Exam 12: Analysis of Variance

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When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the treatment means.

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Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:   What is the critical value of F at the 0.01 level of significance? What is the critical value of F at the 0.01 level of significance?

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The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow.   What are the block and treatment degrees of freedom? What are the block and treatment degrees of freedom?

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A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six MasterCard sales, seven Visa and five Discover sales were recorded. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic?

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A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results:   Based on the comparison between the mean annual computer technology expense for companies in the Education and Tax services industries, Based on the comparison between the mean annual computer technology expense for companies in the Education and Tax services industries,

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A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results:   To compare the mean annual incomes of female executives with a high school education or less and female executives with a Master's degree or more, compute the 90% confidence interval. [31.72, 64.28] To compare the mean annual incomes of female executives with a high school education or less and female executives with a Master's degree or more, compute the 90% confidence interval. [31.72, 64.28]

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An ANOVA showed the following comparison of four treatment means. An ANOVA showed the following comparison of four treatment means.   Which treatment means are significantly different? Which treatment means are significantly different?

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When testing for differences between treatment means, the degrees of freedom for the t statistic are:

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What distribution does the F distribution approach as the sample size increases?

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The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows.   What is the Workout mean square? What is the Workout mean square?

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Several employees have submitted different methods of assembling a subassembly. Sample data for each method are: Several employees have submitted different methods of assembling a subassembly. Sample data for each method are:   How many treatments are there? How many treatments are there?

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To employ ANOVA, the populations should have approximately equal standard deviations.

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In ANOVA, an F statistic is used to test a null hypothesis such as: In ANOVA, an F statistic is used to test a null hypothesis such as:

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A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows.   What is the computed value of F for the operators? _____ What is the computed value of F for the operators? _____

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Given the following Analysis of Variance table for three treatments each with six observations. Given the following Analysis of Variance table for three treatments each with six observations.   What are the degrees of freedom for the treatment and error sum of squares? What are the degrees of freedom for the treatment and error sum of squares?

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A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows.   What is the critical value of F for the machine treatment effect at the 1% level of significance? ____ What is the critical value of F for the machine treatment effect at the 1% level of significance? ____

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Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from manufacturer B, and five from manufacturer C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test, how many degrees of freedom must be in the denominator?

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In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What are the degrees of freedom for the numerator? ______

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If there are 5 levels of Factor A and 7 levels of Factor B for an ANOVA with interaction, what are the interaction degrees of freedom?

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Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:   What are the degrees of freedom for the numerator of the F ratio? What are the degrees of freedom for the numerator of the F ratio?

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