Exam 15: Analysis of Variance

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In a two-way ANOVA,with one observation per cell,if there are 4 groups and 3 blocks,then there are a total of 7 observations.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.    -What is the value of G? -What is the value of "G"?

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B

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In conducting the Kruskal-Wallis test,independent random samples of sizes 5,7,8,and 7 were drawn from four populations and the sum of ranks in each of the samples were 84,100,96,and 98,respectively. -Based on the Kruskal-Wallis test,what is your conclusion?

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The null hypothesis that the four population means are the same cannot be rejected at the 0.05 level of significance.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G." THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a two-factor ANOVA without replication are displayed below with missing values,identified by A through G.     ANOVA: Two-Factor Without Replication SUMMARY     ANOVA    -What value should replace C? ANOVA: Two-Factor Without Replication SUMMARY THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a two-factor ANOVA without replication are displayed below with missing values,identified by A through G.     ANOVA: Two-Factor Without Replication SUMMARY     ANOVA    -What value should replace C? ANOVA THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a two-factor ANOVA without replication are displayed below with missing values,identified by A through G.     ANOVA: Two-Factor Without Replication SUMMARY     ANOVA    -What value should replace C? -What value should replace "C"?

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The Mann-Whitney test is a nonparametric alternative to the one-way analysis of variance.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following analysis of variance table with missing values identified by asterisks. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following analysis of variance table with missing values identified by asterisks.    -Test the null hypothesis of equal population means at the 5% level of significance. -Test the null hypothesis of equal population means at the 5% level of significance.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In conducting the Kruskal-Wallis test,independent random samples of sizes 5,7,8,and 7 were drawn from four populations and the sum of ranks in each of the samples were 84,100,96,and 98,respectively. -State the decision rule for the Kruskal-Wallis test at the 0.05 level of significance.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by A through H summarizes the responses.    -What is the value of H? -What is the value of "H"?

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The mean square error must always be positive in a two-way ANOVA experiment.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations.     Analysis of Variance    -What are the numerator and denominator degrees of freedom of the test ratio in testing the hypotheses in the first question? Analysis of Variance THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations.     Analysis of Variance    -What are the numerator and denominator degrees of freedom of the test ratio in testing the hypotheses in the first question? -What are the numerator and denominator degrees of freedom of the test ratio in testing the hypotheses in the first question?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following analysis of variance table: THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following analysis of variance table:    -Compute mean squares for within groups. -Compute mean squares for within groups.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An investor studied the percentage rates of return of three different types of mutual funds.Random samples of percentage rates of return for four periods were taken from each fund.The results appear in the table below: Mutual Funds THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An investor studied the percentage rates of return of three different types of mutual funds.Random samples of percentage rates of return for four periods were taken from each fund.The results appear in the table below: Mutual Funds    -At the 0.05 level of significance,test the null hypothesis that the mean percentage rates are the same for all three funds. -At the 0.05 level of significance,test the null hypothesis that the mean percentage rates are the same for all three funds.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations.     Analysis of Variance    -If a level of significance of 0.05 is chosen,what is your conclusion? Analysis of Variance THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations.     Analysis of Variance    -If a level of significance of 0.05 is chosen,what is your conclusion? -If a level of significance of 0.05 is chosen,what is your conclusion?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A firm is considering adopting an employee screening exam and has three to choose from.The exams are administered to 10 different people,and their responses are recorded. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A firm is considering adopting an employee screening exam and has three to choose from.The exams are administered to 10 different people,and their responses are recorded.    -Is there sufficient evidence to reject the null hypothesis that there is no difference between the applicants? Use α = 0.05. -Is there sufficient evidence to reject the null hypothesis that there is no difference between the applicants? Use α = 0.05.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Random samples of two freshmen,two sophomores,two juniors,and two seniors each from four dormitories were asked to rate on a scale from 1 (poor)to 10 (excellent)the quality of the dormitory environment for studying.The results are shown in the table. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Random samples of two freshmen,two sophomores,two juniors,and two seniors each from four dormitories were asked to rate on a scale from 1 (poor)to 10 (excellent)the quality of the dormitory environment for studying.The results are shown in the table.    -Test the null hypothesis that the population mean ratings are the same for the four dormitories. -Test the null hypothesis that the population mean ratings are the same for the four dormitories.

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The Kruskal-Wallis test is an example of a parametric test.

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Subject to the value of the sample sizes,the MSE can be negative or positive.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A randomized block design ANOVA has five treatments and three blocks.The analysis of variance table is displayed below with missing values,denoted by asterisks. ANOVA THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A randomized block design ANOVA has five treatments and three blocks.The analysis of variance table is displayed below with missing values,denoted by asterisks. ANOVA    -What is the degrees of freedom value for Blocks? -What is the degrees of freedom value for Blocks?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An analysis of variance table is displayed below with missing values,denoted by asterisks. ANOVA: Single Factor SUMMARY THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An analysis of variance table is displayed below with missing values,denoted by asterisks. ANOVA: Single Factor SUMMARY     ANOVA    -The average for Group 1 is equal to: ANOVA THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An analysis of variance table is displayed below with missing values,denoted by asterisks. ANOVA: Single Factor SUMMARY     ANOVA    -The average for Group 1 is equal to: -The average for Group 1 is equal to:

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The value of the test statistic F at Treatments is:

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