Question

An IQ test is designed so that the mean is 100 and the standard deviation is 12 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 2 IQ points of the true mean. Assume that sigmaequals12 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 97. ​(Round up to the nearest​ integer.) Would it be reasonable to sample this number of​ students? Yes. This number of IQ test scores is a fairly large number. Yes. This number of IQ test scores is a fairly small number. No. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number.

Answer 1

Explanation:

Given that IQ mean is 100 and std dev = 12 for normal adults

`Confidence level =90%\\Z critical value = 1.645\\Margin of error = 2\\Margin of error = 1.645* std error =2\\Std error = 1.216`

Std error =
`(12)/(√(n) ) =1.216`

`n=((12)/(1.216) )^2 =97.38`

i.e. sample size should be atleast 97

The required sample size is 97.

This is reasonable as this is greater than 30

Yes. This number of IQ test scores is a fairly large number.