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# Chapter 22—Bivariate Statistical Analysis: Differences Between Two Variables. All Answers

Chapter 22—Bivariate Statistical Analysis: Differences Between Two Variables TRUE/FALSE 1. Tests are bivariate tests of differences when they involve only two variables: a variable that acts like a dependent variable and a variable that acts as a classification variable. T PTS: 1 DIF: Moderate REF: p. 529 OBJ: LO: 22-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 2. If a researcher is interested in whether males switch jobs more frequently than do females, this is an example of univariate statistics. F This is an example of bivariate statistics. PTS: 1 DIF: Hard REF: p. 529 OBJ: LO: 22-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Application 3. The type of measurement, the nature of the comparison, and the number of groups to be compared influence the statistical choice. T PTS: 1 DIF: Moderate REF: p. 529 OBJ: LO: 22-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 4. A cross-tabulation is a simple way to describe the relationships between two groups. T PTS: 1 DIF: Moderate REF: p. 531 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 5. One way to test the significance of contingency tables is by means of the t-test. F One way to test the significance of contingency tables is by means of the chi-square test. PTS: 1 DIF: Moderate REF: p. 531 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 6. The chi-square test requires the researcher to compare the observed frequencies of the groups with the expected frequencies of the groups. T PTS: 1 DIF: Moderate REF: p. 531 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 7. To use the chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio scale. F A frequency count of data that nominally identify or categorically rank groups is acceptable. PTS: 1 DIF: Moderate REF: p. 531 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 8. The chi-square test requires that the expected frequency in each cell of the contingency table be at least 30. F The expected frequency in each cell should be at least 5. PTS: 1 DIF: Moderate REF: p. 533 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 9. The independent samples t-test tests the differences between means taken from two independent samples or groups. T PTS: 1 DIF: Moderate REF: p. 534 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 10. The t-test for comparing the means of two groups assumes that the data are in nominal scales. F It tests a dichotomous (two-level) independent variable associated with changes in a continuous dependent variable. PTS: 1 DIF: Moderate REF: p. 534 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 11. A pooled estimate of the standard error is a better estimate of the standard error than one based on the variance from either sample. T PTS: 1 DIF: Hard REF: p. 535 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 12. The degrees of freedom are calculated as d.f. = n 1 when using the t-test for comparing two means. F In a test of two means, degrees of freedom are calculated as d.f. = n k, where n = n1 n2 and k = number of groups. PTS: 1 DIF: Hard REF: p. 536 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 13. In practice, computer software is used to compute the t-test results. T PTS: 1 DIF: Easy REF: p. 536 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 14. When no direction of a relationship is stated in the hypothesis, a one-tailed test is appropriate. F A two-tailed test is appropriate. PTS: 1 DIF: Hard REF: p. 536 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 15. The first basic step in interpreting t-test results is to find the p-value associated with a particular t and the corresponding degrees of freedom. F This is the third step. The first step is to examine the difference in means to find the “direction” of any difference. PTS: 1 DIF: Moderate REF: p. 537 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 16. The t-test assumes that the two population means are equal. F The t-test assumes that the two population variances are equal. PTS: 1 DIF: Hard REF: p. 537 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 17. The reason that means that appear to be not so close could be concluded to be statistically the same is due to the variance. T PTS: 1 DIF: Moderate REF: p. 538 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 18. A t-test is not appropriate and should not be used when the sample size is greater than 30. T Researchers often employ a t-test even with large samples. As samples get larger, the t-test and Z-test will tend to yield the same results. PTS: 1 DIF: Moderate REF: p. 538 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 19. A paired-sample t-test is an appropriate test for comparing the scores of two interval variables drawn from related populations. T PTS: 1 DIF: Moderate REF: p. 539 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 20. A Z-test for differences of proportions requires a sample size greater than 100. F It requires a sample size greater than 30. PTS: 1 DIF: Moderate REF: p. 540 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 21. ANOVA involving only one grouping variable is often referred to as one-way ANOVA. T PTS: 1 DIF: Easy REF: p. 542 OBJ: LO: 22-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 22. The null hypothesis for an ANOVA test comparing the means of three groups is: 1 2 3. F The null hypothesis is that the means of the three groups are equal. PTS: 1 DIF: Moderate REF: p. 542 OBJ: LO: 22-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 23. The total mean is the mean of a variable over all observations. F This is called the grand mean. PTS: 1 DIF: Moderate REF: p. 545 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 24. The F-test partitions the total variance into within-group variance and between-group variance. T PTS: 1 DIF: Hard REF: p. 546 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 25. Total variability is the calculated by dividing the within-group variance by the between-group variance. F Total variability is the sum of the two variances. PTS: 1 DIF: Moderate REF: p. 547 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge MULTIPLE CHOICE 1. A _____ is an investigation of a hypothesis stating that two (or more) groups differ with respect to measures on a variable. a. statistical conclusions b. descriptive analysis c. paired comparison d. test of differences D PTS: 1 DIF: Moderate REF: p. 529 OBJ: LO: 22-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 2. A researcher hypothesizes that males and females differ with respect to attitude toward sports sponsorships. To investigate this hypothesis that these two groups’ attitudes differ, he will use a _____. a. bivariate test of differences b. univariate test of differences c. multivariate test of differences d. cluster analysis A PTS: 1 DIF: Hard REF: p. 529 OBJ: LO: 22-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Application 3. All of the following are true regarding cross-tabulation EXCEPT _____. a. The 2 distribution provides a means for testing the statistical significance of a contingency table. b. The 2 for a contingency table compares two means that are not from independent samples. c. Cross-tabulations are much like tallying. d. The 2 test for a contingency table involves comparing the observed frequencies with the expected frequencies in each cell of the table. B PTS: 1 DIF: Hard REF: p. 531 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 4. The formula given below represents the method for calculating the _____. a. Z-test b. F-test c. 2 test d. C PTS: 1 DIF: Hard REF: p. 532 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 5. The formula for the chi-square test uses _____. a. observed and expected frequencies b. observed and expected percentages c. the two sample means d. the two sample standard deviations A PTS: 1 DIF: Moderate REF: p. 532 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 6. how do you determine the degrees of freedom in a four-cell chi-square test? a. (R 1) b. (R - 1) c. (R - 1)(C - 1) d. R(C - 1) C PTS: 1 DIF: Moderate REF: p. 533 OBJ: LO: 22-02 NAT: AACSB Analytic| CB&E Model Research| Blooms Comprehension 7. If 25 of the 35 females in a research study agree with a statement, and 15 of the 35 males agree with this statement, the expected value for males-agree is _____. a. 15 b. 20 c. 25 d. 35 B PTS: 1 DIF: Hard REF: p. 533 OBJ: LO: 22-02 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 8. In a brand awareness study, if 25 of a group of 35 males identify the brand correctly and 15 of a group of 35 females identify this brand correctly, the chi-square value for this study is approximately _____. a. 3.26 b. 4.15 c. 5.84 d. 2.92 C PTS: 1 DIF: Hard REF: p. 533 OBJ: LO: 22-02 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 9. In order to use the chi-square test, the expected frequency in each of the cells of the contingency table should be at least _____. a. 2 b. 5 c. 30 d. 40 B PTS: 1 DIF: Moderate REF: p. 533 OBJ: LO: 22-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 10. When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, a(n) _____ is appropriate. a. p-test b. t-test c. 2 test d. univariate test B PTS: 1 DIF: Moderate REF: p. 534 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 11. A(n) _____ is a test for hypotheses stating that the mean scores from some interval- or ratio-scaled variable group based on some less-than interval classificatory variable are not the same. a. regression b. cluster analysis c. 2 test d. independent samples t-test D PTS: 1 DIF: Moderate REF: p. 534 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 12. Supposed you used a 10-point rating scale to measure intention-to-buy (1 = definitely would not buy and 10 = definitely would buy). If a group of 40 males had a mean of 7 and a standard deviation of 2.5, while a group of 35 females had a mean of 5 and a standard deviation of 1.4, the standard error of the difference between the means would be approximately _____. a. 0.48 b. 1.36 c. 2.45 d. not enough information to determine A PTS: 1 DIF: Hard REF: p. 535 OBJ: LO: 22-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 13. Suppose that you used a 9-point rating scale and that you wanted to compare men who had an annual income over $50,000 (Group 1) with men who had an annual income less than or equal to $50,000 (Group 2) on their liking of a new product. If you studied 40 men in Group 1 and they have a mean of 7 and a standard deviation of 2.5, while the 35 men in Group 2 have a mean of 5 and a standard deviation of 1.4, what is the approximate value of t using the t-test? a. 3.43 b. 4.19 c. 2.64 d. not enough information to determine B PTS: 1 DIF: Hard REF: p. 536 OBJ: LO: 22-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 14. In using the t-test to compare the means of two groups, the degrees of freedom are calculated as _____. a. n1 - n2 - 2 b. n1 n2 - 2 c. n1 x n2 -2 d. n1 / n2 - 2 B PTS: 1 DIF: Hard REF: p. 536 OBJ: LO: 22-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 15. In a study comparing the means of two groups in which there are 45 males in Group 1 and 37 females in Group 2, the degrees of freedom for this study when using the t-test for the difference between means is: a. 84 b. 80 c. 82 d. 160 B PTS: 1 DIF: Hard REF: p. 536 OBJ: LO: 22-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 16. In practice, what is the first step in interpreting the t-test when comparing two means? a. compute the t-test value b. find the p-value associated with the t and the corresponding degrees of freedom c. examine the difference in means to find the “direction” of any difference d. examine if there is a difference at the 50 percent confidence interval before examining the 95 percent confidence interval C PTS: 1 DIF: Moderate REF: p. 537 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 17. Which test is appropriate for comparing the scores of two interval variables drawn from related populations? a. ANOVA b. relative t-test c. relative 2 test d. pair-samples t-test D PTS: 1 DIF: Moderate REF: p. 539 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 18. Which of the following is a requirement for using the Z-test for differences of proportions? a. common sample b. degrees of freedom of at least 50 c. sample size greater than 30 d. ratio measurement of all variables C PTS: 1 DIF: Hard REF: p. 540 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 19. The Z-test for comparing two proportions is appropriate with which null hypothesis (H0)? a. 1 = 2. b. 1 2. c. 1 x 2 = 1 d. 1 - 2 = 1 A PTS: 1 DIF: Moderate REF: p. 540 OBJ: LO: 22-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 20. In using the Z-test for comparing two proportions, if the pooled estimate of the proportion of successes is 0.36, then the pooled estimate of proportion of failures is _____. a. 1 b. 0.36 c. 0.64 d. 0.13 C PTS: 1 DIF: Hard REF: p. 541 OBJ: LO: 22-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 21. _____ involves the investigation of the effects of one treatment variable on an interval-scaled dependent variable and determines whether statistically significant differences in means occur between two or more groups. a. Analysis of variance (ANOVA) b. Regression analysis c. Cross-tabulation d. 2 A PTS: 1 DIF: Moderate REF: p. 542 OBJ: LO: 22-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 22. In an ANOVA test of the differences between the means of three groups, the null hypothesis is _____. a. 1 = 2 = 3 b. 1 2 3 c. 1 - 2 - 3 = 0 d. 1 2 3 = 1 A PTS: 1 DIF: Moderate REF: p. 542 OBJ: LO: 22-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 23. Which should be used when comparing the means of three groups to see if they are significantly different from one another? a. One-group t-test b. ANOVA c. Three-group t-test d. Chi-square test B PTS: 1 DIF: Moderate REF: p. 542 OBJ: LO: 22-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 24. The mean of a variable over all observations is called the _____. a. master mean b. average mean c. grand mean d. ANOVA mean C PTS: 1 DIF: Moderate REF: p. 545 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 25. Which of the following is the sum of differences between the group mean and the grand mean summed over all groups for a given set of observations? a. between-groups variance b. total error variance c. F-statistic d. 2 value A PTS: 1 DIF: Hard REF: p. 545 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 26. The sum of the differences between observed values and the group mean for a given set of observations is known as the _____. a. within-group error b. between-groups variance c. F-ratio d. statistic A PTS: 1 DIF: Hard REF: p. 545 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 27. The key statistical test for an ANOVA model is the _____. a. 2 test b. t-test c. F-test d. Z-test C PTS: 1 DIF: Moderate REF: p. 546 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 28. All of the following are forms of variance considered in an F-test EXCEPT _____. a. SSE b. SSB c. SSR d. SST C PTS: 1 DIF: Hard REF: p. 546 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 29. The F-distribution is a function of _____. a. SSB - SSE b. SSE - SSB c. SSB/SSE d. SSE/SSB C PTS: 1 DIF: Hard REF: p. 547 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 30. Practically speaking, what is the first thing a researcher should do when interpreting ANOVA results? a. examine the actual means for each group b. determine the between-groups variance c. examine the total variance d. check whether or not the overall model F is significant D PTS: 1 DIF: Moderate REF: p. 547 OBJ: LO: 22-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension COMPLETION 1. A test of a hypothesis to determine if two groups differ with respect to the scores on one variable is called a(n) ______. 2. The ______ test studies the significance of a contingency table. 3. The formula for determining the degrees of freedom for a chi-square test is ______. 4. Proper use of the 2 test requires that each expected frequency have a value of at least _____. 5. When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, a(n) _____ test is appropriate. 6. The _____ is an estimate of the standard error for a t-test of independent means that assumes the variances of both groups are equal. 7. In using the t-test to compare the difference between the means of two groups, the formula for determining the degrees of freedom is ______. 8. One way to interpret the meaning of the results of the t-test is to focus on the ________ and the group 9. An appropriate test for comparing the scores of two interval variables drawn from related populations is the _____. 10. The _____ for differences of proportions is a technique used to test the hypothesis that proportions are significantly different for two independent samples or groups. 11. _____ is the appropriate statistical tool to use when comparing the means of three or more groups to see if they are significantly different from one another. 12. The _____ is the mean of a variable over all observations. 13. The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called _____ variance. 14. The statistical test for an ANOVA model is the ______. 15. The F-test partitions total variance into ______ variance and ______ variance. ESSAY 1. Discuss the factors that influence the statistical choice. If a researcher is examining factors that influence an automobile’s gas mileage, which statistical tool (or tools) is appropriate? The factors that influence the statistical choice are (1) type of measurement, (2) the nature of the comparison, and (3) the number of groups to be compared. For nominal level measurement of 2. A researcher has data on viewers’ responses regarding what company sponsored the Super Bowl half-time show for the past two years and has coded it “1” if the response was correct and “0” if not. He would like to examine if there is a statistical difference in correct answers between the two years. Explain what statistical test is appropriate to address this research question. Students should understand that the dependent variable (correct or incorrect company sponsoring the 3. Explain what an independent samples t-test is and the null hypothesis examine. The independent samples t-test tests the differences between means taken from two independent 4. List the practical steps for interpreting t-test results. The basic steps for interpreting t-test results are: (1) Examine the difference in means to find the “directions” on any difference. 5. Discuss when a paired-samples t-test is appropriate and give an example of when it should be used. A paired-samples t-test is an appropriate test for comparing the scores of two interval variables drawn from related populations. This is the appropriate test when the same respondent is measured twice. 6. Explain what a Z-test for comparing two proportions is and the appropriate hypothesis. A Z-test for differences of proportions is a technique used to test the hypothesis that proportions are 7. What is ANOVA and when is it the appropriate statistical technique? What test is used to determine significance? Give an example of a research question that can be analyzed using ANOVA. ANOVA stands for analysis of variance and involves the investigation of the effects of one treatment