Confidence intervals, effects sizes and tennis serves:

Lets assume the average speed of a serve in mens tennis is around 135MPH, with a standard deviation of 6.5MPH. Because these statistics are calculated over many years and many players, we will treat them as population paramaters. We develop a new training method that will increase arm strength, we hope. We recruite 9 proffessional 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 initerval, test the hypothosis that our method makes a difference.

b.Compute the effect side and describe its strength.

c. Calculate statistical power using an alpha of 0.05, or 5%, and a one tailed test.

d. Calculate statistical power using an alpha of 0.10, or 10%, and a one tailed test.

e.Explain how power is affected by alpha in the calculations in parts (c) and (d).