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?

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

[tex]n=884[/tex]

[tex]p=\frac{36}{100}=0.36[/tex]

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

The formula for margin of error is

[tex]ME=z\times \sqrt{\frac{p(1-p)}{n}}[/tex]

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

[tex]ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}[/tex]

[tex]ME=\pm 0.0316425[/tex]

[tex]ME\approx \pm 0.032[/tex]

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