Exam 13: Experimental Design and Analysis of Variance

Information regarding random samples of annual salaries (in thousands of dollars) of doctors in three different specialties is shown below. a.Compute the overall mean . b.State the null and alternative hypotheses to be tested. c.Show the complete ANOVA table for this test including the test statistic. d.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e.Determine the p-value and use it for the test.

Exhibit 13-3 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. -Refer to Exhibit 13-3. The test statistic to test the null hypothesis equals

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The number of degrees of freedom corresponding to between treatments is

Random samples were selected from three populations. The data obtained are shown below. Please note that the sample sizes are not equal. a.Compute the overall mean . b.At 95% confidence, test to see if there is a significant difference among the means.

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

Exhibit 13-3 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. -Refer to Exhibit 13-3. The null hypothesis is to be tested at the 1% level of significance. The p-value is

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The number of degrees of freedom corresponding to within treatments is

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The 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 heating bills for a selected sample of houses using various forms of heating are given below. (Values are in dollars.) a.At $\alpha$ = 0.05, test to see if there is a significant difference among the average heating bills of the homes. Use the p-value approach. b.Test the above hypotheses using the critical value approach. Let $\alpha$ = .05.

The required condition for using an ANOVA procedure on data from several populations is that the

The heating bills for a selected sample of houses using various forms of heating are given below (values are in dollars). At $\alpha$ = 0.05, test to see if there is a significant difference among the average bills of the homes. Use both the critical and p-value approaches.

An experimental design that permits statistical conclusions about two or more factors is a

When an analysis of variance is performed on samples drawn from K populations, the mean square between treatments (MSTR) is

The F ratio in a completely randomized ANOVA is the ratio of

Random samples were selected from three populations. The data obtained are shown below. Please note that the sample sizes are not equal. a.Compute the overall mean . b.At 95% confidence using the critical value and p-value approach, test to see if there is a significant difference among the means.

For four populations, the population variances are assumed to be equal. Random samples from each population provide the following data. Using a .05 level of significance, test to see if the means for all four populations are the same.

Six observations were selected from each of three populations. The data obtained is shown below. Test at the $\alpha$ = 0.05 level to determine if there is a significant difference in the means of the three populations. Use both the critical value and the p-value approaches.

An ANOVA procedure is used for data obtained from five populations. five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The mean square within treatments (MSE) is