The Distribution of Sample Means

Sampling error.

The discrepancy between true population parameters and sampling statistics.

What is the law of large numbers?

*Bigger samples give better estimates The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean. Variability decreases as standard deviation decreases because distribution is more narrow.

Why does the standard error of the means depend on the variability of the original population?

As the sample size increases beyond n=1, the sample becomes a more accurate representative of the population, and the standard error decreases.

What is a distribution of sample means?

Collection of sample means from all possible random samples of size N that can be obtained from the population. Approaches normal distribution with a mean as the sample size increases.

What does the central limit theorem tell you about the distribution of sample means?

Describes the behavior os sample means: 1.Shape of the distribution of sample means will be a normal distribution. 2. The mean of the distribution of sample means will be m, the same mean as the original population 3. The standard deviation of the distribution of sample means will be the standard deviation of the original population divided by the square root of n. Holds best when: N>30 The original population has a normal distribution.

Why does the standard error of the means depends on the sample size?

Sample means will be tightly clustered around mu for large samples. Widely scattered for smaller samples. *Larger samples are more accurate

What does the standard error of the means measure?

The standard amount of difference between a sample mean and the population mean.