SOLUTION: Ages for the 2005 Boston Red Sox pitchers are shown below. (a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample sh

Question 170658This question is from textbook
: Ages for the 2005 Boston Red Sox pitchers are shown below. (a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and show all work. (b) If there is a difference, is it important? (c) Find the p-value and interpret it.
Ages of Boston Red Sox Pitchers, October 2005
Arroyo 28 Foulke 33 Mantei 32
Timlin 39 Clement 31 Gonzalez 30
Miller 29 Wakefield 39 Embree 35
Halama 33 Myers 36 Wells 42

This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Ages for the 2005 Boston Red Sox pitchers are shown below.
(a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and show all work.
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Ho: u <=30
Ha: u > 30
Using a one tail z test with alpha = 5%: z = -1.645
The sample mean = 28.89
z(28.89) = (28.89-30)/10.2646 = -0.1081
This z-value is not in the rejection region so "Fail to reject Ho".
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(b) If there is a difference, is it important?
There is a slight difference but it is not important.
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(c) Find the p-value and interpret it.
p-value = 0.457
There is a 45.7% probability that test results could result
in stronger evidence to reject Ho.
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Cheers,
Stan H.
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Ages of Boston Red Sox Pitchers, October 2005
Arroyo 28 Foulke 33 Mantei 32
Timlin 39 Clement 31 Gonzalez 30
Miller 29 Wakefield 39 Embree 35
Halama 33 Myers 36 Wells 42

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