Question

Small sample: During an economic downturn, companies were sampled and asked whether they were planning to increase their workforce. Only of the companies were planning to increase their workforce. Use the small-sample method to construct a confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places. A confidence interval for the proportion of companies that are planning to increase their workforce is .

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The confidence level interval is  $0.016 \le C \le 0.404$

Step-by-step explanation:

The sample size is  $n = 20$

The number planning to increase workforce is  $x = 3$

 The confidence level is  $c = 98$%

The value of proportion for a plus 4 method is

      $p = \frac{x+2}{n+4}$

substituting values

      $p = \frac{3+2}{20+4}$

       $p =0.21$

The z-critical value at confidence level of 98% is

     $z_{c}=z_{0.98} = 2.33$

This values is obtained from the standard normal table

The confidence level interval can be mathematically represented as

      $C =p \ \pm z_{c} * \sqrt{\frac{p(1-p)}{n+4} }$

substituting values

      $C = 0.21 \pm 2.33 * \sqrt{\frac{0.21(1- 0.21)}{20 +4} }$

       $C = 0.21 \pm 0.194$

=>   $0.016 \le C \le 0.404$