapter 9: Hypothesis Testing II: the Two-Sample Case
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Q1) When testing for the significance of the difference between two sample means,we must first estimate ____ before we can compute the test statistic.
A)the standard deviation of the sampling distribution
B)the standard deviations of the samples
C)the population means
D)the critical region
Q2) When testing for the significance of the difference between two sample means,the standard deviation of the sampling distribution is estimated using A)population standard deviations.
B)the standard error of the means.
C)degrees of freedom.
D)sample standard deviations corrected for bias.
Q3) A difference between samples that is shown to be statistically significant is always
A)theoretically important.
B)practically important.
C)sociologically important.
D)none of the above
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11
Chapter 10: Hypothesis Testing III: the Analysis of Variance
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Q1) In the ANOVA test,degrees of freedom within (dfw)are equal to (N - k)and degrees of freedom between (dfb)are equal to ____.
A)(N - k)
B)(k - 1)
C)(N + k)
D)(k - N)
Q2) Which of the following is an assumption that must be made in Step 1 of the ANOVA test?
A)independent random samples
B)dependent random samples
C)level of measurement is nominal
D)stratified random samples
Q3) A researcher has analyzed differences in average College Board scores for random samples of students from four different colleges.The obtained F score is 0.45.What can be concluded about the null hypothesis?
A)Nothing,more information is needed.
B)Reject,the differences did not occur by random chance.
C)Fail to reject,differences are not statistically significant.
D)Fail to reject,differences are statistically significant.
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Page 12
Chapter 11: Hypothesis Testing Iv: Chi Square
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Q1) For Chi square,a small sample is one in which
A)many expected frequencies are less than 5.
B)many observed frequencies are less than 5.
C)N is less than 100.
D)N is less than 50.
Q2) A problem with large samples in the chi square test is that the test statistic
A)increases at the same rate as sample size and trivial relationships may seem important.
B)decreases as sample size increases and may cause Type I errors.
C)fluctuates so much that the results are completely unreliable.
D)is always elevated above the neutral area.
Q3) An obtained chi square of 10.78 has been calculated.Critical Chi square is 3.841.What should be concluded?
A)nothing,information is incomplete
B)reject the null hypothesis,the variables are not independent
C)reject the null hypothesis,the variables are independent
D)fail to reject the null hypothesis
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Chapter 12: Bivariate Association: Introduction and Basic Concepts
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Sample Questions
Q1) With the independent variable in the columns,the "maximum difference" is the largest difference
A)in column percents in any row.
B)in row percents in any column.
C)between the marginals.
D)between any two cell frequencies.
Q2) If variables are arranged in a bivariate table,we can see if they are associated by
A)adding their scores vertically.
B)subtracting their scores horizontally.
C)computing percentages in the direction of the independent variable.
D)computing percentages in the direction of the dependent variable.
Q3) "As education increases,income rises." This is an example of a A)non-causal relationship.
B)positive relationship.
C)negative relationship.
D)neutral relationship.
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14
Chapter 13: Association Between Variables Measured at the
Nominal Level
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Sample Questions
Q1) Cramer's V differs from phi in that it
A)ranges from 0 to -1.00.
B)is computed using the expression (minimum of r - 1,c - 1).
C)can never exceed .80.
D)has only one degree of freedom.
Q2) According to the logic of proportional reduction of error (PRE),if two variables are associated,then information about the independent variable
A)eliminates errors in the prediction of the dependent variable.
B)reduces the number of errors in predicting the dependent variable.
C)has no effect on the ability to predict the dependent variable.
D)decreases errors of prediction for negative relationships and increases errors for positive relationships.
Q3) Lambda is asymmetric,which means that
A)the value of lambda is the same regardless of which variable is taken as independent.
B)the upper limit of lambda is less than 1.00.
C)the value of lambda may vary depending on which variable is taken as independent.
D)lambda cannot exceed .50.
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Page 15
Chapter 14: Association Between Variables Measured at the
Ordinal Level
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Q1) Gamma is a symmetrical measure of association.This means that A)values of gamma cluster around the center of the range of scores.
B)gamma is just as likely to be negative as positive.
C)gamma cannot exceed the value of the highest score.
D)the value of gamma will be the same regardless of which variable is assumed to be independent.
Q2) The lowest possible value (indicating the weakest possible relationship)for gamma is A)-1.00.
B)-10.00.
C)0.05. D)0
Q3) Gamma is based on two prediction rules.In the first,we ____ and in the second we
A)ignore X,take X into account
B)ignore Y,take X into account
C)ignore X,take Y into account
D)ignore both X and Y,take only Y into account
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Chapter 15: Association Between Variables Measured at the
Interval-Ratio Level
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Sample Questions
Q1) A researcher wants to measure the strength of the association between income (measured in dollars per year)and education (measured in number of years of formal schooling).Which of the following would be the most appropriate measure of association?
A)the slope (b)
B)gamma
C)chi square
D)Pearson's r
Q2) If the regression line on a scattergram slopes upward from left to right,the relationship is
A)bivariate.
B)strong.
C)parallel.
D)positive.
Q3) In regression analysis,the symbol a stands for
A)the scores on the Y variable.
B)the slope.
C)the Y intercept.
D)the X intercept.
Page 17
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Chapter 16: Elaborating Bivariate Tables
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Sample Questions
Q1) The gamma for a bivariate table is 0.42 and the partial gamma (G<sub>p</sub>)is 0.05.This is consistent with
A)interaction between X and Z.
B)interaction between X and Y.
C)a direct relationship between X and Y.
D)a spurious relationship between X and Y.
Q2) With the elaboration technique,it is important to have large samples to A)avoid having to control for a third variable.
B)fill up the cells in the partial tables.
C)eliminate the possibility of spurious relationships.
D)increase the value of the measure of association.
Q3) The elaboration technique controls for a third variable by A)fixing its values so they are no longer free to vary. B)eliminating the variable from the analysis.
C)replacing its values with those of the independent.
D)adding a column to the bivariate table to include the control variable.
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Chapter 17: Partial Correlation and Multiple Regression and Correlation
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Q1) The partial correlation coefficient will reveal an interactive relationship between three variables when
A)the partial correlation coefficients drops to zero.
B)the partial is greater in value than the zero-order correlation coefficient.
C)the partial correlation coefficient is negative.
D)none of the above.Partial correlation will not detect interaction.
Q2) If a = 1,b<sub>1</sub> = 10,b<sub>2</sub> = 10,X<sub>1</sub>= 2,and X<sub>2</sub>
= 3,what would the predicted Y score be?
A)51
B)26
C)5
D)0
Q3) In the analysis of the relationship between crime,poverty,age,and region reported in the text,which independent variable(s)had the strongest effect on the dependent variable according to the beta-weights?
A)region
B)poverty and age had equally strong effects
C)region and age had equally strong effects
D)poverty
Page 19
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