SOLUTION: Consider a normal population with µ = 25 and σ = 7.0.
(A) Calculate the standard score for a value x of 27.
(B) Calculate the standard score for a randomly selected
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Question 701436: Consider a normal population with µ = 25 and σ = 7.0.
(A) Calculate the standard score for a value x of 27.
(B) Calculate the standard score for a randomly selected sample of 45 with xbar = 27.
(C) Explain why the standard scores of 27 are different between A and B above
please walk me through this
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Consider a normal population with µ = 25 and σ = 7.0.
(A) Calculate the standard score for a value x of 27.
z(27) = (27-25)/0.7 = 2.857
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(B) Calculate the standard score for a randomly selected sample of 45 with xbar = 27.
z(27) = (27-25)/(0.7/sqrt(45)) = 2/(0.7/sqrt(45)) = 19.166
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(C) Explain why the standard scores of 27 are different between A and B above
The Central Limit Theorem says:
1. The mean of the sample means = the mean of the population
2. The std of the sample means = (the std of the population)/sqrt(sample size)
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So the population std is much smaller that the std of the population.
As a result the z-score (which is a count of std's) is greater for
sample means than it is for an equal sample element.
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Cheers,
Stan H.
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