Exam 10: Two-Sample Tests

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, suppose α = 0.01. Which of the following represents the correct conclusion?

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, state the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.

TABLE 10-9 The following Excel output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different. -Referring to Table 10-9, construct a 99% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

TABLE 10-7 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Primary Secondary Material Supplier Supplier Difference 1 $55 $45 $10 2 $48 $47 $1 3 $31 $32 -$1 4 $83 $77 $6 5 $37 $37 $0 6 $55 $54 $1 Sum: $309 $292 $17 Sum of Squares: $17,573 $15,472 $139 -Referring to Table 10-7, the null hypothesis should be rejected.

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 value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions?

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.

The F distribution is symmetric.

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(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05?

TABLE 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Table 10-4, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are ________.

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 additional assumption is needed for the test to be valid?

TABLE 10-7 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Primary Secondary Material Supplier Supplier Difference 1 $55 $45 $10 2 $48 $47 $1 3 $31 $32 -$1 4 $83 $77 $6 5 $37 $37 $0 6 $55 $54 $1 Sum: $309 $292 $17 Sum of Squares: $17,573 $15,472 $139 -Referring to Table 10-7, the hypotheses that the buyer should test are a null hypothesis that ________ versus an alternative hypothesis that ________.

In testing for the differences between the means of two related populations, the ________ hypothesis is the hypothesis of "no differences."

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. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Table 10-5, the number of degrees of freedom is

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 correct conclusion?

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 10-11 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 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

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 99% 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 10-15 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 smallest level of significance at which the null hypothesis will still not be rejected?

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

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 standardized value of the estimate of the mean of the sampling distribution for the difference between sample means?