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, what is the standardized value of the estimate of the mean of the sampling distribution for the difference between sample means?

A) 0.2025 B) 0.3544 C) 2.0115 D) 2.2140 A) 0.2025 B) 0.3544 C) 2.0115 D) 2.2140

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. \[\begin{array} { l c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\ \text { BeforeCourse(1) } \end{array} & \begin{array} { c } \text { Exam Score } \\ \text { AfterCourse(2) } \end{array} \\ \hline 1 & 530 & 670 \\ 2 & 690 & 770 \\ 3 & 910 & 1,000 \\ 4 & 700 & 710 \\ 5 & 450 & 550 \\ 6 & 820 & 870 \\ 7 & 820 & 770 \\ 8 & 630 & 610 \end{array}\] -Referring to Scenario 10-5, the value of the sample mean difference is if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

A) 0 B) 50 C) 68 D) 400 A) 0 B) 50 C) 68 D) 400

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, what assumptions are necessary 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 to be valid?

A) Both sampled populations are normally distributed. B) Both samples are random and independent. C) Neither (a)nor (b)is necessary. D) Both (a)and (b)are necessary. A) Both sampled populations are normally distributed. B) Both samples are random and independent. C) Neither (a)nor (b)is necessary. D) Both (a)and (b)are necessary.

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. \[\begin{array}{l} \begin{array} { l c c c c c } \text { ROW } & \text { Location A } & \text { Location B } & \text { Location C } & \text { Location D } & \text { Location E } \\ \hline 1& 28 & 40 & 21 & 37 & 22 \\ 2 & 33 & 35 & 21 & 47 & 19 \\ 3 & 41 & 33 & 27 & 45 & 25 \end{array}\\ \text { Analysis of Variance }\\ \begin{array} { l r r r c c } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\ \hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\ \text { Error } & 10 & 210.0 & & & \\ \text { Total } & & & & & \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 10-5, the null hypothesis for Levene's test for homogeneity of variances is

A) $H _ { 0 } : \mu _ { A } = \mu _ { B } = \mu _ { C } = \mu _ { D }$ B) $H _ { 0 } : M _ { A } = M _ { B } = M _ { C } = M _ { D }$ C) $H _ { 0 } : \sigma _ { A } ^ { 2 } = \sigma _ { B } ^ { 2 } = \sigma _ { C } ^ { 2 } = \sigma _ { D } ^ { 2 }$ D) $H _ { 0 } : \pi _ { A } = \pi _ { B } = \pi _ { C } = \pi _ { D }$ A) $H _ { 0 } : \mu _ { A } = \mu _ { B } = \mu _ { C } = \mu _ { D }$ B) $H _ { 0 } : M _ { A } = M _ { B } = M _ { C } = M _ { D }$ C) $H _ { 0 } : \sigma _ { A } ^ { 2 } = \sigma _ { B } ^ { 2 } = \sigma _ { C } ^ { 2 } = \sigma _ { D } ^ { 2 }$ D) $H _ { 0 } : \pi _ { A } = \pi _ { B } = \pi _ { C } = \pi _ { D }$

Exam 10: Two-Sample Tests

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, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the 3 means other than the mean for Tornado are not significantly different from each other.

(True/False)

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Question 121

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 p-value for a one-tail test (in the hypothesized direction) is.

(Short Answer)

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Question 122

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 _.

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Question 123

SCENARIO 10-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below. $\mathrm{A}: 1.2,1.1,0.9,0.4$ $\quad C: 1.0,1.5,1.1,1.3$ B: $2.5,2.1,1.9,1.6$ $\quad \mathrm{D}: 0.8,1.3,1.1,0.7$ Interpret the results of the analysis summarized in the following table: Source df SS MS F PR > F Neighborhoods 3.1819 1.0606 10.76 0.001 Error 12 Total 4.3644 -Referring to SCENARIO 10-2, the critical value of Levene's test for homogeneity of variances at a 5% level of significance is

(Multiple Choice)

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Question 124

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 critical value for a one-tail test of the null hypothesis of no difference at the $\alpha$ = 0.05 level of significance is .

(Short Answer)

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Question 125

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, what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?

(Short Answer)

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Question 126

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

(Multiple Choice)

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Question 127

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 $\alpha$ = 0.05.Which of the following represents the result of the test on a difference in the variances?

(Multiple Choice)

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Question 128

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, what is the standardized value of the estimate of the mean of the sampling distribution for the difference between sample means?

(Multiple Choice)

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Question 129

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.

(True/False)

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Question 130

In testing the difference between two proportions using the normal distribution, you may use a two-tail Z test.

(True/False)

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Question 131

For all two-sample tests, the sample sizes must be equal in the two groups.

(True/False)

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Question 132

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.

(Short Answer)

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Question 133

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 sample mean difference is if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

(Multiple Choice)

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Question 134

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, what assumptions are necessary 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 to be valid?

(Multiple Choice)

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Question 135

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

(Multiple Choice)

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Question 136

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

(True/False)

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Question 137

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 correct conclusion?

(Multiple Choice)

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Question 138

If we are testing for the difference between the means of 2 related populations with samples of n1= 20 and n2 = 20, the number of degrees of freedom is equal to

(Multiple Choice)

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Question 139

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, the null hypothesis for Levene's test for homogeneity of variances is

(Multiple Choice)

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Question 140

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

In testing the difference between two proportions using the normal distribution, you may use a two-tail Z test.

For all two-sample tests, the sample sizes must be equal in the two groups.

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

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

If we are testing for the difference between the means of 2 related populations with samples of n1= 20 and n2 = 20, the number of degrees of freedom is equal to

Defining and Collecting Data

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The Normal Distribution

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Fundamentals of Hypothesis Testing: One-Sample Tests

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