Question

The researcher decided to use a 95% confidence interval with a maximum error of 0.05 to estimate p, the proportion of old factory sites in the U.S. where toxic clean-up will be required before the sites can be reused. How large a sample does she need?

Answer 1

The sample size is
`n = 384`

Explanation:

From the question we are told that

The margin of error is
`E = 0.05`

Here we will assume that the sample proportion is
`\^ p = 0.5`

From the question we are told the confidence level is 95% , hence the level of significance is

`\alpha = (100 - 95 ) \%`

=>
`\alpha = 0.05`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.96`

Generally the sample size is mathematically represented as

`n = [\frac{Z_{(\alpha )/(2) }}{E} ]^2 * \^ p (1 - \^ p )`

=>
`n = [(1.96 )/(0.05) ]^2 * 0.5 (1 - 0.5  )`

=>
`n = 384`