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 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 (standard error) is σ/√n, not 2.5 ounces. The shape is approximately normal only if n is large enough, typically n ≥ 30, so it may not be normal for n = 15.

Suppose a Sample of N = 50 Items Is Selected