SCENARIO 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. \[\begin{array} { l l l } & \text { American } & \text { Japanese } \\ \text { Sample Size } & 211 & 100 \\ \text { Sample Mean SSATL Score } & 65.75 & 79.83 \\ \text { Sample Std. Dev. } & 11.07 & 6.41 \end{array}\] -Referring to Scenario 10-1, find the p-value if we assume that the alternative hypothesis was a two-tail test.

A) Smaller than 0.01 B) Between 0.01 and 0.05 C) Between 0.05 and 0.10 D) Greater than 0.10 A) Smaller than 0.01 B) Between 0.01 and 0.05 C) Between 0.05 and 0.10 D) Greater than 0.10

SCENARIO 10-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. \[\begin{array}{l} \begin{array} { l c c c c c } \text { ROW } & \text { Location A } & \text { Location B } & \text { Location C } & \text { Location D } & \text { Location E } \\ \hline 1& 28 & 40 & 21 & 37 & 22 \\ 2 & 33 & 35 & 21 & 47 & 19 \\ 3 & 41 & 33 & 27 & 45 & 25 \end{array}\\ \text { Analysis of Variance }\\ \begin{array} { l r r r c c } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\ \hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\ \text { Error } & 10 & 210.0 & & & \\ \text { Total } & & & & & \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 10-5, what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

The answer of SCENARIO 10-5 A hotel chain has identically small...

SCENARIO 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. \[\begin{array} { | l | r | } \hline \text { Hypothesized Difference } & 0 \\ \hline \text { Level of Significance } & 0.05 \\ \hline { \text { Group 1 } } \\ \hline \text { Number of Items of Interest } & 160 \\ \hline \text { Sample Size } & \mathbf { 2 0 0 } \\ \hline { \text { Group 2 } } \\ \hline \text { Number of Items of Interest } & 172 \\ \hline \text { Sample Size }&250 \\ \hline \\ \hline { \text { Intermediate Calculations } } \\ \hline \text { Group 1 Proportion } & 0.8 \\ \hline \text { Group 2 Proportion } &0.688\\ \hline \text { Difference in Two Proportions } &0.112 \\ \hline \text { Average Proportion } &0.737777778 \\ \hline \text { Z Test Statistic } & 2.684103363 \\ \hline \\\hline { \text { Two-Tail Test } } \\ \hline \text { Lower Critical Value } & - 1.959963985 \\ \hline \text { Upper Critical Value } & 1.959963985 \\ \hline \text { 2-tailed p-Value } & 0.007272462 \\ \hline \end{array}\] -Referring to Scenario 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 SCENARIO 10-9 The following EXCEL output contains the...

SCENARIO 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. $\begin{array}{|l|r|} \hline \text { Hypothesized Difference } & 0 \\ \hline \text { Level of Significance } & 0.05 \\ \hline\text { Population 1 Sample }\\ \hline \text { Sample Size } & 18 \\ \hline \text { Sample Mean } & 99210 \\ \hline \text { Sample Standard Deviation } & 13577 \\ \text { Population 2 Sample } \\ \hline \text { Sample Size } & 12 \\ \hline \text { Sample Mean } & 105820 \\ \hline \text { Sample Standard Deviation } & 11741 \\\hline\\\hline \text { Difference in Sample Means } & -6610 \\ \hline t \text { Test Statistic } & -1.37631 \\\hline\\\hline {\text { Lower-Tail Test }} \\ \hline \text { Lower Critical Value } & -1.70113 \\ \hline \text { p-Value } & 0.089816 \\ \hline \end{array}$ -Referring to Scenario 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.The proper conclusion for this test is:

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

SCENARIO 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. \[\begin{array} { | l | r | } \hline \text { Hypothesized Difference } & 0 \\ \hline \text { Level of Significance } & 0.05 \\ \hline { \text { Group 1 } } \\ \hline \text { Number of Items of Interest } & 160 \\ \hline \text { Sample Size } & \mathbf { 2 0 0 } \\ \hline { \text { Group 2 } } \\ \hline \text { Number of Items of Interest } & 172 \\ \hline \text { Sample Size }&250 \\ \hline \\ \hline { \text { Intermediate Calculations } } \\ \hline \text { Group 1 Proportion } & 0.8 \\ \hline \text { Group 2 Proportion } &0.688\\ \hline \text { Difference in Two Proportions } &0.112 \\ \hline \text { Average Proportion } &0.737777778 \\ \hline \text { Z Test Statistic } & 2.684103363 \\ \hline \\\hline { \text { Two-Tail Test } } \\ \hline \text { Lower Critical Value } & - 1.959963985 \\ \hline \text { Upper Critical Value } & 1.959963985 \\ \hline \text { 2-tailed p-Value } & 0.007272462 \\ \hline \end{array}\] -Referring to Scenario 10-9, construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

The answer of SCENARIO 10-9 The following EXCEL output contains the...

Moving companies are required by the government to publish a Carrier Performance Report each year.One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed.Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table. \[\begin{array} { | l | c | c | } \hline & \text { Econo-Move } & \text { On-the-Move } \\ \hline \text { Total shipments sampled } & 900 & 750 \\ \hline \text { Number of shipments with a claim } \geq \$ 50 & 162 & 60 \\ \hline \end{array}\] The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed.Which test would be used to properly analyze the data in this experiment?

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

Exam 10: Two-Sample Tests

SCENARIO 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 Scenario 10-1, find the p-value if we assume that the alternative hypothesis was a two-tail test.

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Question 261

SCENARIO 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. $SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: \bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \mathrm { S } _ { \mathrm { M } } { } ^ { 2 } = 1050 -Referring to Scenario 10-3, what is the 95% confidence interval estimate for the difference in the two means?$ Gotham: $\bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \mathrm { S } _ { \mathrm { M } } { } ^ { 2 } = 1050$ $SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: \bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \mathrm { S } _ { \mathrm { M } } { } ^ { 2 } = 1050 -Referring to Scenario 10-3, what is the 95% confidence interval estimate for the difference in the two means?$ -Referring to Scenario 10-3, what is the 95% confidence interval estimate for the difference in the two means?

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Question 262

SCENARIO 10-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. ROW Location A Location B Location C Location D Location E 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 Analysis of Variance Source df SS MS F p Location 4 963.6 11.47 0.001 Error 10 210.0 Total -Referring to SCENARIO 10-5, what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

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Question 263

The F test in a completely randomized model is just an expansion of the t test for independent samples.

(True/False)

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Question 264

SCENARIO 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 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 2-tailed p-Value 0.007272462 -Referring to Scenario 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 265

SCENARIO 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 t Test Statistic -1.37631 Lower-Tail Test Lower Critical Value -1.70113 p-Value 0.089816 -Referring to Scenario 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.The proper conclusion for this test is:

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Question 266

SCENARIO 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Scenario 10-4, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the $\alpha$ = 0.05 level of significance are .

(Short Answer)

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Question 267

SCENARIO 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 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 2-tailed p-Value 0.007272462 -Referring to Scenario 10-9, 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 268

SCENARIO 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. $SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: \bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \mathrm { S } _ { \mathrm { M } } { } ^ { 2 } = 1050 -Referring to Scenario 10-3, suppose \alpha = 0.10.Which of the following represents the result of the relevant hypothesis test?$ Gotham: $\bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \mathrm { S } _ { \mathrm { M } } { } ^ { 2 } = 1050$ $SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: \bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \mathrm { S } _ { \mathrm { M } } { } ^ { 2 } = 1050 -Referring to Scenario 10-3, suppose \alpha = 0.10.Which of the following represents the result of the relevant hypothesis test?$ -Referring to Scenario 10-3, suppose $\alpha$ = 0.10.Which of the following represents the result of the relevant hypothesis test?

(Multiple Choice)

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Question 269

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

(Multiple Choice)

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Question 270

When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

(True/False)

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Question 271

An airline wants to select a computer software package for its reservation system.Four software packages (1, 2, 3, and 4) are commercially available.The airline will choose the package that bumps the fewest mean number of passengers as possible during a month.An experiment is setup in which each package is used to make reservations for 5 randomly selected weeks.(A total of20 weeks was included in the experiment.) The number of passengers bumped each week is given below.How should the data be analyzed? Package 1: $12,14,9,11,16$ Package 2: $2,4,7,3,1$ Package 3: $10,9,6,10,12$ Package 4: $7,6,6,15,12$

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Question 272

SCENARIO 10-1 An airline wants to select a computer software package for its reservation system.Four software packages (1, 2, 3, and 4) are commercially available.The airline will choose the package that bumps as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks.(A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output: ANOVA Source of Variation SS df MS F P-value F crit Between Groups 212.4 3 8.304985 0.001474 3.238867 Within Groups 136.4 8.525 Total 348.8 -Referring to SCENARIO 10-1, the total degrees of freedom is

(Multiple Choice)

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Question 273

Moving companies are required by the government to publish a Carrier Performance Report each year.One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed.Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table. Econo-Move On-the-Move Total shipments sampled 900 750 Number of shipments with a claim \geq\ 50 162 60 The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed.Which test would be used to properly analyze the data in this experiment?

(Multiple Choice)

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Question 274

SCENARIO 10-4 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants 15 fields, 5 with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomized design, the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to SCENARIO 10-4, the test is valid only if the population of crop yields has the same variance for the 3 varieties.

(True/False)

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Question 275

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

(Multiple Choice)

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Question 276

The F test used for testing the difference in two population variances is always a one-tail test.

(True/False)

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Question 277

SCENARIO 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 =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Scenario 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?

(Short Answer)

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Question 278

SCENARIO 10-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to SCENARIO 10-3, construct the ANOVA table from the sample data.

(Short Answer)

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Question 279

SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives.Two different processes can be used to manufacture the flash drives.He suspects that the Kohler method produces a greater proportion of defects than the Russell method.He samples 150 of the Kohler and 200 of the Russell flash drives and finds that 27 and 18 of them, respectively, are defective.If Kohler is designated as "Group 1" and Russell is designated as "Group 2," perform the appropriate test at a level of significance of 0.01. -Referring to Scenario 10-12, the p-value of the test is _.

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Question 280

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The F test in a completely randomized model is just an expansion of the t test for independent samples.

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

When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

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

The F test used for testing the difference in two population variances is always a one-tail test.

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