Question

Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 3 points, what minimum sample size is needed to be 90% confident that the sample mean is within 2 points of the true population mean?

Answer 1

Answer:  6

Step-by-step explanation:

Given : Level of confidence = 0.90

Significance level : $\alpha=1-0.90=0.10$

Critical value : $z_{\alpha/2}=1.645$

Margin of error : $E=\text{ 2 points}$

Standard deviation: $\sigma=\text{ 3 points}$

The formula to find the sample size : $n=(\dfrac{z_{\alpha/2}\sigma}{E})^2$

$n=(\dfrac{(1.645)(3)}{2})^2=6.08855625\approx6$

Hence, the minimum sample size needed= 6.