Question: Superbrain University students believe their mean SAT score differs from the national average.

1. If they believe their SAT average is 510, with a plan to use a sample of 20 students, compute the power of the statistical test of the mean of a single population that the SAT score of Superbrain University students is higher than the national average (one-tail test). What would the power be for a difference in either direction (two-tailed test)?
2. Recalculate the power values in part (a), this time, supposing that Superbrain University students expect their average to be 50 points higher than the national SAT average for both a one-tailed and two-tailed test.
3. Why are the power values higher for part (b) than they are for part (a)?
4. Why are power values higher for one-tailed rather two-tailed tests?
5. Redo the power values in part (a) assuming that a sample of 100 students is planned for the research.
6. Why are the power values higher for part (d) than they are for part (a)?
7. Given the expected effect size (d) in part a, what sample size would be needed to obtain power = .85 for two-tailed test at the .05 level.

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