Question

An IQ test is designed so that the mean is 100 and the standard deviation is 15 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 95​% confidence that the sample mean is within 3 IQ points of the true mean. Assume that sigmaequals15 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answer 1

The sample size is 96. Yes, a relatively small number is the number of IQ test scores.

Explanation:

Consider the provided information.

Standard deviation is 15 with 95​% confidence that the sample mean is within 3 IQ points of the true mean.

Now use the formula:

`n=(\sigma * (z_(\alpha/2))/(e))^2 ; e=3`

As it is given that confidence interval is 95% thus α = 1 - 0.95 = 0.05

Now use the normal curve table:

`z_{(0.05)/(2)}=z_(0.025)=1.96`

Substitute the respective values in the above formula.

`n=(15* (1.96)/(3))^2`

`n=(5* 1.96)^2`

`n=96.04`

Therefore, the sample size is 96.

Yes, a relatively small number is the number of IQ test scores.