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

Answer:

The sample size is    $n = 68$

Step-by-step 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  $\frac{\alpha }{2}$ is  

   $Z_{\frac{\alpha }{2} } =  1.881$

Generally the sample size is mathematically represented as  

   $n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2$

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

=>  $n = 68$