Instruction 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. \[\begin{array}{l} \begin{array} { |l | l| } \hline \text {Hypothesised Difference }&0\\ \hline \text {Level of Significance }&0.05\\ \hline \text {Population 1 Sample }&\\ \hline \text {Sample Size }&18\\ \hline \text {Sample Mean }&48266.7\\ \hline \text {Sample Standard Deviation }&13577.63\\ \hline \text { Population 2 Sample}&\\ \hline \text {Sample Size }&12\\ \hline \text { Sample Mean}&55000\\ \hline \text {Sample Standard Deviation }&11741.29\\ \hline \text {Difference in Sample Means }&-6733.3\\ \hline \text {-Test Statistic }&-1.40193\\ \hline \text {Lower-Tail Test }&\\ \hline \text {Lower Critical Value }&-1.70113\\ \hline \text { $ p $-Value}&0.085962\\\hline \end{array} \end{array}\] -Referring to Instruction 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 is the proper conclusion for this test?

A) At the ? = 0.10 level,there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. B) At the ? = 0.10 level,there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. C) At the ? = 0.10 level,there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. D) At the ? = 0.10 level,there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates. A) At the ? = 0.10 level,there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. B) At the ? = 0.10 level,there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. C) At the ? = 0.10 level,there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. D) At the ? = 0.10 level,there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

Instruction 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. \[\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\ \text { Before Course (1) } \end{array} & \begin{array} { c } \text { Exam Score } \\ \text { After Course (2) } \end{array} \\ \hline { 3 - 3 } 2 & 530 & 670 \\ 2 & 690 & 770 \\ 3 & 910 & 1,000 \\ 4 & 700 & 710 \\ 5 & 450 & 550 \\ 6 & 820 & 870 \\ 7 & 820 & 770 \\ 8 & 630 & 610 \end{array}\] -Referring to Instruction 10-5,at the 0.05 level of significance,the conclusion for this hypothesis test is that there is sufficient evidence that

A) the business school preparation course does not improve exam score. B) the business school preparation course does improve exam score. C) the business school preparation course has no impact on exam score. D) No conclusion can be drawn from the information given. A) the business school preparation course does not improve exam score. B) the business school preparation course does improve exam score. C) the business school preparation course has no impact on exam score. D) No conclusion can be drawn from the information given.

Instruction 10-9 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 πS1U1B11S1U1B0 and πS1U1B12S1U1B0 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 Instruction 10-9,if the firm wanted to test whether this proportion has changed from the previous study,which represents the relevant hypotheses?

A) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0 C) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0 D) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0 A) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0 C) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0 D) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0

Instruction 10-9 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 πS1U1B11S1U1B0 and πS1U1B12S1U1B0 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 Instruction 10-9,the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study.Which of the following is most correct?

A) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. B) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. C) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. D) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years. A) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. B) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. C) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. D) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years.

Instruction 10-8 The following MicosoftS1U1P1S1S1P0 Excel output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different. \[\begin{array}{l} \begin{array} {| l | l |} \hline \text {Hypothesised Difference }&0\\ \hline \text {Level of Significance }&0.05\\ \hline \text {Group 1 }&\\ \hline \text {Number of Successes }&160\\ \hline \text { Sample size}&200\\ \hline \text {Group 2 }&\\ \hline \text {Number of Successes }&172\\ \hline \text {Sample Size }&250\\ \hline \text {Intermediate Calculations }&\\ \hline \text {Group 1 Proportion }&0.8\\ \hline \text {Group 2 Proportion }&0.688\\ \hline \text { Difference in Two Proportions}&0.112\\ \hline \text {Average Proportion }&0.737777778 \\ \hline \text { Test Statistic}&2.684103363 \\ \hline \text {Two-Tailed Test }&\\ \hline \text { Lower Critical Value}&-1.95996398 \\ \hline \text {Upper Critical Valuse }&1.959963985 \\ \hline \text {p-Value }&0.007272462\\ \hline \end{array} \end{array}\] -Referring to Instruction 10-8,construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

The answer of Instruction 10-8 The following MicosoftS1U1P1S1S1P0 Excel output contains...

Exam 10: Hypothesis Testing: Two Sample Tests

Instruction 10-4 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: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$ Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$ -Referring to Instruction 10-4,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.01?

(Multiple Choice)

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Question 81

Instruction 10-10 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 students and 52 economics students had job offers.If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2",perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 10-10,construct a 95% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

(Short Answer)

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Question 82

Instruction 10-10 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 students and 52 economics students had job offers.If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2",perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 10-10,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 83

Instruction 10-6 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 similar various 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: \3 09 \2 92 \1 7 Sum of Squares. \ 17,573 \ 15,472 \ 139 -Referring to Instruction 10-6,the hypotheses that the buyer should test are a null hypothesis that versus an alternative hypothesis that .

(Short Answer)

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Question 84

Instruction 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. Hypothesised Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 48266.7 Sample Standard Deviation 13577.63 Population 2 Sample Sample Size 12 Sample Mean 55000 Sample Standard Deviation 11741.29 Difference in Sample Means -6733.3 -Test Statistic -1.40193 Lower-Tail Test Lower Critical Value -1.70113 p -Value 0.085962 -Referring to Instruction 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 is the proper conclusion for this test?

(Multiple Choice)

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Question 85

Instruction 10-13 To investigate the efficacy of a diet,a random sample of 16 male patients is drawn 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 kilograms with the standard deviation of differences computed as 6.0 kilograms. -Referring to Instruction 10-13,what is the 90% confidence interval estimate for the mean difference in weight before and after the diet?

(Short Answer)

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Question 86

Instruction 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) 3-3 2 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Instruction 10-5,at the 0.05 level of significance,the conclusion for this hypothesis test is that there is sufficient evidence that

(Multiple Choice)

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Question 87

Instruction 10-9 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 Instruction 10-9,if the firm wanted to test whether this proportion has changed from the previous study,which represents the relevant hypotheses?

(Multiple Choice)

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Question 88

If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2,the appropriate test to use is

(Multiple Choice)

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Question 89

A business statistics lecturer wanted to test whether the grades on a business statistics test were the same for upper and lower students.The lecturer took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the lecturer should use a t test with related samples.

(True/False)

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Question 90

Instruction 10-10 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 students and 52 economics students had job offers.If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2",perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 10-10,the null hypothesis should be rejected.

(True/False)

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Question 91

Instruction 10-13 To investigate the efficacy of a diet,a random sample of 16 male patients is drawn 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 kilograms with the standard deviation of differences computed as 6.0 kilograms. -Referring to Instruction 10-13,the computed t statistic is ________.

(Short Answer)

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Question 92

Instruction 10-9 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 Instruction 10-9,the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study.Which of the following is most correct?

(Multiple Choice)

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Question 93

Instruction 10-6 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 similar various 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: \3 09 \2 92 \1 7 Sum of Squares. \ 17,573 \ 15,472 \ 139 -Referring to Instruction 10-6,the p-value of the test is between and .

(Short Answer)

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Question 94

Instruction 10-12 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 Instruction 10-12,what is the 99% confidence interval estimate for the difference in the two means?

(Short Answer)

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Question 95

Instruction 10-4 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: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$ Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$ -Referring to Instruction 10-4,what is the 99% confidence interval estimate for the difference in the two means?

(Short Answer)

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Question 96

Instruction 10-8 The following Micosoft Excel output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different. Hypothesised Difference 0 Level of Significance 0.05 Group 1 Number of Successes 160 Sample size 200 Group 2 Number of Successes 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 Test Statistic 2.684103363 Two-Tailed Test Lower Critical Value -1.95996398 Upper Critical Valuse 1.959963985 p-Value 0.007272462 -Referring to Instruction 10-8,construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

(Short Answer)

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Question 97

Instruction 10-10 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 students and 52 economics students had job offers.If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2",perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 10-10,construct a 99% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

(Short Answer)

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Question 98

Instruction 10-11 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 Instruction 10-11,the hypotheses that should be tested are

(Multiple Choice)

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Question 99

Instruction 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. Hypothesised Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 48266.7 Sample Standard Deviation 13577.63 Population 2 Sample Sample Size 12 Sample Mean 55000 Sample Standard Deviation 11741.29 Difference in Sample Means -6733.3 -Test Statistic -1.40193 Lower-Tail Test Lower Critical Value -1.70113 p -Value 0.085962 -Referring to Instruction 10-2,what is the 95% confidence interval estimate for the difference between two means?

(Short Answer)

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Question 100

Showing 81 - 100 of 160

If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2,the appropriate test to use is

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

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