Considered the sampling distribution of a sample mean obtained by random sampling from an infinite population. This population has a distribution that is highly skewed toward the larger values.

Question

a) How is the mean of the sampling distribution related to the mean of the population?

b) How is the standard deviation of the sampling distribution related to the standard deviation of the population?

c) How is the shape if the sampling distribution affected by the sample size?

*please explain the analyses to the answer of each question*

The mean of the sampling distribution of the mean is always equal to the population mean. The standard deviation of the sampling distribution of the mean is called the standard error of the mean and represents the average deviation of the sample means from the population mean. The shape of the sampling distribution approaches a normal distribution as sample size increases.

Answer 1

Evaluate the following expressions for the given set of scores:
a. ΣX  b. ΣX2  c. (ΣX)2  d. Σ2X  e. Σ(X – 2)
Scores:
                                 X
                                      0
                                      5
                                      3
                                      2