STA 5.4 Sampling Distribution and the central limit theorem

A __________ is a deduction or conclusion.

Inference

Statistical inference

The process of drawing conclusions about an entire population based on the information in a sample.

Sampling Distribution

Is the probability distribution of a sample statistic that is formed when random samples of size n are repeatedly from the population.

Every sample statistic has _________

a sampling distribution

The standard error of the mean

the standard deviation of the sampling distribution of sample means

Central Limit Theorem (CLT) Why is it important? 2 reasons

1. Describes the relationship between the sampling distribution of sample means and the population from which the samples are taken

2 Gives information needed to use sample statistics to make inferences about population mean

Central limit Theorem holds if...

1. If random samples of size n, where n ≥ 30, are drawn from any population with mean μ and the standard deviation σ, then the sampling distribution of sample means approximates a normal distribution.

2. If random samples of size n are drawn from a population that is normally distributed, then the sampling distribution of sample means is normally distributed for any sample size n

The _______ the sample, the _________ the approximation

1. greater
2. better

in either case of the CLT theorem, the sampling distribution of sample means has a mean equal to the __________

population mean

As the size of a sample​ __________, the standard deviation of the distribution of sample means​ __________

1. Increases
2. Decreases

As the size of a sample​ ___________, the mean of the distribution of sample means does not change.

increases