4. Following are the 29 players on the opening-day roster of the 2019 Boston Red Sox Major League Baseball team, fielding positions, and salaries. Player Position Salary (US$) David Price Starting Pitcher $ 31,000,000 J.D. Martinez Outfield $ 23,750,000 Rick Porcello Starting Pitcher $ 21,125,000 Mookie Betts Relief Pitcher $ 20,000,000 Nathan Eovaldi Starting Pitcher $ 17,000,000 Chris Sale Starting Pitcher $ 15,000,000 Dustin Pedroia Infield $ 14,521,686 xander Bogaerts Infield $ 12,000,000 Jackie Bradley Jr. Outfield $ 8,550,000 Mitch Moreland Infield $ 6,500,000 Steve Pearce Infield $ 6,250,000 Eduardo Nunez Infield $ 5,000,000 Eduardo Rodriguez Starting Pitcher $ 4,300,000 Brock Holt Infield $ 3,575,000 Christian Vazquez Catcher $2,933,333 Tyler Thornburg Relief Pitcher $ 1,750,000 Matt Barnes Relief Pitcher $ 1,600,000 Steven Wright Starting Pitcher $ 1,375,000 Heath Hembree Relief Pitcher $ 1,312,500 Brandon Workman Relief Pitcher $ 910,000 Blake Swihart Catcher $ 717,500 Andrew Benintendi Outfield $ 614,500 Rafael Devers Infield $ 577,500 Ryan Brasier Relief Pitcher $ 575,000 Brian Johnson Relief Pitcher $ 568,500 Hector Velazquez Relief Pitcher $ 564,000 Marco Hernandez Infield $ 558,500 Sam Travis Infield $ 557,000 Colten Brewer Relief Pitcher $ 548,000 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. a. State the null and alternative hypothesis. H0: the means are same H1: the means are different b. What is the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between ________and ______ c. Calculate the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic ________ d. What is your decision regarding H0? Do not reject H0 e. Is there a difference in the mean salaries of pitchers and position players? no (I need the answer for B and C all the other parts are correct for this question.)

4. Following are the 29 players on the opening-day roster of the 2019 Boston Red Sox Major League Baseball team, fielding positions, and salaries. Player Position Salary (US$) David Price Starting Pitcher $ 31,000,000 J.D. Martinez Outfield $ 23,750,000 Rick Porcello Starting Pitcher $ 21,125,000 Mookie Betts Relief Pitcher $ 20,000,000 Nathan Eovaldi Starting Pitcher $ 17,000,000 Chris Sale Starting Pitcher $ 15,000,000 Dustin Pedroia Infield $ 14,521,686 xander Bogaerts Infield $ 12,000,000 Jackie Bradley Jr. Outfield $ 8,550,000 Mitch Moreland Infield $ 6,500,000 Steve Pearce Infield $ 6,250,000 Eduardo Nunez Infield $ 5,000,000 Eduardo Rodriguez Starting Pitcher $ 4,300,000 Brock Holt Infield $ 3,575,000 Christian Vazquez Catcher $2,933,333 Tyler Thornburg Relief Pitcher $ 1,750,000 Matt Barnes Relief Pitcher $ 1,600,000 Steven Wright Starting Pitcher $ 1,375,000 Heath Hembree Relief Pitcher $ 1,312,500 Brandon Workman Relief Pitcher $ 910,000 Blake Swihart Catcher $ 717,500 Andrew Benintendi Outfield $ 614,500 Rafael Devers Infield $ 577,500 Ryan Brasier Relief Pitcher $ 575,000 Brian Johnson Relief Pitcher $ 568,500 Hector Velazquez Relief Pitcher $ 564,000 Marco Hernandez Infield $ 558,500 Sam Travis Infield $ 557,000 Colten Brewer Relief Pitcher $ 548,000 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. a. State the null and alternative hypothesis. H0: the means are same H1: the means are different b. What is the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between and c. Calculate the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic __ d. What is your decision regarding H0? Do not reject H0 e. Is there a difference in the mean salaries of pitchers and position players? no (I need the answer for B and C all the other parts are correct for this question.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

4. Following are the 29 players on the opening-day roster of the 2019 Boston Red Sox Major League Baseball team, fielding positions, and salaries.

Player	Position	Salary (US$)
David Price	Starting Pitcher	$ 31,000,000
J.D. Martinez	Outfield	$ 23,750,000
Rick Porcello	Starting Pitcher	$ 21,125,000
Mookie Betts	Relief Pitcher	$ 20,000,000
Nathan Eovaldi	Starting Pitcher	$ 17,000,000
Chris Sale	Starting Pitcher	$ 15,000,000
Dustin Pedroia	Infield	$ 14,521,686
xander Bogaerts	Infield	$ 12,000,000
Jackie Bradley Jr.	Outfield	$ 8,550,000
Mitch Moreland	Infield	$ 6,500,000
Steve Pearce	Infield	$ 6,250,000
Eduardo Nunez	Infield	$ 5,000,000
Eduardo Rodriguez	Starting Pitcher	$ 4,300,000
Brock Holt	Infield	$ 3,575,000
Christian Vazquez	Catcher	$2,933,333
Tyler Thornburg	Relief Pitcher	$ 1,750,000
Matt Barnes	Relief Pitcher	$ 1,600,000
Steven Wright	Starting Pitcher	$ 1,375,000
Heath Hembree	Relief Pitcher	$ 1,312,500
Brandon Workman	Relief Pitcher	$ 910,000
Blake Swihart	Catcher	$ 717,500
Andrew Benintendi	Outfield	$ 614,500
Rafael Devers	Infield	$ 577,500
Ryan Brasier	Relief Pitcher	$ 575,000
Brian Johnson	Relief Pitcher	$ 568,500
Hector Velazquez	Relief Pitcher	$ 564,000
Marco Hernandez	Infield	$ 558,500
Sam Travis	Infield	$ 557,000
Colten Brewer	Relief Pitcher	$ 548,000

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.

a. State the null and alternative hypothesis.

H₀: the means are same

H₁: the means are different

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

Reject H₀ if t is not between ________and ______

c. Calculate the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic ________

d. What is your decision regarding H₀?
Do not reject H₀

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

(I need the answer for B and C all the other parts are correct for this question.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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