A sample of n = 25 scores is selected from a population with μ = 70 and σ = 20.It is very unlikely that the sample mean will be greater than 72.

Question

Quizplus · Accepted Answer

We can use the central limit theorem to determine that the distribution of sample means for samples of size 25 will have a mean of μ = 70 and a standard deviation of σ/√n = 4. Therefore, the probability of obtaining a sample mean greater than 72 can be calculated as follows:

z = (72 - 70) / 4 = 0.5
P(x > 72) = P(z > 0.5) = 0.3085

This probability is not very low, indicating that it is actually quite possible to obtain a sample mean greater than 72 by chance alone. Therefore, the statement is false and the answer is B.

A Sample of N = 25 Scores Is Selected from a Population