Question 188973: 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
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?
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Ho: u = 30
Ha: u > 30
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State your hypotheses and decision rule and show all work.
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1st: Find the mean value of the sample (xbar); note the standard deviation (s).
2nd : Find the Critical value for "t" when df = n-2 and alpha = 5%
3rd: Find the test statistic using t(xbar) = (xbar-30)/[s/sqrt(n)]
4th: Find the p-value = P(t > t(xbar) when df= n-1)
(b) If there is a difference, is it important?
(c) Find the p-value and interpret it.
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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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Comment:
Let me know if you need more help.
Cheers,
Stan H.
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