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

Answer:

The sample required is  $n = 135$

Step-by-step 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  $\frac{\alpha }{2}$ from the normal distribution table(reference  math dot armstrong dot edu) , the value is  

             $Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58$

The  sample size is mathematically represented as

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

substituting values

           $n = [ \frac{ 2.58 * 9 }{2} ]^2$

            $n = 135$