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

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_{(\alpha )/(2)}}{E}\right )p\left ( 1-p\right )`

n=
`(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_{(\alpha )/(2)}}{E}\right )p\left ( 1-p\right )`

n=
`(1.64)/(0.04)^(2)0.5\left ( 1-0.5\right )`

n=420.25
`\approx 420`