Question

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 plus or minus8 IQ points of the true mean. Assume that the standard deviation is 13 and determine the required sample size. nequals nothing ​(Round up to the nearest​ integer.)

Answer 1

Answer: 18

Explanation:

The formula to find the minimum sample size is given by :_

`n=((z^*\cdot \sigma)/(E))^2`

, where
`\sigma` = population standard deviation.

z*= critical z-value.

E= Margin of error.

Given :
`\sigma= 13`

E= ± 8

We know that critical value corresponding to 99% confidence level = z*=2.576 [Using z-table]

Then, the required sample size would be :

`n=(((2.576)\cdot (13))/(8))^2`

`\Rightarrow\ n=(4.186)^2`

`\Rightarrow\ n=17.522596\approx18` [Round to next integer.]

Hence, the required minimum sample size = 18