It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is
A) 25
B) 74
C) 189
D) 75

Question

Quizplus · Accepted Answer

The formula for calculating the sample size needed to estimate the population mean with a certain level of confidence and margin of error is:

n = ((z-score)^2 * population variance) / (margin of error)^2

Where:

- n is the sample size
- z-score is the critical value for the desired level of confidence (in this case, .95 corresponds to a z-score of 1.96)
- population variance is given as 484
- margin of error is given as 5

Plugging in those values, we get:

n = ((1.96)^2 * 484) / (5)^2
n ≈ 74.42

Since we cannot have a fraction of a person in a sample, we round up to the nearest whole number to get n = 75. Therefore, the best choice is D.

It Is Known That the Population Variance Equals 484