Question

(6 points) The 30 Major League Baseball teams are divided into two "leagues" of 15 teams each: the American League and the National League. A random sample of 48 American League players and a random sample of 48 National League players were selected. The sample mean and standard deviation of the salaries of the sampled players is shown in the table below.

League	Mean salary in millions USD	SD of salary in millions USD
American	5.694	4.467
National	3.038	9.397

Note: The degrees of freedom for this problem is df = 67.209359. Round all results to 4 decimal places. Remember not to round for intermediate calculations!

1. A statistically-minded baseball fan wants to use statistical inference to determine if the salaries of the players in the American League are different from the salaries of the players in the National League. Select the appropriate hypotheses for this research question.
A. H0H0 : μ1μ1 = μ2μ2 vs. HAHA : μ1μ1 < μ2μ2
B. H0H0 : μ1μ1 = μ2μ2 vs. HAHA : μ1≠μ1≠ μ2μ2
C. H0H0 : μ1μ1 = μ2μ2 vs. HAHA : μ1μ1 > μ2μ2

2. Calculate the appropriate test statistic. ?ztX^2F =

3. Calculate the p-value.

4. Construct a 99% confidence interval for the difference in American League and National League salaries.

Answer 1

The statistical software output for this problem is

Two sample T summary hypothesis test: 41 : Mean of Population 1 U2 : Mean of Population 2 H1 - H2 : Difference between two means Ho : H1 - H2 = 0 HA: H1 - H270 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value H1-42 2.656 1.5017885 67.209359 1.768558 0.0815

Option B is correct.

Test statistics = 1.7686

P-value = 0.0815

Two sample T summary confidence interval: H1 : Mean of Population 1 H2: Mean of Population 2 H1 - H2: Difference between two means (without pooled variances) 99% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit 1 - 12 2.656 1.5017885 67.209359 -1.325209 6.637209

The 99% CI is : (-1.3252 , 6.6372)