In his first 80 at bats, a baseball prospect has 28 hits. We want to examine this prospect's hitting ability. Let p denote the prospect's true batting average (probability of getting a hit in each at bat). (a) Calculate a point estimate of p, and its standard error. (b) Calculate a two-sided 95% confidence interval for p. (c) If we want to reduce the half width of the 95% confidence interval to 0.05, how many more at bats do we need to observe? (d) We want to examine whether this prospect is an above average hitter. Suppose the league's batting average is 0.253. Perform a one-sided hypothesis test H0 :p0.253 against H1 :p>0.253.Compute the test statistic and the P-value. If we perform the test at significance level alpha= 0.05, what is your conclusion?