Exam 13: Experimental Design and Analysis of Variance

Three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds (in miles per hour) of the tested cars are given below. Please note the sample sizes are not equal. ​ At α = .05, test to see if there is a significant difference in the average racing speeds of the cars of the three auto manufacturers. Use both the critical and p-value approaches.

The mean square is the sum of squares divided by

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. ​ ​ The null hypothesis is to be tested at the 1% level of significance. The p-value is

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. ​ ​ The mean square due to treatments (MSTR) equals

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 25 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

In ANOVA, which of the following is not affected by whether or not the population means are equal?

The F ratio in a completely randomized ANOVA is given by

In order to determine whether or not the means of two populations are equal,

Part of an ANOVA table is shown below. ​ If we want to determine whether or not the means of the populations are equal, the p-value is

Consider the following information. ​ SSTR = 6750 H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅ SSE = 8000 H_a: At least one mean is different ​ The null hypothesis is to be tested at the 5% level of significance. The p-value is

Consider the following information. ​ SSTR = 6750 H₀: μ₁ =μ₂ =μ₃ =μ₄ = μ₅ SSE = 8000 H_a: At least one mean is different ​ The mean square due to treatments (MSTR) equals

At α = .01, test to determine if the means of the three populations (from which the following samples are selected) are equal. Use both the critical and p-value approaches.

The ANOVA procedure is a statistical approach for determining whether or not the means of _____ are equal.

In a completely randomized design involving three treatments, the following information is provided: ​ The overall mean (the grand mean) for all the treatments is

Part of an ANOVA table is shown below. ​ The test statistic is

In an analysis of variance where the total sample size for the experiment is n_T and the number of populations is k, the mean square due to error is

Consider the following ANOVA table. ​ ​ The null hypothesis is to be tested at the 1% level of significance. The null hypothesis should

Part of an ANOVA table is shown below. ​ The mean square due to treatments (MSTR) is

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information. ​ SSTR = 300 (Sum of Squares Due to Treatments) SST = 800 (Total Sum of Squares) ​ The mean square due to treatments (MSTR) is

In an ANOVA procedure, a term that means the same as the term "variable" is