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

Step-by-step explanation:

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

$n=(\dfrac{z^*\cdot \sigma}{E})^2$

, 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 :

$n=(\dfrac{(2.576)\cdot (13)}{8})^2$

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

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

Hence, the required minimum sample size = 18