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. \[\begin{array}{l} \text { t-Test: Two-Sample Assuming Unequal Variances }\\ \begin{array} { l r r } \hline & \text { Hotel 1 } & \text { Hotel 2 } \\ \hline \text { Mean } & 2.214 & 2.0115 \\ \text { Variance } & 2.951657 & 3.57855 \\ \text { Observations } & 20 & 20 \\ \text { Hypothesized Mean Difference } & 0 & \\ \text { df } & 38 & \\ \text { t Stat } & 0.354386 & \\ \text { P } ( T < = t ) \text { one-tail } & 0.362504 & \\ \text { t Critical one-tail } & 1.685953 & \\ \text { P } ( \text { T } < \text { t) two-tail } & 0.725009 & \\ \text { t Critical two-tail } & 2.024394 & \\ \hline \end{array} \end{array}\] -Referring to Scenario 10-13, suppose $\alpha$ = 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?

A) The alternative hypothesis is rejected. B) The null hypothesis is rejected. C) The null hypothesis is not rejected. D) Insufficient information exists on which to decide. A) The alternative hypothesis is rejected. B) The null hypothesis is rejected. C) The null hypothesis is not rejected. D) Insufficient information exists on which to decide.

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. \[\begin{array}{l} \text { t-Test: Two-Sample Assuming Unequal Variances }\\ \begin{array} { l r r } \hline & \text { Hotel 1 } & \text { Hotel 2 } \\ \hline \text { Mean } & 2.214 & 2.0115 \\ \text { Variance } & 2.951657 & 3.57855 \\ \text { Observations } & 20 & 20 \\ \text { Hypothesized Mean Difference } & 0 & \\ \text { df } & 38 & \\ \text { t Stat } & 0.354386 & \\ \text { P } ( T < = t ) \text { one-tail } & 0.362504 & \\ \text { t Critical one-tail } & 1.685953 & \\ \text { P } ( \text { T } < \text { t) two-tail } & 0.725009 & \\ \text { t Critical two-tail } & 2.024394 & \\ \hline \end{array} \end{array}\] -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?

A) There is no evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels. B) 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. C) There is no evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same. D) There is evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same. A) There is no evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels. B) 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. C) There is no evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same. D) There is evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.

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. $\begin{array}{lllll} \text { Trial}&\text { Barth}&\text { Tornado }&\text {Reiser}&\text { Shaw }\\ 1 & 43 & 37 & 41 & 43 \\ 2 & 46 & 38 & 45 & 45 \\ 3 & 43 & 39 & 42 & 46 \end{array}$ -Referring to SCENARIO 10-3, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

A) There is insufficient evidence that the variances are all the same. B) There is sufficient evidence that the variances are all the same. C) There is insufficient evidence that the variances are not all the same. D) There is sufficient evidence that the variances are not all the same. A) There is insufficient evidence that the variances are all the same. B) There is sufficient evidence that the variances are all the same. C) There is insufficient evidence that the variances are not all the same. D) There is sufficient evidence that the variances are not all the same.

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. \[\begin{array} { | l | r | } \hline \text { Hypothesized Difference } & 0 \\ \hline \text { Level of Significance } & 0.05 \\ \hline { \text { Group 1 } } \\ \hline \text { Number of Items of Interest } & 160 \\ \hline \text { Sample Size } & \mathbf { 2 0 0 } \\ \hline { \text { Group 2 } } \\ \hline \text { Number of Items of Interest } & 172 \\ \hline \text { Sample Size }&250 \\ \hline \\ \hline { \text { Intermediate Calculations } } \\ \hline \text { Group 1 Proportion } & 0.8 \\ \hline \text { Group 2 Proportion } &0.688\\ \hline \text { Difference in Two Proportions } &0.112 \\ \hline \text { Average Proportion } &0.737777778 \\ \hline \text { Z Test Statistic } & 2.684103363 \\ \hline \\\hline { \text { Two-Tail Test } } \\ \hline \text { Lower Critical Value } & - 1.959963985 \\ \hline \text { Upper Critical Value } & 1.959963985 \\ \hline \text { 2-tailed p-Value } & 0.007272462 \\ \hline \end{array}\] -Referring to Scenario 10-9, if you want to test the claim that "Resort 1 (Group 1) has a lowerproportion of satisfied customers compared to Resort 2 (Group 2)", you will use

A) a t-test for the difference between two proportions. B) a Z-test for the difference between two proportions. C) an F test for the difference between two proportions. D) an F test for the ratio of two variances. A) a t-test for the difference between two proportions. B) a Z-test for the difference between two proportions. C) an F test for the difference between two proportions. D) an F test for the ratio of two variances.

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. \[\begin{array}{l} \text { t-Test: Two-Sample Assuming Unequal Variances }\\ \begin{array} { l r r } \hline & \text { Hotel 1 } & \text { Hotel 2 } \\ \hline \text { Mean } & 2.214 & 2.0115 \\ \text { Variance } & 2.951657 & 3.57855 \\ \text { Observations } & 20 & 20 \\ \text { Hypothesized Mean Difference } & 0 & \\ \text { df } & 38 & \\ \text { t Stat } & 0.354386 & \\ \text { P } ( T < = t ) \text { one-tail } & 0.362504 & \\ \text { t Critical one-tail } & 1.685953 & \\ \text { P } ( \text { T } < \text { t) two-tail } & 0.725009 & \\ \text { t Critical two-tail } & 2.024394 & \\ \hline \end{array} \end{array}\] -Referring to Scenario 10-13, which of the following represents the relevant hypotheses tested?

A) $H _ { 0 } : \mu _ { I } - \mu _ { I I } \geq 0 \text { versus } H _ { 1 } : \mu _ { I } - \mu _ { I I } 0$ C) $H _ { 0 } : \mu - \mu _ { I I } = 0 \text { versus } H _ { 1 } : \mu _ { I } - \mu _ { I I } \neq 0$ D) $H _ { 0 } : \mu _ { I } - \mu _ { I I } \neq 0 \text { versus } H _ { 1 } : \mu _ { I } - \mu _ { I I } = 0$ A) $H _ { 0 } : \mu _ { I } - \mu _ { I I } \geq 0 \text { versus } H _ { 1 } : \mu _ { I } - \mu _ { I I } 0$ C) $H _ { 0 } : \mu - \mu _ { I I } = 0 \text { versus } H _ { 1 } : \mu _ { I } - \mu _ { I I } \neq 0$ D) $H _ { 0 } : \mu _ { I } - \mu _ { I I } \neq 0 \text { versus } H _ { 1 } : \mu _ { I } - \mu _ { I I } = 0$

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. $\begin{array}{lllll} \text { Trial}&\text { Barth}&\text { Tornado }&\text {Reiser}&\text { Shaw }\\ 1 & 43 & 37 & 41 & 43 \\ 2 & 46 & 38 & 45 & 45 \\ 3 & 43 & 39 & 42 & 46 \end{array}$ -Referring to SCENARIO 10-3, what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

A) Reject the null hypothesis because the p-value is smaller than the level of significance. B) Reject the null hypothesis because the p-value is larger than the level of significance. C) Do not reject the null hypothesis because the p-value is smaller than the level of significance. D) Do not reject the null hypothesis because the p-value is larger than the level of significance. A) Reject the null hypothesis because the p-value is smaller than the level of significance. B) Reject the null hypothesis because the p-value is larger than the level of significance. C) Do not reject the null hypothesis because the p-value is smaller than the level of significance. D) Do not reject the null hypothesis because the p-value is larger than the level of significance.

Exam 10: Two-Sample Tests

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?" Some24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and200 men were interviewed.Construct a 95% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

(Short Answer)

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Question 281

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 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?

(Multiple Choice)

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Question 282

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?

(Multiple Choice)

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Question 283

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 should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

(Multiple Choice)

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Question 284

When you test for differences between the means of two independent populations, you can only use a two-tail test.

(True/False)

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Question 285

In testing for the differences between the means of two independent populations, you assume that the 2 populations each follow a distribution.

(Short Answer)

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Question 286

The p-value is the probability of obtaining a test statistic more extreme than the sample result given the null hypothesis is true.

(True/False)

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Question 287

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 250 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, if you want to test the claim that "Resort 1 (Group 1) has a lowerproportion of satisfied customers compared to Resort 2 (Group 2)", you will use

(Multiple Choice)

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Question 288

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 result of the relevant hypothesis test?

(Multiple Choice)

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Question 289

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, the value of MSA is , while MSW is _.

(Short Answer)

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Question 290

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.

(True/False)

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Question 291

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. Material Primary Supplier Secondary Supplier Difference 1 \ 55 \ 45 \ 10 2 \ 48 \ 47 \ 1 3 \ 31 \ 32 -\ 1 4 \ 83 \ 77 \ 6 5 \ 37 \ 37 \ 0 6 \ 55 \ 54 \ 1 Sum: \ 309 \ 292 \ 17 Sum of Squares: \ 17,573 \ 15,472 \ 139 -Referring to Scenario 10-7, what is the 99% confidence interval estimate for the mean difference in prices?

(Short Answer)

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Question 292

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, which of the following represents the relevant hypotheses tested?

(Multiple Choice)

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Question 293

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.Construct a 99% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

(Short Answer)

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Question 294

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

(True/False)

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Question 295

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 hypotheses that should be tested are:

(Multiple Choice)

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Question 296

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

(Multiple Choice)

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Question 297

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 should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

(Multiple Choice)

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Question 298

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, the value of the test statistic is .

(Short Answer)

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Question 299

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

(Short Answer)

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Question 300

When you test for differences between the means of two independent populations, you can only use a two-tail test.

In testing for the differences between the means of two independent populations, you assume that the 2 populations each follow a distribution.

The p-value is the probability of obtaining a test statistic more extreme than the sample result given the null hypothesis is true.

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

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

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