Exam 10: Two-Sample Tests

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 highest level of significance at which a test on a difference in the variances will 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 same decision would be made with this test if the level of significance had been 0.05 rather than 0.01.

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,construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

SCENARIO 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. 10-20 Two-Sample Tests -Referring to Scenario 10-7,the test to perform is a

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,suppose α = 0.05.Which of the following represents the result of the test on a difference in the variances?

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 one-tail test is .

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,what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

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 0.10 rather than 0.05.

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,if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past,which represents the relevant hypotheses?

SCENARIO 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. 10-20 Two-Sample Tests -Referring to Scenario 10-7,the null hypothesis should be rejected.

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 calculated value of the test statistic is .

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 independent samples.