Home Ownership An urban economist wishes to estimate the

Step 1 of 2

We need to determine the size of the sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if

(a) The sample size required to obtain a  confidence interval for with a margin of error is given by

\(n=\widehat{p}(1-\widehat{p})\left[\frac{Z \alpha / 2}{E}\right]^{2}\)

Using \(\widehat{p}=0.669\), E = 0.02 and the Z-score corresponding to 90% confidence level is 1.645.

\(\begin{aligned} n & =0.669(1-0.669)\left[\frac{1.645}{0.02}\right]^{2} \\ n & =0.669(0.331)\left[\frac{1.645}{0.02}\right]^{2} \\ \mathrm{n} & =1498.0486 \approx 1499 \end{aligned}\)