Question

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 94%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 22 years.

Answer 1

The sample size is
`n = 68`

Explanation:

From the question we are told that

The margin of error is
`E = 5 \ years`

The standard deviation is
`\sigma = 22`

From the question we are told the confidence level is 94% , hence the level of significance is

`\alpha = (100 - 94 ) \%`

=>
`\alpha = 0.06`

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

`Z_{(\alpha )/(2) } =  1.881`

Generally the sample size is mathematically represented as

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

=>
`n = [\frac{1.881 } *  22 }{5} ] ^2`

=>
`n = 68`