Question

How large a sample must we take if we want the margin of error to be at most 0.01 pound with 95% confidence

Answer 1

Answer:

The sample size  is  $n = 153664$  

Step-by-step explanation:

From the question we are told that

    The margin of error is  E  =  0.01

From the question we are told the confidence level is  95% , hence the level of significance is    

      $\alpha = (100 - 95 ) \%$

=>   $\alpha = 0.05$

Generally from the normal distribution table the critical value  of  $\frac{\alpha }{2}$ is  

   $Z_{\frac{\alpha }{2} } =  1.96$

Let take the standard deviation to be $\sigma = 2 \ pounds$

Gnerally the sample size is mathematically represented as

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

=>    $n = [\frac{1.96 *2 }{0.01} ]^2$

=>    $n = 153664$