Question

The NFL rates each quarterback after every game according to a formula that involves pass attempts, passing yards, touchdown passes, and interceptions. Suppose, under the old rules, the mean quarterback rating per game is 52.1. There is some speculation that rule changes benefiting receivers have also increased quarterback ratings. In a random sample of 24 quarterback 2012 season ratings, the sample mean was 57.09 with a standard deviation of 9.70. Is there any evidence that the quarterback rating has increased? Perform this test at the 5% significance level? Assume that the quarterback ratings are normally distributed. Use this information to answer the following three questions 6. State the null and alternative hypothesis. ANS: 7. Compute and identify the test statistic ANS 8. Can we say that the quarterback rating has benefited under the new rules? Why or why not.

Answer 1

Given that mean(mu) = 52.1, n = 24, x^- = 57.09, S = 9.70, alpha = 0.05 Null and alternative hypothesis: H_0: mu = 52.1 H_a: mu_52.1 Test statistic: t = 2.52 P - value: with t - score = 2.52, df = 23 we get P - value = 0.0096 Decision: P - value < 1.0.5 0.0096 < 0.05 So reject H_0 Yes, we can say that the quadratic rating has benefied under the new rules. quarterback rating has increased.