Exam 12: Experimental Design and Analysis of Variance

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In one-way ANOVA,a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

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If sample mean plots look essentially parallel,we can intuitively conclude that there is an interaction between the two factors.

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A researcher has used a one-way analysis of variance model to test whether the average starting salaries differ among recent graduates from the nursing,engineering,business,and education disciplines.She has randomly selected four graduates from each of the four areas. If MSE = 4,and SSTO = 120,complete the following ANOVA table.Is there a significant difference in the starting salaries among the four disciplines? (H0: No difference)

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Looking at four different diets,a researcher randomly assigned 20 equally overweight women into each of the four diets.What are the degrees of freedom for the error?

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Suppose you are a researcher investigating the annual sales differences among five categories of businesses.The study looks at a total of 55 companies equally divided among category groups A,B,C,D,and E. Complete the following ANOVA table and determine the value of the F statistic. Source SS df MS F Treatment 583.39 Error Total 1555.57 Source SS df MS F Treatment 583.39 4 145.85 7.501 Error 972.18 50 19.4436 Total 1555.57 54

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Consider the one-way ANOVA table.

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Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments.

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Looking at four different diets,a researcher randomly assigned 20 equally overweight women into each of the four diets.What are the degrees of freedom for the treatments?

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In a ___________________ experimental design,independent random samples of experimental units are assigned to the treatments.

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Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments.

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Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments.

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When computing a confidence interval for the difference between two means,the width of the (1 - α)confidence interval based on Tukey's procedure will be __________ the width of the (1 - α)individual confidence interval based on the t statistic.

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Consider the following one-way ANOVA table.

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Suppose you are a researcher investigating the annual sales differences among five categories of businesses.Looking at a total of 55 companies equally divided among categories groups A,B,C,D,and E. Determine degrees of freedom treatment,degrees of freedom error and degrees of freedom total and state the critical value of the F statistic at α = .05.

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