Question

A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 90​% confidence if ​(a) she uses a previous estimate of 0.38​? ​(b) she does not use any prior​ estimates?

Answer 1

Answer:a-396

b-420

Step-by-step explanation:

$\alpha$ =0.1

Margin of Error=0.04

Level of significance is z$\left ( 0.1\right )=1.64$

Previous estimate$\left ( p\right ) =0.38$

sample size is given by:

n=$\left (\frac{Z_{\frac{\alpha }{2}}}{E}\right )p\left ( 1-p\right )$

n=$\frac{1.64}{0.04}^{2}0.38\left ( 1-0.38\right )=396.0436\approx 396$

$\left ( b\right )$Does not use prior estimate

Assume

$\alpha$=0.1

Margin of Error=0.04

Level of significance is z$\left ( 0.1\right )=1.64$

Population proportion$\left ( p\right )$=0.5

n=$\left (\frac{Z_{\frac{\alpha }{2}}}{E}\right )p\left ( 1-p\right )$

n=$\frac{1.64}{0.04}^{2}0.5\left ( 1-0.5\right )$

n=420.25$\approx 420$