Exam 10: Two-Sample Tests

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 hypotheses that should be tested are

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, construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

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.

TABLE 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Table 10-6, the p-value for a two-tail 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 I (public accounting): $\bar{X}$ ₁ = 60.35, S₁ = 3.25, n₁ = 12 Sample II (financial planning): $\bar{X}$ 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.

TABLE 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Table 10-6, what is the 90% confidence interval estimate for the mean difference in weight before and after the diet?

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: $\bar{X}$ 1 G = 35 months, SG² = 900 Metropolis: $\bar{X}$ M = 50 months, SM² = 1050 -Referring to Table 10-3, what is the test statistic for the difference between sample means?

TABLE 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Table 10-6, a one-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α = 0.05 level of significance.

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 $\bar{X}$ I = 106.4 hours II = 96.54 hours $\bar{X}$ 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?

When testing for differences between the means of 2 related populations, you can use either a one-tail or two-tail 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): $\bar{X}$ ₁ = 60.35, S₁ = 3.25, n₁ = 12 Sample II (financial planning): $\bar{X}$ 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 = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variances?

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. t-Test: Two-Sample Assuming Unequal Variances Hotel 1 Hotel 2 Mean 2.214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386 P(T <=t) one-tail 0.362504 t Critical one-tail 1.685953 P(T<=t) two-tail 0.725009 t Critical two-tail 2.024394 -Referring to Table 10-13, what is the 95% confidence interval estimate for the difference in the two means if the two population variances are assumed to be the same?

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: $\bar{X}$ 1 G = 35 months, SG² = 900 Metropolis: $\bar{X}$ M = 50 months, SM² = 1050 -Referring to Table 10-3, what is a point estimate for the mean of the sampling distribution of the difference between the 2 sample means?

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, there are ________ degrees of freedom for this test.

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. Find the value of the test statistic.

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 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Table 10-6, the t test should be ________ -tail.

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 should be rejected.

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): $\bar{X}$ ₁ = 60.35, S₁ = 3.25, n₁ = 12 Sample II (financial planning): $\bar{X}$ 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 critical value for testing whether there is evidence of a difference in the variances at the 5% level of significance?