Question

g Suppose the investigators had made a rough guess of 0.14 for the value of the sample standard deviation, s, before collecting data. What sample size would be necessary to obtain an interval width of 0.04 from a confidence level of 99% for a two-sided confidence interval

Answer 1

Answer:

The sample size is   $n =326$

Step-by-step explanation:

From the question we are told that

  The rough estimate of the standard deviation is  $\sigma = 0.14$

   The interval width is  $w = 0.04$

   

Generally the margin of error is mathematically represented as

          $E = \frac{w}{2}$

=>       $E = \frac{0.04}{2}$

=>       $E = 0.02$

From the question we are told the confidence level is   99% , hence the level of significance is    

      $\alpha = (100 - 99 ) \%$

=>   $\alpha = 0.01$

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

   $Z_{\frac{\alpha }{2} } = 2.58$

Generally the sample size is mathematically represented as

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

=>   $n = [\frac{ 2.58 * 0.14 }{0.02} ] ^2$

=>   $n =326$