Confidence intervals, effect sizes, and tennis serves: Let's assume the average speed of a serve in men's tennis is around 135 mph, with a standard deviation of 6.5 mph. Because these statistics are calculated over many years and many players, we will treat them as population parameters. We develop a new training method that will increase arm strength, the force of the tennis swing, and the speed of the serve, we hope. We recruit 9 professional tennis players to use our method. After 6 months, we test the speed of their serves and compute an average of 138 mph.

1. Using a 95% confidence interval, test the hypothesis that our method makes a difference.
2. Compute the effect size and describe its strength.
3. Calculate statistical power using an alpha of 0.05, or 5%, and a one-tailed test.
4. Calculate statistical power using an alpha of 0.10, or 10%, and a one-tailed test.
5. Explain how power is affected by alpha in the calculations in parts (c) and (d).