Question

An experiment to determine the most effective way to teach safety principles applied four different teaching methods. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. A sample of five tests was selected from each group. The test grade results were: Sample Number Programmed Instruction Lecture TV Group Discussion 1 6 8 7 8 2 7 5 9 5 3 6 8 6 6 4 5 6 8 6 5 6 8 5 5 At the 0.01 level, what is the critical value? Select one: a. 1.00 b. 1.96 c. 3.24 d. 5.29

Answer 1

Explanation:

Answer 2

Based on the table or calculations, the critical value for the F-statistic at the 0.01 significance level is approximately 5.29. Option d

How to determine the critical value

To determine the critical value at the 0.01 level for the given experiment, perform a hypothesis test.

Since we have multiple groups and want to compare their means, use an analysis of variance (ANOVA) test.

The critical value for the F-statistic in an ANOVA test at a specific significance level is obtained from an F-distribution table.

In this case, since we have four groups, the degrees of freedom for the numerator (between-group variability) would be 3, and the degrees of freedom for the denominator (within-group variability) would be (n - k), where n is the total number of observations and k is the number of groups.

Given the sample size of 5 tests in each group, we have a total of 4 groups, so n = 5 * 4 = 20.

Degrees of freedom:

Degrees of freedom numerator (dfn) = k - 1 = 4 - 1 = 3

Degrees of freedom denominator (dfd) = n - k = 20 - 4 = 16

To find the critical value from the F-distribution table, look for the value that corresponds to the significance level of 0.01, with dfn = 3 and dfd = 16.

Based on the table or calculations, the critical value for the F-statistic at the 0.01 significance level is approximately 5.29.

Therefore, the correct answer is:

d. 5.29