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?

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