SOLUTION: I am struggling with this problem...I am getting a headache because I have been working on it forever now...PLEASE HELP AND THANK YOU VERY MUCH Consider a normal population with

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Question 492456: I am struggling with this problem...I am getting a headache because I have been working on it forever now...PLEASE HELP AND THANK YOU VERY MUCH
Consider a normal population with � = 25 and σ = 8.0.SHOW ALL WORK
(A)Calculate the standard score for a value x of 22.
(B)Calculate the standard score for a randomly selected sample of 30 with = 22.
(C)Explain why the standard scores of 22 are different between A and B above.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Consider a normal population with � = 25 and σ = 8.0.SHOW ALL WORK
(A)Calculate the standard score for a value x of 22.
z(22) = (22-25)/8 = -3/8
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(B)Calculate the standard score for a randomly selected sample of 30
with xbar = 22
t(22) = (22-25)/[8/sqrt(30)] = -3/1.4606 = -2.0540
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(C)Explain why the standard scores of 22 are different between A and B above.
A based on z-distribution ; B based on t-distribution
A has std = 8 ; B has std = 8/sqrt(30)
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Note: These differences relate to the Central Limit Theorem
It's also possible that your text would call for the following
for "B": z(22) = (22-25)/[8/sqrt(30)] = -2.0540
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Cheers,
Stan H.