Baseball teams in League 1 play their games with a rule that they believe produces more runs and generates more interest among fans. The data shown below include the average numbers of runs scored per game by League 1 and League 2 teams for one season. Complete parts a through d. League 1 11.8 10.4| League 2 10.4 10.4 10.2 9.9 a) Write the null and alternative hypotheses. 10.1 9.6 + 9.9 9.9 9.9 9.8 9.7 9.2 9.4 9.3 9.2 9.2 9.1 9.1 + 8.6 8.8 8.6 8.6 8.6 8.3 Let group 1 correspond to League 1 games and group 2 correspond to League 2 games. Choose the correct answer below. OA. Ho H1 H20 HA H1-H₂=0 OC. Ho H₁₂ =0 HA: H1-H₂<0 b) Find a 95% confidence interval for the positive difference in mean runs per game and interpret your interval. The 95% confidence interval for the positive difference in means is (.). (Round to two decimal places as needed.) OB. Ho H1 H2>0 HAH₁₂=0 OD. Ho Hi-t=0 HA: H1-H₂>0 Interpret your interval. Choose the correct answer below. OA. We are 95% confident that the runs scored per game in both leagues will fall in the interval. B. We are 95% confident that the amount by which the runs scored in League 2 games exceed the runs scored in League 1 games will fall in the interval. OC. We are 95% confident that the amount by which the runs scored in League 1 games exceed the runs scored in League 2 games will fall in the interval. c) Test the hypothesis stated above in part a and find the P-value. t= (Round to two decimal places as needed.) P = (Round to three decimal places as needed.) d) Interpret the P-value and state your conclusion. Does the test suggest that League 1 teams score more runs on average? Use a = 0.05. Since P-value 0.05, Ho and conclude that there evidence that the mean number of runs scored by League 1 teams is greater than the mean number of runs scored by League 2 teams.