College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 90% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 10 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?
A) 910
B) 1,537
C) 1,083
D) 1,221
E) 2,654

Question

Quizplus · Accepted Answer

We can use the sample proportion from the pilot survey to estimate the population proportion with a margin of error of 2%.

Sample proportion: p-hat = 10/50 = 0.2

Margin of error: E = 0.02

We can use the formula for sample size for estimating a population proportion:

n = [z^2 * p-hat * (1 - p-hat)] / E^2

At 90% confidence level, z = 1.645

Plugging in the values:

n = [1.645^2 * 0.2 * (1 - 0.2)] / 0.02^2

n ≈ 1082.57

Rounding up to the nearest whole number, we get n = 1,083.

Therefore, the best choice is C, with a sample size of 1,083.

College X Is Concerned About Their Employees Making Use of Their