8.48 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 nine professional tennis players to use our method. After 6 months, we test the speed of their serves and compute an average of 138 mph.

a. Using a 95% confidence interval, test the hypothesis that our method makes a difference.

b. Compute the effect size and describe its strength.