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 value of the sample mean difference is_____ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

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 the point estimate for the difference between the two population proportions?

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen.The professor took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the professor should use a t test with related samples.

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,give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

SCENARIO 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 Scenario 10-11,construct a 95% 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.What is the value of the test statistic?

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

SCENARIO 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 Scenario 10-11,the null hypothesis will be rejected if the test statistic 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,suppose α = 0.05.Which of the following represents the result of the relevant hypothesis test?

SCENARIO 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 Scenario 10-11,the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

In testing for differences between the means of 2 related populations where the variance of the differences is unknown,the degrees of freedom are

If you wish to determine whether there is evidence that the proportion of items of interest is higher in group 1 than in group 2,the appropriate test to use is

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 less 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,the p-value of the test is .

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 p-value for a two-tail 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,what is a point estimate for the mean of the sampling distribution of the difference between the 2 sample means?

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

When testing H₀ : $\pi$ ₁ - $\pi$ ₂ = 0 versus H₁ : $\pi$ ₁ - $\pi$ ₂ $\neq$ 0 ,the observed value of the Z test statistic was found to be - 2.13.The p-value for this test 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 = 0.05.Which of the following represents the correct conclusion?