Exam 10: Two-Sample Tests

SCENARIO 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 Scenario 10-5,the p-value of the test statistic is .

SCENARIO 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: x̄ _G = 35 months,S_G ² = 900 Metropolis: x̄ _M = 50 months,S _M² = 1050 -Referring to Scenario 10-3,suppose α = 0.10.Which of the following represents the correct conclusion?

SCENARIO 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 Scenario 10-14,what is the value of the test statistic for testing if the population variances differ for preservatives I and II?

SCENARIO 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. Two-Sample Tests 10-31 -Referring to Scenario 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

SCENARIO 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: x̄ _G = 35 months,S_G ² = 900 Metropolis: x̄ _M = 50 months,S _M² = 1050 -Referring to Scenario 10-3,what is the test statistic for the difference between sample means?

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?

SCENARIO 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,p_M = 0.422018 Females: n = 52,p_F = 0.25 p_M - p_F = 0.172018 Z = 2.11825 -Referring to Scenario 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.

SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives.Two different processes can be used to manufacture the flash drives.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 flash drives 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 Scenario 10-12,construct a 95% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

SCENARIO 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): 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 Scenario 10-15,what is the smallest level of significance at which the null hypothesis will still not be rejected?

SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives.Two different processes can be used to manufacture the flash drives.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 flash drives 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 Scenario 10-12,the value of the test statistic is .

SCENARIO 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): 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 Scenario 10-15,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.10?

SCENARIO 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 Scenario 10-1,find the p-value if we assume that the alternative hypothesis was a two-tail test.

SCENARIO 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 $\pi$ ₁ and $\pi$ ₂ 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 Scenario 10-10,what is/are the critical value(s)when testing whether population proportions are different if ? = 0.10?

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.

SCENARIO 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 Scenario 10-5,the number of degrees of freedom is

SCENARIO 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 Two-Sample Tests 10-41 -Referring to Scenario 10-13,which of the following represents the relevant hypotheses tested?

SCENARIO 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): 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 Scenario 10-15,what additional assumption is needed for the test to be valid?

SCENARIO 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 Scenario 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 .

SCENARIO 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 Scenario 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?

SCENARIO 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 Scenario 10-1,judging from the way the data were collected,which test would likely be most appropriate to employ?