Question: (10 points) Power curves for two-sample test.

a. (5 points). Below is a graph of three power curves as a function of d, the true difference between the means in the two samples. The standard deviations of both populations are s = 1. Hence, think of d as being in standard deviation units. The curves are for 29, 9 and 4 degrees of freedom. Give a reason why the valley in the middle becomes increasingly steeper and narrower as the degrees of freedom increases.