Exam 12: Analysis of Variance

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The F distribution's curve is positively skewed.

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When the null hypothesis for an ANOVA analysis comparing four treatment means is rejected, _________________.

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In ANOVA analyses, when the null hypothesis is rejected, we can test for differences between treatment means by _____________.

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Given the following ANOVA table for three treatments each with six observations: Given the following ANOVA table for three treatments each with six observations:   What is the computed value of F? What is the computed value of F?

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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. The 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. The 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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The annual dividend rates for a random sample of 16 companies in three different industries, utilities, banking, and insurance were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. The mean square error (MSE) was 3.36. The following table summarized the results: The annual dividend rates for a random sample of 16 companies in three different industries, utilities, banking, and insurance were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. The mean square error (MSE) was 3.36. The following table summarized the results:   Based on the comparison between the mean annual dividend rate for companies in utilities and banking, the 95% confidence interval shows an interval of 1.28 to 6.28 for the difference. This result indicates that _____________________. Based on the comparison between the mean annual dividend rate for companies in utilities and banking, the 95% confidence interval shows an interval of 1.28 to 6.28 for the difference. This result indicates that _____________________.

(Multiple Choice)
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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.   Which source of variation significantly affects peak heart rate? Which source of variation significantly affects peak heart rate?

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A random sample of 30 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 243.7. The following table summarized the results: A random sample of 30 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 243.7. The following table summarized the results:   When comparing the mean annual incomes for executives with undergraduate and master's degrees or more, which of the following 95% confidence interval can be constructed? When comparing the mean annual incomes for executives with undergraduate and master's degrees or more, which of the following 95% confidence interval can be constructed?

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Interaction between two factors occurs when the effect of one factor on the response variable is the same for any value of another factor.

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When a second source of variance is included in the ANOVA analysis without interaction, that source is called a _________________.

(Short Answer)
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A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown next. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown next.   What is the critical value of F at the 5% level of significance? What is the critical value of F at the 5% level of significance?

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In a two-way ANOVA, when is an interaction source of variance included?

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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. The 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. The ANOVA table follows.   What is the mean square for operators? What is the mean square for operators?

(Essay)
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A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. 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 surveyed and asked to indicate their industry and annual computer technology expense. 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, _________________.

(Multiple Choice)
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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 Interaction sum of squares? What is the Interaction sum of squares?

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The F distribution is a ______________ distribution.

(Short Answer)
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Assuming that the larger of two variances is in the numerator of an F-statistic, the rejection region to test a null hypothesis is in the _________ tail of the F distribution.

(Short Answer)
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A random sample of 30 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 243.7. The following table summarized the results: A random sample of 30 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 243.7. The following table summarized the results:   When comparing the mean annual incomes for executives with a high school education or less and those with an undergraduate degree, the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference. This result indicates that __________________. When comparing the mean annual incomes for executives with a high school education or less and those with an undergraduate degree, the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference. This result indicates that __________________.

(Multiple Choice)
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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. The 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. The ANOVA table follows.   What are the degrees of freedom for the machines? What are the degrees of freedom for the machines?

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ANOVA requires that the populations should be ______, ______, and have _____.

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