Question

Estimating Sample Size: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 54 % . You would like to be 90% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required? (please do not do any intermediate rounding)

Answer 1

The value is
`n = 2887`

Explanation:

From the question we are told that

The population proportion is
`p = 0.54`

The margin of error is
`E = 1.5 \% = 0.015`

From the question we are told the confidence level is 90% , hence the level of significance is

`\alpha = (100 - 90 ) \%`

=>
`\alpha = 0.10`

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

`Z_{(\alpha )/(2) } =  1.645`

Generally the sample size is mathematically represented as

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

=>
`n = [(1.645 )/(0.015) ]^2 * 0.54(1-0.54)`

=>
`n = 2887`