Exam 10: Two-Sample Tests

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,the calculated value of the test statistic is ________.

Moving companies are required by the government to publish a Carrier Performance Report each year.One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed.Suppose two companies,Econo-Move and On-the-Move,each decide to estimate this figure by sampling their records,and they report the data shown in the following table. The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed.Which test would be used to properly analyze the data in this experiment?

When testing for the difference between 2 population variances with sample sizes of n₁ = 8 and n₂ = 10,where n₁ has the larger variance,the number of degrees of freedom are

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 critical value for a one-tail test of the null hypothesis of no difference at the α = 0.05 level of significance is ________.

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

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

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,what is the 90% confidence interval estimate for the difference between two means?

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 10-14 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,suppose α = 0.05.Which of the following represents the result of the relevant hypothesis test?

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

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 critical value for testing whether there is evidence of a difference in the variances at the 5% level of significance?

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 less than the females.Using the test statistic given,compute the appropriate p-value for the 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 value of the test statistic?

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 0.10?

In testing the difference between two proportions using the normal distribution,you may use a two-tail Z test.

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 95% confidence interval estimate for the mean difference in weight before and after the diet?

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 will be rejected if the test statistic 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,the p-value of the test 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): 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?