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: 11.5 10.5 10.1 10.1 9.9 9.7 9.6 9.6 9.3 8.8 8.7 8.6

League 2: 10.9 10.1 10.1 9.8 9.7 9.2 9.1 9.1 8.9 8.9 8.8 8.8 8.6 7.8

a) Write the null and alternative hypotheses.

Let group 1 correspond to League 1 games and group 2 correspond to League 2 games. Choose the correct answer below.

A. H0: 12=0, HA: 12>0

B. H0: 120, HA: 12=0

C. H0: 12>0, HA: 12=0

D. H0: 12=0, HA: 12<0

b) Find a 99% confidence interval for the positive difference in mean runs per game and interpret your interval. (Round to two decimal places asneeded.)

The 99% confidence interval for the positive difference in means is (__,__)

Interpret your interval. Choose the correct answer below.

A. We are 99% 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.

B. We are 99% confident that the runs scored per game in both leagues will fall in the interval.

C. We are 99% 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.

c) Test the hypothesis stated above in part a and find theP-value.

t = __ (Round to two decimal places asneeded.)

P = __ (Round to three decimal places asneeded.)

d) Interpret theP-value and state your conclusion. Does the test suggest that League 1 teams score more runs onaverage? Use =0.01.

Since P-value (drop-down: less than <, greater than >) 0.01, (drop-down: reject, do not reject) H0 and conclude that there (drop-down: is, is not) 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.

Please show all work! Thanks