Exam 2 - Central Limit Theorem

Question 0

Center : the mean of the sampling distribution of x-bar equals the

Answer 0

Population mean, mu

Question 1

Sampling distribution of x-bar is the distribution of

Answer 1

Values taken by x- bar from all possible samples of the same size from the same population

Question 2

Spread: the standard deviation of the sampling distribution of x- bar equals

Answer 2

Sigma over square root of n

Question 3

Shape: population normal - the shape of the sampling distribution of x- bar is

Answer 3

Normal

Question 4

Shape: population non-normal- the shape of the sampling distribution of x-bars is

Answer 4

Approximately normal when n is large

Question 5

Central Limit Theorem:

If……
Then…,,

Answer 5

If you take a large SRS of size n from any population
Then
The sampling distribution of x- bar is approximately Normal

Question 6

As n increases shape gets more

Answer 6

Normal

Question 7

n is considered to be large if it is

Answer 7

Bigger than 30, n>30

Question 8

CLT allows us to use …….. ….. ……to compute approximate probabilities on x-bar

Answer 8

Standard normal table

Question 9

T/F Increased sample size does not affect the shape of the population, only the shape of sampling distribution.

Answer 9

True

Question 10

How to predict sampling distribution of x- bar in statistical practice?

1. Take
2. Use sample

Answer 10

1. Take only 1 sample of size n

2. Use sample results to make inference about population

Question 11

What 2 facts allow us do predictions without creating sampling distribution of x- bar?

Answer 11

1. Mean = mu and standard deviation of x- bar = sigma over square root of n
2. Shape is approx normal if the sample size is large (CLT)