In baseball, league A allows a designated hitter (DH) to bat for the pitcher, wh

Question

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 fewer runs 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. Does the designated hitter result in more runs scored at the alpha = 0.05 level of significance? Note that X_a = 6.0, sa = 3.5, Xb = 4.2 and Sb = 2.6 Determine the null and alternative hypotheses for this test H0: mu A = mu B H1: mu A ne mu B H0: mu A > mu B H1: mu A = mu B H0: mu A = mu B H1: mu A mu B P Value = State the appropriate conclusion. Choose the correct answer below. Do not reject H0. There is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. Reject H0. There is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. Reject H0. There is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. Do not reject H0. There is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

Explanation / Answer

Null and alternative hypothesis for this test is given as below:

Correct Answer is D.

H0: µA = µB

H1: µA > µB

Now, we have to find P-value

For finding P-value, we need to find test statistic which is given as below:

Test statistic = t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]

Test statistic = t = (6 – 4.2) / sqrt[(3.5^2/30)+(2.6^2/30)]

Test statistic = t = 2.2612

Degrees of freedom = 29+29 = 58

P-value = 0.0138 (by using t-table)

Alpha value = 0.05

P-value is less than alpha value.

Correct Answer is B.

Reject H0. There is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

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