Question

The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.09 gallons. A previous study found that for an average family the variance is 5.29 gallons and the mean is 15.6 gallons per day. If they are using a 99% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.

Answer 1

Answer:

4347

Step-by-step explanation:

Given that:

The margin of error = 0.09

Variance $\sigma^2$ = 5.29

Mean = 15.6

Level of significance = 0.99

The objective is to determine the sample size used in this study to estimate the mean usage of water.

From the given information:

The critical value $Z_{\alpha/2} = Z_{0.01/2}$ = 2.58

Sample size n = $Z_{\alpha/2}^2 \times \begin{pmatrix} \dfrac{\sigma^2}{M.O.E^2} \end {pmatrix}$

Sample size n = $2.58^2 \times \begin {pmatrix} \dfrac{5.29}{0.09^2}\end {pmatrix}$

Sample size n = 4347