Leroy, a starting player for a major college basketball team, made only 38.4% of his free throws last season. During the summer he worked on developing a softer shot in the hope of improving his free-throw accuracy. In the first eight games of this season Leroy made 25 free throws in 40 attempts. Let p be his probability of making each free throw he shoots this season.
a. State the null hypothesis H0 that Leroy's free-throw probability has remained the same as last year and the alternative Ha that his work in the summer resulted in a higher probability of success.
b. Calculate the z statistic for testing H0 versus Ha.
c. Do you accept or reject H0 for a = 0.05? Find the P-value.
d. Give a 90% confidence interval for Leroy's free-throw success probability for the new season. Are you convinced that he is now a better free-throw shooter than last season?
e. What assumptions are needed for the validity of the test and confidence interval calculations that you performed?