Question

Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.

Answer 1

Answer:

The standard error is 0.033.

Step-by-step explanation:

We are given that Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.

Let $\hat p$ = proportion of employees who planned to take an extended vacation next year

$\hat p$ = $\frac{X}{n}$ = $\frac{21}{125}$ = 0.168

n = number of employees at her company = 125

Now, the standard error is calculated by the following formula;

       Standard error, S.E. =  $\sqrt{\frac{\hat p(1-\hat p)}{n} }$

                                         =  $\sqrt{\frac{0.168(1-0.168)}{125} }$

                                         =  $\sqrt{\frac{0.168 \times 0.832}{125} }$  = 0.033

Hence, the standard error is 0.033.