In baseball, League A allows a designated hitter (DH) to bat for the pitcher, who is typically a weak hitter. In League B, the pitcher must bat. The common belief is that this results in League A teams scoring more runs. In interleague play, when League A teams visit League B teams, the League A pitcher must bat. So, if the DH does result in more runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this claim, a random sample of runs scored by league A teams with and without their DH is given in the accompanying table. Complete parts a) through d) below. Click the icon to view the data table. O B. No but the number of runs scored in a League A park appear to be slightly higher than the number of runs scored in a League B park. O C. Yes because the number of runs scored in a League B park appear to have a higher median than the number of runs scored in a League A park. D. Yes because the number of runs scored in a League A park appear to have a higher median than the number of runs scored in a League B park. b) Explain why a hypothesis test may be used to test whether the mean number of runs scored for the two types of ballparks differ. Select all that apply. A. Each sample has the same sample size. LY B. Each sample size is large. LY C. Each sample size is small relative to the size of its population. LY D. Each sample is obtained independently of the other. LY E. Each sample is a simple random sample. c) Test whether the mean number of runs scored in a League A park is greater than the mean number of runs scored in a League B park at the a = 0.05 level of significance. Determine the null and alternative hypotheses for this test. Let HA represent the mean number of runs scored by a League A team in a League A park and let up represent the mean number of runs scored by a League A team in a League B park. Ho: HA HB versus H1: HA HB Find to, the test statistic for this hypothesis test. to =(Round to two decimal places as needed.)- X Sample of Runs Full data set League A Park (with DH) 7 3 6 8 C N 2 6 4 12 5 6 13 6 9 5 6 4 2 5 5 14 14 7 League B Park (without DH) 5 5 4 6 2 CO N 2 10 WW AO- O NW CO N-A