Exam 10: Two-Sample Tests and One-Way ANOVA

TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. -Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

TABLE 10-10 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Table 10-10, what is the estimated standard error of the difference between the two sample proportions?

In testing for differences between the means of two related populations, the null hypothesis is

TABLE 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions. Sample 1 (public accounting): 1 = 60.35, S1 = 3.25, n1 = 12 Sample 2 (financial planning): 2 = 58.20, S2 = 2.48, n2 = 14 Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning, assuming that the two population variances are the same. -Referring to Table 10-15, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.10?

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.

TABLE 10-14 The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below. Preservative I Preservative II I = 106.4 hours II= 96.54 hours SI = 10.3 hours SII = 13.4 hours -Referring to Table 10-14, suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test?

TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. -Referring to Table 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

If we are testing for the difference between the means of two independent populations presuming equal variances with samples of n₁ = 20 and n₂ = 20, the number of degrees of freedom is equal to

TABLE 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. -Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?

TABLE 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Table 10-11, the null hypothesis should be rejected.

TABLE 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Microsoft Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. -Referring to Table 10-13, suppose α = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels?

TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. -Referring to Table 10-1, find the p-value if we assume that the alternative hypothesis was a two-tail test.

TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. -Referring to Table 10-5, at the 0.05 level of significance, the decision for this hypothesis test would be:

TABLE 10-12 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2," perform the appropriate test at a level of significance of 0.01. -Referring to Table 10-12, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, the among group variation or SSA is ________.

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, what is the value of the test statistic for Levene's test for homogeneity of variances?

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, in testing the null hypothesis that the mean downhill coasting speeds of the four brands of bicycles are equal, the value of the test statistic is ________.

TABLE 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Table 10-11, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic?

TABLE 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: G = 35 months, SG2 = 900 Metropolis: M = 50 months, SM2 = 1,050 -Referring to Table 10-3, what is the test statistic for the difference between sample means?