Exam 10: Two-Sample Tests

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 pooled (i.e., combined) variance is ________.

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 buyer should decide that the primary supplier is

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 95% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

TABLE 10-8 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: n = 109, pM = 0.422018 Females: n = 52, pF = 0.25 pM - pF = 0.172018 Z = 2.11825 -Referring to Table 10-8, suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females. Using the test statistic given, compute the appropriate p-value for the test.

F tests are one-tail tests.

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 population proportions are different if α = 0.10?

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, at the 0.05 level of significance, the decision for this hypothesis test would be

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 10 degrees of freedom.

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, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied customers compared to Resort 2 (Group 2)", the p-value of the test will be

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Assuming W designates women's responses and M designates men's, which of the following are the appropriate null and alternative hypotheses to test the group's claim?

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, state the null and alternative hypotheses for testing whether there is evidence of a difference in the variances of the starting annual salaries.

The statistical distribution used for testing the difference between two population variances is the ________ distribution.

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. 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, what is the largest level of significance at which a test of whether the population variances differ for preservatives I and II will not be rejected?

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, the null hypothesis will be rejected if the test statistic is ________.

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, construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

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 90% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

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, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.

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, what is the critical value for testing if the population variances differ for preservatives I and II at the 5% level of significance?

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 result of the relevant hypothesis test?