Mathematics: 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,

1Step-by-step explanation:1*1=1...

An organization consists of 8,684 employees. they

Ответ:

christingle2004

07.01.2022

Mathematics

The correct option is A.

Step-by-step 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

$p=\frac{36}{100}=0.36$

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

The formula for margin of error is

$ME=z\times \sqrt{\frac{p(1-p)}{n}}$

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

$ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}$

$ME=\pm 0.0316425$

$ME\approx \pm 0.032$

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

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