Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?
A) The mean of the sampling distribution is 6 ounces.
B) The standard deviation of the sampling distribution is 2.5 ounces.
C) The shape of the sampling distribution is approximately normal.
D) All of the above are correct.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 6 ounces. The standard deviation of the sampling distribution is not 2.5 ounces; it is the population standard deviation divided by the square root of the sample size (σ/√n). The shape of the sampling distribution is approximately normal only if the sample size is large enough (typically n ≥ 30), so with n = 15, we cannot assume normality unless the population distribution is normal.

Suppose a Sample of N = 50 Items Is Selected