Exam 10: Two-Sample Tests

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.The proper conclusion for this test is

TABLE 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction.Below is the 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,what is the smallest level of significance at which the null hypothesis will still not 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 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,what is the value of the test statistic?

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. -Referring to Table 10-14,state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.

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.

A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen.The professor took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the professor should use a t test with related samples.

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?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed.Construct a 90% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

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,construct a 99% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

Given the following information,calculate sp²,the pooled sample variance that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6 N₁ = 16 n₂ = 25

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.Which of the following is an appropriate alternative hypothesis?

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 = 1050 -Referring to Table 10-3,suppose α = 0.05.Which of the following represents the result of the relevant hypothesis test?

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. -Referring to Table 10-14,what assumptions are necessary for testing if the population variances differ for preservatives I and II?

A researcher is curious about the effect of sleep on students' test performances.He chooses 60 students and gives each two tests: one given after two hours' sleep and one after eight hours' sleep.The test the researcher should use would be a related samples test.

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 I (public accounting): ₁ = 60.35,S₁ = 3.25,n₁ = 12 Sample II (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 the highest level of significance at which a test on a difference in the variances will not be rejected?

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom.

In testing for the differences between the means of two independent populations,you assume that the 2 populations each follow a ________ distribution.

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/are the critical value(s)when testing whether the current population proportion is higher than before if α = 0.05?

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 10-3 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 = 1050 -Referring to Table 10-3,what is the 99% confidence interval estimate for the difference in the two means?

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