Question

Determine the minimum sample size required when you want to be 99​% confident that the sample mean is within one unit of the population mean and sigmaequals15.2. Assume the population is normally distributed.

Answer 1

Answer: 1534

Step-by-step explanation:

The formula used to find the sample size :-

$n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2$ , where $\sigma=$ Population standard deviation.

E= Margin of error

$z_{\alpha/2}$= Two-tailed z-value for significance level of $\alpha$.

Given : Confidence level : 99%

Then significance level : $\alpha=1-0.99=0.01$

Two-tailed z-value: $z_{\alpha/2}=z_{0.005}=2.576$  [using z-value table]

$\sigma= 15.2$

Margin of error : 1 unit.

We assume the population is normally distributed.

Then, the required minimum sample size :-

$n=(\dfrac{(2.576)\cdot15.2}{1})^2$

Simplify ,

$n=1533.12968704\approx1534$

∴ Required minimum sample size = 1534