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 55 American League players and a random sample of 55 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	5.492	4.552
National	5.544	6.075

Note: The degrees of freedom for this problem is df = 100.103603. 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: ?1≠μ1≠ ?2μ2
C. ?0H0: ?1μ1 = ?2μ2 vs.  ??HA: ?1μ1 > ?2μ2

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

3. Calculate the p-value.

4. Construct a 99% confidence interval for the difference in American League and National League salaries, ?????????μAmerican - ?????????μNational. ( ,  )

Answer 1

1) the appropriate hypotheses for this research question is

B. ?0:μ1 = ?2 vs.  ??:μ1≠ ?2

2. using excel>addin phstat>two sample t

we have

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.01
Population 1 Sample
Sample Size	55
Sample Mean	5.492
Sample Standard Deviation	4.5520
Population 2 Sample			Lower limit	Upper limit
Sample Size	55		-2.739854453	2.635854453
Sample Mean	5.544
Sample Standard Deviation	6.0750
Intermediate Calculations		Calculations Area
Numerator of Degrees of Freedom	1.0978		Pop. 1 Sample Variance	20.7207
Denominator of Degrees of Freedom	0.0110		Pop. 2 Sample Variance	36.9056
Total Degrees of Freedom	100.1036		Pop. 1 Sample Var./Sample Size	0.3767
Degrees of Freedom	100		Pop. 2 Sample Var./Sample Size	0.6710
Standard Error	1.0236		For one-tailed tests:
Difference in Sample Means	-0.0520		T.DIST.RT value	0.4798
Separate-Variance t Test Statistic	-0.0508		1-T.DIST.RT value	0.5202
Two-Tail Test
Lower Critical Value	-2.6259
Upper Critical Value	2.6259
p-Value	0.9596
Do not reject the null hypothesis

3. the p-value =0.9596 the appropriate test statistic t = -0.0508

4. a 99% confidence interval for the difference in American League and National League salaries is (-2.7399 , 2.6359 )