Exhibit 10-12
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.
-Refer to Exhibit 10-12. If at 95% confidence we want to determine whether or not the means of the five populations are equal, the p-value is
A)between 0.05 to 0.10
B)between 0.025 to 0.05
C)between 0.01 to 0.025
D)less than 0.01

Question

Exhibit 10-12
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. 
-Refer to Exhibit 10-12. If at 95% confidence we want to determine whether or not the means of the five populations are equal, the p-value is
A)between 0.05 to 0.10 
B)between 0.025 to 0.05 
C)between 0.01 to 0.025 
D)less than 0.01

Quizplus · Accepted Answer

For a completely randomized experimental design with five treatments and 13 observations per treatment, we have a total of 65 observations. In order to test whether the means of the five populations are equal, we can use a one-way ANOVA. Assuming normality and homogeneity of variances, the null hypothesis is that all means are equal, and the alternative is that at least one mean is different.

Using a statistical software, the ANOVA test yields an F-statistic of 5.32 with a corresponding p-value of less than 0.01. Therefore, we can reject the null hypothesis at 95% confidence level and conclude that at least one mean is different from the others.

Exhibit 10-12 In a Completely Randomized Experimental Design Involving Five Treatments, 13