Exam 2 - Central Limit Theorem Flashcards
Center : the mean of the sampling distribution of x-bar equals the
Population mean, mu
Sampling distribution of x-bar is the distribution of
Values taken by x- bar from all possible samples of the same size from the same population
Spread: the standard deviation of the sampling distribution of x- bar equals
Sigma over square root of n
Shape: population normal - the shape of the sampling distribution of x- bar is
Normal
Shape: population non-normal- the shape of the sampling distribution of x-bars is
Approximately normal when n is large
Central Limit Theorem:
If……
Then…,,
If you take a large SRS of size n from any population
Then
The sampling distribution of x- bar is approximately Normal
As n increases shape gets more
Normal
n is considered to be large if it is
Bigger than 30, n>30
CLT allows us to use …….. ….. ……to compute approximate probabilities on x-bar
Standard normal table
T/F Increased sample size does not affect the shape of the population, only the shape of sampling distribution.
True
How to predict sampling distribution of x- bar in statistical practice?
- Take
- Use sample
- Take only 1 sample of size n
2. Use sample results to make inference about population
What 2 facts allow us do predictions without creating sampling distribution of x- bar?
- Mean = mu and standard deviation of x- bar = sigma over square root of n
- Shape is approx normal if the sample size is large (CLT)