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?