Question

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	4.244	7.067
National	3.481	7.525

Note: The degrees of freedom for this problem is df = 93.631761. 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. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1μ1 > ?2μ2
B. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1μ1 < ?2μ2
C. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1≠μ1≠ ?2μ2

2. Calculate the appropriate test statistic.  ? z t X^2 F  =

3. Calculate the p-value.

4. Construct a 90% confidence interval for the difference in American League and National League salaries, ?????????μAmerican - ?????????μNational. ( ,  )

Answer 1

The statistical software output for this problem is :

Option C is correct.

Test statistics = t = 0.5121

P-value = 0.6098

The 90% confidence interval is :  (-1.7124 , 3.2384)