Chapter 12, Problem 21P

To create the following data we started with the sane sample means and variances that appeared in problem 20 but increased the sample size to $n=\text{25}$ .

$M=2$	$M=3$	$M=4$
$n=25$	$n=25$	$n=25$
$T=50$	$T=75$	$T=100$
$s^2=2.67$	$s^2=2.00$	$s^2=1.33$

a. Predict how the increase in sample size should affect the F-ratio for these data compared to the F ratio in problem 20. Use an ANOVA to check your prediction. Note: Because the samples are all the same size, $M{S}_{\text{within}}$is the average of the three sample variances.

b. Predict how the increase in sample size should affect the value of ${\eta }^2$ for these data compared to the ${\eta }^2$ in problem 10. Calculate ${\eta }^2$ to check your prediction.