(21 point) During the first 15 weeks of the 2016 seasons, the home team won 137 of the 238 regular-season National Football League games. Does this provide strong evidence of a home field advantage in professional football? (a) Test an appropriate hypothesis and state your conclusion. Use α=0.05. Be sure the appropriate assumptions and conditions are satisfied before you proceed. (Hint: conduct a one-proportion z-test and use one-sided alternative hypothesis. ) Step 1: State null and alternative hypothesis. Step 2: Assumptions and conditions check, and decide to conduct a one-proportion z-test. Step 3: Compute the sample statistics and find p-value. Step 4: Interpret you p-value, compare it with α=0.05 and make your decision. (b) Construct a 95% confidence interval for the proportion that the home team won and interpret it. (Hint: construct a one-proportion z-interval and be sure the appropriate assumptions and conditions are satisfied before you proceed. )