Question

You should explain the confidence intervals you create along with explanations of the meaning of your answers and business implications for each problem.

Scenario:

You have been asked once again to study the mean tuition at private universities throughout the United States. You will also again study the proportions of universities throughout the United States that regularly award more than 50% of their students some form of financial aid. The specific questions you will be asked to answer are stated below. In addition, appropriate sample data for the studies you will be accomplishing is given below. Answer the following questions concerning the situations posed.

The organization for which you are working in your study of private university tuition has been quite impressed with your work. Its CEO has a relative who works for the Major-League Baseball Players’ Union. Your services and abilities have been recommended to union leadership. You have been asked to perform a study that will result in a comparison of the average salaries per player for major league baseball teams. This information will be needed as historical data to be used in upcoming labor negotiations. The average player salary data for two recent years for all 30 major league baseball teams is shown below in appendix two. At the 1% level of significance, has the average player salary increased from the first year to the second year? For the purposes of the study, you may assume that this data is sample data drawn from a much larger population of teams. Once again, should the procedure you choose to accomplish this task allow for it, construct a 99% confidence interval for the difference in the mean salary per player from year one to year two. Explain the meaning of this interval.

Appendix Two (Salaries)

Year

Team Two One New York Yankees $7,663,361 $6,862,918

Philadelphia Phillies $4,055,455 $3,393,916

Boston Red Sox $4,581,533 $4,196,967

Chicago White Sox $3,458,400 $4,501,832

Chicago Cubs $4,630,693 $4,675,883

St. Louis Cardinals $4,416,937 $3,342,380

San Francisco Giants $2,899,400 $2,391,955

New York Mets $3,765,567 $3,916,288

Detroit Tigers $4,434,909 $4,148,959

Atlanta Braves $3,680,180 $2,693,161

Minnesota Twins $2,664,878 $1,934,886

Los Angeles Dodgers $4,334,605 $4,371,154

Los Angeles Angels $4,223,942 $4,110,408

Texas Rangers $2,402,506 $1,991,413

Baltimore Orioles $1,684,182 $1,995,760

Tampa Bay Rays $2,297,365 $1,594,997

Colorado Rockies $2,926,721 $2,554,035

Seattle Mariners $3,377,771 $3,270,666

Cincinnati Redlegs $2,153,075 $1,748,586

Milwaukee Brewers $2,937,499 $3,562,592

Toronto Blue Jays $1,825,987 $2,829,826

Houston Astros $3,464,718 $3,610,588

Oakland Athletics $1,469,254 $1,740,764

Washington Nationals $1,685,950 $1,349,305

Kansas City Royals $2,621,263 $1,820,423

San Diego Padres $ 959,165 $1,720,590

Arizona Diamondbacks $2,168,853 $3,015,390

Florida Marlins $1,327,968 $ 868,261

Cleveland Indians $2,007,420 $1,905,804

Pittsburgh Pirates $ 790,167 $1,201,117

Answer 1

using minitab>stat>basic stat>two sample t test

we have

Two-Sample T-Test and CI: first year, second year

Two-sample T for first year vs second year

N Mean StDev SE Mean
first year 30 3001452 1425767 260308
second year 30 2859883 1317997 240632

Difference = μ (first year) - μ (second year)
Estimate for difference: 141569
99% CI for difference: (-802544, 1085682)
T-Test of difference = 0 (vs <): T-Value = 0.40 P-Value = 0.654 DF = 58
Both use Pooled StDev = 1372939.8503

let us consider the null and alternative hypothesis are

H0:μ (first year) - μ (second year) = 0

Ha:= μ (first year) - μ (second year) <0

the value of test stat is 0.40

p value is 0.654

since p value is greater than 0.01 ( significance level ) so we reject the claim that  the average player salary increased from the first year to the second year

99% confidence interval for the difference in the mean salary per player from year one to year two is (-802544, 1085682)

we are 99 % confident that the average difference between the salary of player from  first year to second year lies in the interval (-802544, 1085682)