Exam 10: Two-Sample Tests

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. -Referring to Scenario 10-3, what is the test statistic for the difference between 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. 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?

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. Assuming W designates women's responses and M designates men's, which of the following are the appropriate null and alternative hypotheses to test the group's claim?

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, at the 0.05 level of significance, the conclusion for this hypothesis test is that there is sufficient evidence that:

Repeated measurements from the same individuals is an example of data collected from two related populations.

F tests are one-tail 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. 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 t test should be _______-tail.

In testing for the differences between the means of two related populations, you assume that the differences follow a _______ distribution.

True or False : A low p-value indicates a small probability the null hypothesis will not be rejected.

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. 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 value of the test statistic for testing whether there is evidence of a difference in the variances?

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. 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 = 0.01.Which of the following represents the correct conclusion?

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. -Referring to Scenario 10-7, what is the 99% confidence interval estimate for the mean difference in prices?

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 90% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

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

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 99% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are

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. -Referring to Scenario 10-3, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.01?

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 ________.

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. -Referring to Scenario 10-13, suppose = 0.10.Which of the following represents the correct conclusion?