Two separate samples, each with n = 12 individuals, receive two different treatments. After treatment, the first sample has SS = 1740 and the second has SS = 1560.
a. Find the pooled variance for the two samples.
b. Compute the estimated standard error for the sample mean difference.
c. If the sample mean difference is 8 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two-tailed test at the .05 level?
d. If the sample mean difference is 12 points, is this enough to indicate a significant difference for a two-tailed test at the .05 level?
e. Calculate the percentage of variance accounted for (r2) to measure the effect size for an 8-point mean difference and for a 12-point mean difference.