TABLE 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. $\begin{array}{|l|r|} \hline \text { Hypothesized Difference } & 0 \\ \hline \text { Level of Significance } & 0.05\\ \hline\quad\quad\quad\quad\quad\quad \text { Group } 1\\ \hline \text { Number of Items of Interest } & 160 \\ \hline \text { Sample Size } & 200 \\ \hline \quad\quad\quad\quad\quad\quad\text { Group } 2\\ \hline \text { Number of Items of Interest } & 172 \\ \hline \text { Sample Size } & 250 \\ \hline\quad\quad\quad\quad {\text { Intermediate Calculations }} \\ \hline \text { Group 1 Proportion } & 0.8 \\ \hline \text { Group 2 Proportion } & 0.688 \\ \hline \text { Difference in Two Proportions } & 0.112 \\ \hline \text { Average Proportion } & 0.737777778 \\ \hline \text { Z Test Statistic } & 2.684103363 \\ \hline\\ \hline\quad\quad\quad\quad\quad\quad\text { Two-Tail Test }\\ \hline \text { Lower Critical Value } & -1.959963985 \\ \hline \text { Upper Critical Value } & 1.959963985 \\ \hline p \text {-Value } & 0.007272462 \\ \hline \end{array}$ -Referring to Table 10-9, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

The answer of TABLE 10-9 The following Excel output contains the...

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

TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. \[\begin{array} { | l | l | l | } \hline & \text { American } & \text { Japanese } \\ \hline \text { Sample Size } & 211 & 100 \\ \hline \text { Sample Mean SSATL Score } & 65.75 & 79.83 \\ \hline \text { Sample Std. Dev. } & 11.07 & 6.41 \\ \hline \end{array}\] -Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

A) H₀: μA - μJ ≥ 0 versus H₁: μA - μJ 0 C) H₀: μA - μJ = 0 versus H₁: μA - μJ ≠ 0 D) $ H_{0}: \bar{X}_{A}-\bar{X}_{J}=0 $ versus $ H_{1}: \bar{X}_{A}-\bar{X}_{J} \neq 0 $ A) H₀: μA - μJ ≥ 0 versus H₁: μA - μJ 0 C) H₀: μA - μJ = 0 versus H₁: μA - μJ ≠ 0 D) $ H_{0}: \bar{X}_{A}-\bar{X}_{J}=0 $ versus $ H_{1}: \bar{X}_{A}-\bar{X}_{J} \neq 0 $

TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. \[\begin{array} { | l | l | l | } \hline & \text { American } & \text { Japanese } \\ \hline \text { Sample Size } & 211 & 100 \\ \hline \text { Sample Mean SSATL Score } & 65.75 & 79.83 \\ \hline \text { Sample Std. Dev. } & 11.07 & 6.41 \\ \hline \end{array}\] -Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

A) Paired t test B) Pooled-variance t test for the difference between two means C) F test for the ratio of two variances D) Z test for the difference between two proportions A) Paired t test B) Pooled-variance t test for the difference between two means C) F test for the ratio of two variances D) Z test for the difference between two proportions

TABLE 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. $\begin{array}{|l|r|} \hline \text { Hypothesized Difference } & 0 \\ \hline \text { Level of Significance } & 0.05 \\ \hline \quad \quad \quad \quad \quad \quad{\text { Population 1 Sample }} \\ \hline \text { Sample Size } & 18 \\ \hline \text { Sample Mean } & 99210 \\ \hline \text { Sample Standard Deviation } & 13577 \\ \hline \quad \quad \quad \quad \quad \quad{\text { Population 2 Sample }} \\ \hline \text { Sample Size } & 12 \\ \hline \text { Sample Mean } & 105820 \\ \hline \text { Sample Standard Deviation } & 11741 \\ \hline & \\ \hline \text { Difference in Sample Means } & -6610 \\ \hline \boldsymbol{t} \text { Test Statistic } & -1.37631 \\ \hline \quad \quad \quad \quad \quad \quad \quad \quad{\text { Lower-Tail Test }} \\ \hline \text { Lower Critical Value } & -1.70113 \\ \hline \boldsymbol{p} \text {-Value } & \mathbf{0 . 0 8 9 8 1 6} \\ \hline \end{array}$ -Referring to Table 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?

A) Both populations of salaries (male and female) must have approximate normal distributions. B) The population variances are approximately equal. C) The samples were randomly and independently selected. D) All of the above assumptions were necessary. A) Both populations of salaries (male and female) must have approximate normal distributions. B) The population variances are approximately equal. C) The samples were randomly and independently selected. D) All of the above assumptions were necessary.

Exam 10: Two-Sample Tests

TABLE 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, pM = 0.422018 Females: n = 52, pF = 0.25 pM - pF = 0.172018 Z = 2.11825 -Referring to Table 10-8, construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

(Short Answer)

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Question 141

TABLE 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, S₁ = 3.25, n₁ = 12 Sample II (financial planning): $\bar{X}$ ₂ = 58.20, S₂ = 2.48, n₂ = 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 Table 10-15, suppose α = 0.10. Which of the following represents the correct conclusion?

(Multiple Choice)

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Question 142

TABLE 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 200 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 p -Value 0.007272462 -Referring to Table 10-9, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

(Short Answer)

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Question 143

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

(Multiple Choice)

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Question 144

TABLE 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 Table 10-13, suppose α = 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 145

TABLE 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 Table 10-4, what is the 90% confidence interval estimate for the difference in the two means?

(Short Answer)

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Question 146

TABLE 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, S₁ = 3.25, n₁ = 12 Sample II (financial planning): $\bar{X}$ ₂ = 58.20, S₂ = 2.48, n₂ = 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 Table 10-15, what is the 95% confidence interval estimate for the difference in the two means?

(Short Answer)

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Question 147

Given the following information, calculate sp², the pooled sample variance that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6 N₁ = 16 n₂ = 25

(Multiple Choice)

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Question 148

TABLE 10-12 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. 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 disks 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 Table 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 149

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?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 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 150

TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 100 Sample Mean SSATL Score 65.75 79.83 Sample Std. Dev. 11.07 6.41 -Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

(Multiple Choice)

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Question 151

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?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic?

(Multiple Choice)

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Question 152

TABLE 10-12 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. 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 disks 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 Table 10-12, the p-value of the test is ________.

(Short Answer)

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Question 153

TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 100 Sample Mean SSATL Score 65.75 79.83 Sample Std. Dev. 11.07 6.41 -Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

(Multiple Choice)

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Question 154

TABLE 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 Table 10-4, what is the 99% confidence interval estimate for the difference in the two means?

(Short Answer)

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Question 155

TABLE 10-10 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Table 10-10, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions?

(Multiple Choice)

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Question 156

TABLE 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 Test Statistic -1.37631 Lower-Tail Test Lower Critical Value -1.70113 -Value -Referring to Table 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?

(Multiple Choice)

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Question 157

TABLE 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 $\bar{X}$ I = 106.4 hours II = 96.54 hours $\bar{X}$ SI = 10.3 hours SII = 13.4 hours -Referring to Table 10-14, what is the critical value for testing if the population variances differ for preservatives I and II at the 5% level of significance?

(Essay)

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Question 158

TABLE 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. Gotham: $\bar{X}$ 1 G = 35 months, SG² = 900 Metropolis: $\bar{X}$ M = 50 months, SM² = 1050 -Referring to Table 10-3, suppose α = 0.10. Which of the following represents the correct conclusion?

(Multiple Choice)

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Question 159

TABLE 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. Primary Secondary 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 Table 10-7, the test to perform is a

(Multiple Choice)

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Question 160

Showing 141 - 160 of 210

Given the following information, calculate sp², the pooled sample variance that should be used in the pooled-variance t test. s₁² = 4 s₂² = 6 N₁ = 16 n₂ = 25

Introduction

Organizing and Visualizing Data

Numerical Descriptive Measures

Basic Probability

Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling and Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Introduction to Multiple Regression

Multiple Regression Model Building

Time-Series Forecasting

Statistical Applications in Quality Management

A Roadmap for Analyzing Data

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