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.From the analysis in Instruction 10-2,the correct test statistic is

A) -1.4019. B) 0.0860. C) -6,733.33. D) -1.7011. A) -1.4019. B) 0.0860. C) -6,733.33. D) -1.7011.

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,if you want to test the claim that "Resort 1 (Group 1)has a higher proportion of satisfied guests compared to Resort 2 (Group 2)",the p-value of the test will be

A) 2*(0.00262). B) 1-(0.00262/2). C) 0.00262/2. D) 0.00262. A) 2*(0.00262). B) 1-(0.00262/2). C) 0.00262/2. D) 0.00262.

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,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 guests in the two resorts?

A) 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 enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. C) 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. 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) 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 enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. C) 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. 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.

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 assumptions were necessary to conduct this hypothesis test?

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

Exam 10: Hypothesis Testing: Two Sample Tests

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 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 121

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 null hypothesis will be rejected if the test statistic is ________.

(Short Answer)

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Question 122

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 90% 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 123

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

(Short Answer)

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Question 124

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 p-value for a one-tailed test whose computed t statistic is 2.00 is between and .

(Short Answer)

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Question 125

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.From the analysis in Instruction 10-2,the correct test statistic is

(Multiple Choice)

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Question 126

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 calculated value of the test statistic is ________.

(Short Answer)

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Question 127

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,if you want to test the claim that "Resort 1 (Group 1)has a higher proportion of satisfied guests compared to Resort 2 (Group 2)",the p-value of the test will be

(Multiple Choice)

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Question 128

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,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 guests in the two resorts?

(Multiple Choice)

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Question 129

Instruction 10-3 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 A and 15 are treated with preservative B,and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat.The results are summarised in the table below. PreservativeA PreservativeB =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Instruction 10-3,state the null and alternative hypotheses for testing if the population variances differ for preservatives A and B.

(Multiple Choice)

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Question 130

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 assumptions were necessary to conduct this hypothesis test?

(Multiple Choice)

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Question 131

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,a one-tailed test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α = 0.05 level of significance.

(Short Answer)

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Question 132

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,if the buyer had decided to perform a two-tailed test,the p-value would have been between and .

(Short Answer)

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Question 133

In testing for the differences between the means of two related populations,the ________ hypothesis is the hypothesis of "no differences".

(Short Answer)

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Question 134

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 p-value of the test is ________.

(Short Answer)

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Question 135

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,a two-tailed test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α= 0.05 level of significance.

(Short Answer)

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Question 136

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,what is the 99% confidence interval estimate for the mean difference in prices?

(Short Answer)

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Question 137

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 Australia.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.

(Short Answer)

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Question 138

The t test for the mean difference between two related populations assumes that the

(Multiple Choice)

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Question 139

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 p-value of the test is ________.

(Short Answer)

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Question 140

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

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

In testing for the differences between the means of two related populations,the ________ hypothesis is the hypothesis of "no differences".

The t test for the mean difference between two related populations assumes that the

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

Filters

Exam 10: Hypothesis Testing: Two Sample Tests

When testing H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

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

In testing for the differences between the means of two related populations,the ________ hypothesis is the hypothesis of "no differences".

The t test for the mean difference between two related populations assumes that the

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

Filters

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is