Question

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

What is the standard error?

Answer 1

.10 - .23

Explanation:

.168 +/- 1.96 ( sqrt ((.168 * .832)/125))

Answer 2

The standard error is 0.033.

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` =
`(X)/(n)` =
`(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{(\hat p(1-\hat p))/(n) }`

=
`\sqrt{(0.168(1-0.168))/(125) }`

=
`\sqrt{(0.168 * 0.832)/(125) }` = 0.033

Hence, the standard error is 0.033.