TABLE 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. \[\begin{array} { l c c } \underline { \text { Student } } & \begin{array} { c } \text { Exam Score } \\ \text { Before Course (1) } \end{array} & \begin{array} { c } \text { Exam Score } \\ \text { After Course (2) } \end{array} \\ 1 & 530 & 670 \\ 2 & 690 & 770 \\ 3 & 910 & 1,000 \\ 4 & 700 & 710 \\ 5 & 450 & 550 \\ 6 & 820 & 870 \\ 7 & 820 & 770 \\ 8 & 630 & 610 \end{array}\] -Referring to Table 10-5, the calculated value of the test statistic is ________.

The answer of TABLE 10-5 To test the effectiveness of a...

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. Which of the following is an appropriate alternative hypothesis?

A) H?: ?f?m?l?s > ?m?l?s B) H?: ?f?m?l?s ?m?l?s B) H?: ?f?m?l?s < ?m?l?s C) H?: ?f?m?l?s ? ?m?l?s D) H?: ?f?m?l?s = ?m?l?s

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, allowing for 1% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied customers in the two resorts?

A) Do not reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. B) Do not reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. C) Reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. D) Reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. A) Do not reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. B) Do not reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. C) Reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. D) Reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.

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, 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

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, if you want to test the claim that "Resort 1 (Group 1)has a \[\text { lower }\]proportion 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.

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 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 make a decision. 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 make a decision.

Exam 10: Two-Sample Tests

TABLE 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. 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 Table 10-5, the calculated value of the test statistic is ________.

(Short Answer)

4.8/5

(71)

Question 161

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. Which of the following is an appropriate alternative hypothesis?

(Multiple Choice)

4.7/5

(78)

Question 162

The t test for the difference between the means of 2 independent populations assumes that the respective

(Multiple Choice)

4.8/5

(76)

Question 163

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, allowing for 1% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied customers in the two resorts?

(Multiple Choice)

4.8/5

(77)

Question 164

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 99% 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)

4.8/5

(87)

Question 165

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(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?

(Short Answer)

4.9/5

(89)

Question 166

TABLE 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 Table 10-6, there are ________ degrees of freedom for this test.

(Short Answer)

4.8/5

(74)

Question 167

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, 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.

(Multiple Choice)

4.9/5

(81)

Question 168

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 additional assumption is needed for the test to be valid?

(Multiple Choice)

4.7/5

(70)

Question 169

Repeated measurements from the same individuals is an example of data collected from two related populations.

(True/False)

4.8/5

(84)

Question 170

If we wish to determine whether there is evidence that the proportion of items of interest is higher in Group 1 than in Group 2, and the test statistic for Z = -2.07 where the difference is defined as Group 1's proportion minus Group 2's proportion, the p-value is equal to ________.

(Short Answer)

4.8/5

(80)

Question 171

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

(Essay)

4.9/5

(84)

Question 172

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

(Multiple Choice)

4.9/5

(76)

Question 173

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 90% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

(Essay)

4.7/5

(78)

Question 174

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, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

(Multiple Choice)

4.8/5

(97)

Question 175

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 point estimate for the difference between the two population proportions?

(Multiple Choice)

4.7/5

(80)

Question 176

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. For a 0.01 level of significance, what is the critical value for the rejection region?

(Multiple Choice)

4.9/5

(89)

Question 177

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, if you want to test the claim that "Resort 1 (Group 1)has a $\text { lower }$ proportion of satisfied customers compared to Resort 2 (Group 2)," you will use

(Multiple Choice)

4.8/5

(87)

Question 178

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

(Short Answer)

4.7/5

(87)

Question 179

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 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)

4.7/5

(86)

Question 180

The t test for the difference between the means of 2 independent populations assumes that the respective

Repeated measurements from the same individuals is an example of data collected from two related populations.

If we wish to determine whether there is evidence that the proportion of items of interest is higher in Group 1 than in Group 2, and the test statistic for Z = -2.07 where the difference is defined as Group 1's proportion minus Group 2's proportion, the p-value is equal to ________.

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

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

Filters