Statistics and data science 188 Sampling Distributions
Chapter 7
Introduction
In this chapter the following will be covered:
▪ The concept of the sampling distribution.
▪ To calculate probabilities related to the sample mean and the sample
proportion.
▪ The importance of the Central Limit Theorem.
Sampling Distributions
- Distribution of all possible values of a sample statistic
- Sampling distribution of the mean
▪ Usually normally distributed
- Sampling distribution of the proportion
Sampling distributions of the mean
• The sampling distribution of the mean is the distribution of all possiblesample means calculated
from all possible samples of a given size.
-
-
Developing a Sampling Distribution
- Sample with replacement
- This distribution of sample-means should be normally distributed
, Summary Measures of a Sample Distribution
Population distribution vs sample mean distribution
- Unbiased if:
- Means are equal
- The standard deviation is likely to differ
- Even if the data is unbiased
Standard error of the mean
- Different samples of the same size
- From the same population
▪ Will yield different sample means
- Standard Error decreases as sample size increases
When the population is normal:
When organising and visualising data one needs to be mindful of:
- mean = ¿ and standard deviation = Ã
- The sampling distribution of X-bar is also normally distributedwith:
Chapter 7
Introduction
In this chapter the following will be covered:
▪ The concept of the sampling distribution.
▪ To calculate probabilities related to the sample mean and the sample
proportion.
▪ The importance of the Central Limit Theorem.
Sampling Distributions
- Distribution of all possible values of a sample statistic
- Sampling distribution of the mean
▪ Usually normally distributed
- Sampling distribution of the proportion
Sampling distributions of the mean
• The sampling distribution of the mean is the distribution of all possiblesample means calculated
from all possible samples of a given size.
-
-
Developing a Sampling Distribution
- Sample with replacement
- This distribution of sample-means should be normally distributed
, Summary Measures of a Sample Distribution
Population distribution vs sample mean distribution
- Unbiased if:
- Means are equal
- The standard deviation is likely to differ
- Even if the data is unbiased
Standard error of the mean
- Different samples of the same size
- From the same population
▪ Will yield different sample means
- Standard Error decreases as sample size increases
When the population is normal:
When organising and visualising data one needs to be mindful of:
- mean = ¿ and standard deviation = Ã
- The sampling distribution of X-bar is also normally distributedwith:
