Exam 12: Experimental Design and Analysis of Variance

The 95 percent individual confidence interval for μ₁ − μ₂ (treatment mean 1 − treatment mean 2) will always be smaller than the Tukey 95 percent simultaneous confidence interval for μ₁ − μ₂.

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. What is the mean square error?

We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test. Assume that we are able to perform a randomized block design ANOVA on the same data. For the randomized block design ANOVA, the null hypothesis for equal treatments will ________ be rejected.

A sum of squares that measures the variability among the sample means is referred to as the

Consider the randomized block design with 4 blocks and 3 treatments given above. Test H₀: there is no difference between blocks at α = .05.

Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below. What are the levels of factor A and factor B?

In the one-way ANOVA, the treatment sum of squares equals

Which of the following is not an assumption for one-way analysis of variance?

A ________ design is an experimental design that compares v treatments by using d blocks, where each block is used exactly once to measure the effect of each treatment.

Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below. If there is an equal number of observations in each cell, what is the number of observations in each cell? (number of cells = level of factor A × level of factor B)

Suppose you are a researcher investigating the annual sales differences among five categories of businesses. The study looks at 55 companies equally divided among categories 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.

In one-way ANOVA, the numerator of the F statistic is an estimate of the population variance based on between-treatment variation.

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. Test H₀: There is no difference between blocks at α = .05.

Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below. Compute the mean squares and F to test the null hypothesis that no interaction exists between factor A and B at α = .05.

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations equally divided into 4 treatments. The response variable is sales in millions of dollars and the four treatment levels represent the four regions that the company serves. MSE = 101.25 = 39 = 33 = 43 = 49 = 31 Perform a pairwise comparison between treatment mean 1 and treatment mean 4 by computing a Tukey 95 percent simultaneous confidence interval.

Interaction exists between two factors if the relationship between the mean response and one factor depends on the other factor.

In a one-way ANOVA table, the ________ the value of MSE, the higher the probability of rejecting the hypothesis that all treatment means are equal.

After rejecting the null hypothesis of equal treatments, a researcher decided to compute a 95 percent confidence interval for the difference between the mean of treatment 1 and mean of treatment 2 based on the Tukey procedure. At α = .05, if the confidence interval includes the value of zero, then we can reject the hypothesis that the two population means are equal.

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. What is the mean square error?

A vitamin-water manufacturer wants to compare the effects on sales of three water colors: green, blue, and red. Four regions are selected for the test, with the following ANOVA results. If there is no interaction effect, test the individual null hypotheses on the effect of each factor on mean sales at α = .01.