Question

In order to officailly bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 4.5 hours. How large a sample must be selected?

Answer 1

Answer: 20

Step-by-step explanation:

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

Given : Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

Margin of error : $E<\text{2 hours}$

Standard deviation: $\sigma=\text{ 4.5 hours}$

Then, we have

$n=(\dfrac{4.5\times(1.96)}{2})^2=19.4481\approx20$

Hence, the minimum sample size must be 20.