It is known that the variance of a population equals 1,936. A random sample of 121 has been selected from the population. There is a .95 probability that the sample mean will provide a margin of error of _____.
A) 7.84 or less
B) 31.36 or less
C) 344.96 or less
D) 1,936 or less

Question

Quizplus · Accepted Answer

The margin of error (ME) in the context of a sample mean can be calculated using the formula ME = Z * (σ/√n), where Z is the Z-score corresponding to the desired confidence level (for a .95 probability, Z ≈ 1.96), σ is the population standard deviation, and n is the sample size. Given that the variance of the population is 1,936, the standard deviation σ is the square root of 1,936, which is 44. The sample size n is 121. Therefore, ME = 1.96 * (44/√121) = 1.96 * 4 = 7.84.

It Is Known That the Variance of a Population Equals