The sample size needed to estimate a population mean to within 50 units was found to be 97.If the population standard deviation was 250,then the confidence level used was
A)90%
B)95%
C)99%
D)None of these choices.

Question

Quizplus · Accepted Answer

The formula to calculate the sample size required to estimate a population mean with a level of precision is:

n = (Z^2 * s^2) / (d^2)

where:
n = sample size
Z = Z-value for the desired level of confidence
s = population standard deviation
d = desired level of precision

Substituting the given values, we get:

97 = (Z^2 * 250^2) / (50^2)

Simplifying this equation, we get:

Z^2 = (97 * 50^2) / (250^2)
Z^2 = 0.0196
Z = 1.96 (using a Z-table or calculator)

Therefore, the confidence level used must be 95%, using the Z-value of 1.96.

The Sample Size Needed to Estimate a Population Mean to Within