A population has a known standard deviation of 25. A simple random sample of 49 items is taken from the selected population. The sample mean (x-bar) is 300. What is the margin of error at the 95% confidence level?
A) 8
B) 293
C) 7
D) 308

Question

Quizplus · Accepted Answer

The formula for calculating margin of error is:
Margin of Error = z* (σ/√n)
where z* is the z-score for the desired confidence level, σ is the population standard deviation, and n is the sample size.

For a 95% confidence level, the z-score is 1.96. 
Plugging in the values, we get:
Margin of Error = 1.96*(25/√49) = 7.14

Rounding the answer to the nearest whole number, we get a margin of error of 7. Therefore, the correct answer is C.

A Population Has a Known Standard Deviation of 25