Question

An organization consists of 8,684 employees. They decided to conduct a survey about their new vacation policies. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. Assuming a 95% confidence level, which of the following statements holds true?

A. As the sample size is appropriately large, the margin of error is ±0.032.

B. As the sample size is too small, the margin of error is ±0.032.

C. As the sample size is appropriately large, the margin of error is ±0.0265.

D. As the sample size is too small, the margin of error cannot be trusted..


I think the answer is A. am I correct?

Answer 1

A is the correct answer

Answer 2

The correct option is A.

Explanation:

An organization consists of 8,684 employees. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. It means

`n=884`

`p=(36)/(100)=0.36`

The value of z-score for 95% confidence level is 1.96.

The formula for margin of error is

`ME=z* \sqrt{(p(1-p))/(n)}`

Where, z is z-score at given confidence level, p is sample proportion and n is number of samples.

`ME=\pm 1.96* \sqrt{(0.36(1-0.36))/(884)}`

`ME=\pm 0.0316425`

`ME\approx \pm 0.032`

The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.