Billy Wants to Test Whether the Average Speed of His

Essay

Billy wants to test whether the average speed of his favorite pitcher's fastball differs from the league average of 92 miles per hour. He takes a sample of 36 of the pitcher's fastballs and computes a sample mean of 94 miles per hour. Assume that the standard deviation of the population is 4 miles per hour.
A) Specify the null and alternative hypotheses to test Billy's claim.
B) Calculate the value of the test statistic and the p-value.
C) At the 5% significance level, can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average?
D) At the 1% significance level, can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average?