Exam 10: Two-Sample Tests

SCENARIO 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. Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 99210 Sample Standard Deviation 13577 Population 2 Sample Sample Size 12 Sample Mean 105820 Sample Standard Deviation 11741 Difference in Sample Means -6610 t Test Statistic -1.37631 Lower-Tail Test Lower Critical Value -1.70113 p-Value 0.089816 -Referring to Scenario 10-2, what is the 95% confidence interval estimate for the difference between two means?

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. Student Exam Score BeforeCourse(1) Exam Score AfterCourse(2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Scenario 10-5, the calculated 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): $\bar { X } _ { 1 } = 60.35 , S _ { 1 } = 3.25 , n _ { 1 } = 12$ Sample II (financial planning): $\bar { X } _ { 2 } = 58.20 , S _ { 2 } = 2.48 , n _ { 2 } = 14$ 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 Scenario 10-15, suppose $\alpha$ = 0.01.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 null hypothesis will be rejected if the test statistic is _.

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. Hypothesized Difference 0 Level of Significance 0.05 Group 1 Number of Items of Interest 160 Sample Size Group 2 Number of Items of Interest 172 Sample Size Intermediate Calculations Group 1 Proportion 0.8 Group 2 Proportion 0.688 Difference in Two Proportions 0.112 Average Proportion 0.737777778 Z Test Statistic 2.684103363 Two-Tail Test Lower Critical Value -1.959963985 Upper Critical Value 1.959963985 2-tailed p-Value 0.007272462 -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 10-8 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,=0.422018 Females: n=52,=0.25 -=0.172018Z=2.11825 -Referring to Scenario 10-8, construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

SCENARIO 10-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to SCENARIO 10-3, what is the value of the test statistic for Levene's test for homogeneity of variances?

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.

SCENARIO 10-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to SCENARIO 10-3, the among group variation or SSA is _.

SCENARIO 10-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. ROW Location A Location B Location C Location D Location E 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 Analysis of Variance Source df SS MS F p Location 4 963.6 11.47 0.001 Error 10 210.0 Total -Referring to SCENARIO 10-5, what is the p-value of the test statistic for Levene's test for homogeneity of variances?

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. Student Exam Score BeforeCourse(1) Exam Score AfterCourse(2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -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 10-5 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. Student Exam Score BeforeCourse(1) Exam Score AfterCourse(2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Scenario 10-5, the value of the standard error of the difference scores is

A completely randomized design with 4 groups would have 6 possible pairwise comparisons.

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,=0.422018 Females: n=52,=0.25 -=0.172018Z=2.11825 -Referring to Scenario 10-8, suppose that the two-tail p-value was really 0.0734.State the proper conclusion.

The test for the equality of two population variances is based on

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 Hotel 1 Hotel 2 Mean 2.214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386 P (T<=t) one-tail 0.362504 t Critical one-tail 1.685953 P ( T < t) two-tail 0.725009 t Critical two-tail 2.024394 -Referring to Scenario 10-13, suppose $\alpha$ = 0.05.Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels?

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. Preservative I Preservative II =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Scenario 10-14, suppose $\alpha$ = 0.05.Which of the following represents the correct conclusion?

SCENARIO 10-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to SCENARIO 10-3, the null hypothesis that the mean downhill coasting speeds of the4 brands of bicycles are equal will be rejected at a level of significance of 0.05 if the value of the test statistic is greater than _.

SCENARIO 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. Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 99210 Sample Standard Deviation 13577 Population 2 Sample Sample Size 12 Sample Mean 105820 Sample Standard Deviation 11741 Difference in Sample Means -6610 t Test Statistic -1.37631 Lower-Tail Test Lower Critical Value -1.70113 p-Value 0.089816 -Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.What assumptions were necessary to conduct this hypothesis test?

SCENARIO 10-4 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants 15 fields, 5 with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomized design, the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to SCENARIO 10-4, using an overall level of significance of 0.01, the critical range for the Tukey-Kramer procedure is _.