Question

A population is estimated to have a standard deviation of 9. We want to estimate the population mean within 2, with a 99% level of confidence. How large a sample is required? (Round up your answer to the next whole number.)

Answer 1

The sample required is
`n = 135`

Explanation:

From the question we are told that

The standard deviation is
`\sigma = 9`

The margin of error is
`E = 2`

Given that the confidence level is 99% then the level of significance is mathematically evaluated as

`\alpha = 100-99`

`\alpha = 1 \%`

`\alpha = 0.01`

Next we will obtain the critical value
`(\alpha )/(2)` from the normal distribution table(reference math dot armstrong dot edu) , the value is

`Z_{(\alpha )/(2) } = Z_{(0.05 )/(2) } = 2.58`

The sample size is mathematically represented as

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

substituting values

`n = [ ( 2.58 * 9 )/(2) ]^2`

`n = 135`