STA1510 SUMMARY NOTES CHAPTER 7

, STUDY UNIT 7


SAMPLING DISTRIBUTION

Sampling distribution- the distribution of possible samples selected or the proportion of
items. It is classified as either sampling distribution of the mean or a sampling distribution of
proportion.

Sampling distribution of the mean

- the distribution of the mean of all possible samples of a given size.
- Sample mean: X

- Population mean: µ

E (X) =µ

Standard error of the mean

The standard error of the mean (𝜎𝑥) is equal to the standard deviation (𝜎) in the

population of all possible sample means.

𝜎𝑥= 𝜎
√𝑛

The probability of sampling distribution of the mean

Steps of how to calculate the probability of sampling distribution of the mean

1. Determine the population mean 𝜇.
2. Determine the sample mean 𝑥.
3. Determine sample size 𝑛.
4. Determine the number of the sample mean (𝑥) for which we want to find the
probability.
5. Find the test statistic 𝑍

𝑥−𝜇
Z= 𝜎
√𝑛