Question

Listed below are the 25 players on the opening-day roster of the 2016 New York Yankees Major League Baseball team, their salaries, and fielding positions.

Player	Position				Salary (US$)
C.C. Sabathia		Starting Pitcher			$	25,000,000
Mark Teixeira		First Base			$	23,125,000
Masahiro Tanaka		Starting Pitcher			$	22,000,000
Jacoby Ellsbury		Center Field			$	21,142,857
Alex Rodriguez		Designated Hitter			$	21,000,000
Brian McCann		Catcher			$	17,000,000
Carlos Beltran		Right Field			$	15,000,000
Brett Gardner		Left Field			$	13,500,000
Chase Headley		Third Base			$	13,000,000
Andrew Miller		Relief Pitcher			$	9,000,000
Starlin Castro		Second Base			$	7,857,142
Nathan Eovaldi		Starting Pitcher			$	5,600,000
Michael Pineda		Starting Pitcher			$	4,300,000
Ivan Nova		Relief Pitcher			$	4,100,000
Dustin Ackley		Left Field			$	3,200,000
Didi Gregorius		Shortstop			$	2,425,000
Aaron Hicks		Center Field			$	574,000
Austin Romine		Catcher			$	556,000
Chasen Shreve		Relief Pitcher			$	533,400
Luis Severino		Starting Pitcher			$	521,300
Kirby Yates		Relief Pitcher			$	511,900
Ronald Torreyes		Second Base			$	508,600
Johnny Barbato		Relief Pitcher			$	507,500
Dellin Betances		Relief Pitcher			$	507,500
Luis Cessa		Relief Pitcher			$	507,500

Sort the players into two groups, all pitchers (relief and starting) and position players (all others). Assume equal population standard deviations for the pitchers and the position players. Test the hypothesis that mean salaries of pitchers and position players are equal using the 0.01 significance level.

1. State the null and alternative hypothesis.

2. What is the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

3. Calculate the test statistic. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. What is your decision regarding H₀?

• Do not reject H₀

• Reject H₀

5. Is there a difference in the mean salaries of pitchers and position players?

• Yes

• No

Answer 1

Ana a ) the null and alternative hypothesis is

Ho: u(pitchers)=u(position players)

Ha: u(pitchers)u(position players) (two tailed)

Ans b ) using excel>data>data analysis>two sample t

we have

t-Test: Two-Sample Assuming Equal Variances
	all pitchers	position players
Mean	6090758	10683738
Variance	7.39E+13	7.36E+13
Observations	12	13
Pooled Variance	7.37E+13
Hypothesized Mean Difference	0
df	23
t Stat	-1.33609
P(T<=t) one-tail	0.097295
t Critical one-tail	1.713872
P(T<=t) two-tail	0.194591
t Critical two-tail	2.068658

b ) the value of t statistic from t table with 23 degrees of freedom at 0.05 is 2.069

so we reject the null hypothesis if t is t > 2.069

c ) the value of test statistic t is -1.336

d )since absolute value of test statistic t is less than 2.069 so we don't reject the null hypothesis

Do not reject H0

No ,  there is no difference in the mean salaries of pitchers and position players