11 An IQ test is designed so that the mean is 100 and the standard deviation is

Question

11

An IQ test is designed so that the mean is 100 and the standard deviation is 22 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 8 IQ points of the true mean.

Assume that ?=22 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The required sample size is_____?

(Round up to the nearest integer.)?

?

Is this sample size reasonable?

____No. 21 IQ test scores is a fairly small number.

OR

___Yes. 21 IQ test scores is a fairly small number.

OR

___Yes 21 IQ testscores is a fairly large number.

OR

___No. 21 IQ testscores is a fairly large number.

Explanation / Answer

Given a=0.1, Z(0.05) = 1.645 (from standard normal table)

So n=(Z*s/E)^2

=(1.645*22/8)^2

=20.46431

Take n=21

--------------------------------------------------------------------------------------------------------------------------

Yes. 21 IQ test scores is a fairly small number.

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