Question

If a researcher wants to compute a 90% confidence interval from a population with a known standard deviation of 5 units and have a margin of error of no more than 1 unit, what is the smallest sample size that can be used

Answer 1

Answer: The smallest sample size that can be used = 68

Step-by-step explanation:

Formula to find the sample size when population standard deviation$(\sigma)$ is known:

$n=(\dfrac{z^c\times\sigma}{E})^2$, where $z^c$ = critical z value , E -= Margin of error.

Given: $\sigma=5,\ E=1$

Critical z- value for 90% confidence level = 1.645

Then, the required sample size :

$n=(\dfrac{5\times1.645}{1})^2=(8.225)^2\approx68$

Hence, the smallest sample size that can be used = 68