Exam 11: The Analysis of Variance

Interaction in an experimental design can be tested in:

In a two-way factor ANOVA with replications, the null hypothesis for testing whether interaction exists is that no interaction exists, while the alternative hypothesis is that interaction does exist.

Which of the following is not a required condition for one-way ANOVA?

The numerator or MST degrees of freedom are 3 and the denominator or MSE degrees of freedom are 18. The total number of observations in the completely randomized design must equal 20.

One-way ANOVA is applied to three independent samples having means 10, 13, and 18, respectively. If each observation in the third sample were increased by 30, the value of the F-statistics would:

The analysis of variance is a procedure that allows statisticians to compare two or more population:

Which of the following correctly describes the F statistic for the completely randomized design?

Based on public demand, price for seeds, and average yield, a farmer must choose which variety of wheat to grow. In the first step toward making a decision, the farmer planted eight test plots each with three varieties of wheat. The recorded yields (in pounds per plot) were used in an analysis of variance. Use the output from the analysis of variance to test the null hypothesis of no difference among the mean yields of the three varieties of wheat. Use to draw conclusions. Test statistic F = ______________ The rejection region is ______________. ______________ The sample in this problem ______________ that the mean yields for the three varieties are not the same.

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

In a two-way ANOVA, where a is the number of factor A levels and b is the number of factor B levels, the number of the degrees of freedom for the "error term" is:

Tukey's method for paired comparisons assumes that the sample means are equal and independent of each other.

The following statistics were calculated based on samples drawn from three normal populations: Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Test statistic = ______________ Critical Value(s) = ______________ Conclusion: ______________ Interpretation: Differences ______________ exist among the population means.

An avid runner was interested in whether there is a significant difference in the average wear (measured in weeks of use) among three brands of running shoes. To answer the question, the runner randomly selected six runners and assigned them to wear each of the three brands of running shoes until the shoes wore out. Each of the runners wore the brands of shoes in a random order. After the data had been recorded, the following output was generated using Minitab: What are the blocks? ______________ What are the treatments? ______________ The p-value ______________ indicate significant results. Is blocking necessary in this problem? ______________ Justify your answer. ________________________________________________________ Use the p-value approach to determine whether there is a significant difference in the average wear between the three brands of running shoes. Let = 0.05. The p-value ______________ indicate significant results. ______________ of the brands of running shoes has a significantly different average wear than the others.

In the randomized block design for ANOVA where k is the number of treatments and b in the number of blocks, the degrees of freedom for error is given by:

A complete 3 x 2 factorial experiment is called balanced if:

A company conducted an experiment to determine the effect of two types of incentive pay plans on worker productivity for workers of two shifts. The company used an equal number of production workers from each of the two shifts and one-half of these workers were assigned to each plan. Then five workers from each pay plan-shift combination were selected and their productivity (in number of items produced) recorded for a one week period. The following output was generated using Minitab: Is there significant interaction present in this problem? Let = 0.05. The p-value ______________ indicate significant interaction. Based on the previous answer, is testing for the main effects, plan and shift, appropriate? ________________________________________________________

For which of the following departures from the conditions required for a completely randomized design is the procedure not considered robust?

In a one-way ANOVA, the following null and alternative hypotheses are appropriate: .

A textile company is interested in knowing if there is a difference in the breaking strength of four different kinds of thread. Test whether there is a significant difference in mean breaking strength of the four kinds of thread. Calculate the test statistic. F = ______________ Set up the rejection region for = 0.05. The rejection region is ______________. What conclusion can be drawn? ______________ ______________ of the mean breaking strengths of the four kinds of threads is significantly different from the others. Find the approximate p-value. CI = ______________ Enter (n1, n2) Find a 90% confidence interval for . CI = ______________ Enter (n1, n2)

The one-way ANOVA assumes that the population means are equal.