Suppose that the students at Bigbrain University are planning to test whether the mean math SAT score for their school is higher than the national average (μ) of 500 (assume that σ = 100). a. If they believe that their mean is 520, and they plan to sample 25 students, what is the power of their statistical test at the .05 level, two-tailed? What would the power be for a one-tailed test? Explain why power is higher for the one tailed test.

a. If they believe that their mean is 520, and they plan to sample 25 students, what is the power of their statistical test at the .05 level, two-tailed? What would the power be for a one-tailed test? Explain why power is higher for the one-tailed test.

b. Recalculate the one- and two-tailed power values in part (a) assuming that the Bigbrain students expect their average to be 50 points higher than the national average. Explain why these power values are higher than the ones you calculated in part (a).

c. Redo part (a) assuming that a sample of 100 Bigbrain students is being planned. Explain why these power values are higher than the ones you calculated in part (a).

d. Given the expected effect size in part (a), what sample size would be needed to obtain a power of .8 for a two-tailed .05 test? For a two-tailed .01 test?

e. Repeat part (d) given the expected effect size in part (b).