, 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
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
