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 46 American League players and a random sample of 46 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 5.716 7.489 National 6.149 8.896 Note: The degrees of freedom for this problem is df = 87.458012. 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. Ho: Mi = uz vs. HAHI > U2 B. Ho: Mi = H2 vs. Ha:ui # uz C. Ho: Hi = H2 vs. HA: Mi <H2 2. Calculate the appropriate test statistic. ? = 3. Calculate the p-value. 4. Construct a 90% confidence interval for the difference in American League and National League salaries, American - U National

Answer 1

Given : ni 46 x = 5.716 si : 7.489 n2 = 46 72 = 6.149 S2 = 8.896 1. Ho: M = 42 vs Haus & 42 12. Test statistic, t. XI-X2 3,2 52 vn 5.716-6.149 7.4892 I 46 8.8962 46 -0.433 1.7145 t = -0.2525 3. p-value at x = 0.10 ; df = 87.458012 þ - Value = piltl < -0.2525) = 0.8012 4. The got confidence interval is (71-72) t t* 2 52 unin2 (5.716 - 6.149) † 16623 7.489?, 8.8962 St*:1,6623 at 20.052. 46 df = 87.458012, t- table] -0.433 + 2.85oo 46 The 90% confidence interval is (-0.718 2.4171