An IQ test is designed so that the mean is 100 and the standard deviation is 14 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 99% confidence that the sample mean is within 8 IQ points of the true mean. Assume that sigmaequals14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Given : An IQ test is designed so that the mean is [tex]\mu=100[/tex] and the standard deviation is [tex]\sigma= 14[/tex] for the population of normal adults.

Significance level : [tex]1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=2.576[/tex]

Margin of error : [tex]E=8[/tex]

Standard deviation : [tex]\sigma= 14[/tex]

The formula to find the sample size : -

[tex]n=(\dfrac{z_{\alpha/2}\ \sigma}{E})[/tex]

[tex]\Rightarrow\ n=(\dfrac{(2.576)(14)}{8})^2=20.322064\approx20[/tex]

Hence, the minimum reasonable sample size for a real world calculation must be 20