Exam 10: Two-Sample Tests

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 Critical one-tail 1.685953 (<=) two-tail 0.725009 Critical two-tail 2.024394 -Referring to Scenario 10-13, what is the standardized value of the estimate of the mean of the sampling distribution for the difference between sample 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 Before Course (1) Exam Score After Course (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, at the 0.05 level of significance, the conclusion for this hypothesis test is that there is sufficient evidence that:

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 11 degrees of freedom.

SCENARIO 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Scenario 10-4, there are _______ degrees of freedom for this test.

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. Total shipments sampled 900 750 Number of shipments with a claim \geq\ 50 162 60 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?

When testing $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0$ , the observed value of the Z test statistic was found to be - 2.13. The p-value for this test 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, the same decision would be made with this test if the level of significance had been 0.05 rather than 0.01.

SCENARIO 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Scenario 10-4, the computed t statistic is _______.

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 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

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 Critical one-tail 1.685953 (<=) two-tail 0.725009 Critical two-tail 2.024394 -Referring to Scenario 10-13, what is the largest level of significance at which a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels will not be rejected?

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 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 10-13 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 Critical one-tail 1.685953 (<=) two-tail 0.725009 Critical two-tail 2.024394 -Referring to Scenario 10-13, state the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer Service representative between the two hotels. a) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \geq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } < 0$ b) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \leq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } > 0$ c) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } = 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \neq 0$ d) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \neq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } = 0$

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, a one-tail test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the $\alpha = 0.05$ level of significance.

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. If the p-value turns out to be 0)035 (which is not the real value in this data set), then a) at $\alpha = 0.05$ , you should fail to reject $H _ { 0 }$ b) at $\alpha = 0.04$ , you should reject $H _ { 0 }$ c) at $\alpha = 0.03$ , you should reject $H _ { 0 }$ d) None of the above would be correct statements.

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, the decision rule is to reject the null hypothesis if ________.

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 should be rejected.

When testing $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } = 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } \neq 0$ , the observed value of the Z test statistic was found to be - 2.13. The p-value for this test is

When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

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 null hypothesis should be rejected.

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 Critical one-tail 1.685953 (<=) two-tail 0.725009 Critical two-tail 2.024394 -Referring to Scenario 10-13, suppose ? = 0.05. Which of the following represents the result of the test on a difference in the variabilities of the amount of time required to reach a customer Service representative between the two hotels?