Lecture 17- Sampling Distribution of Mean

Question 1

What is the sampling distribution of the means?

Answer 1

Do lots of samples from the population and plot the means

Question 2

What is central limit theorem?

Answer 2

It doesn’t matter what the original population distribution is so long as our sample size is big enough the sampling distribution of the means will be approximately normal

Question 3

How do you get the mean of a sampling distribution of means?

Answer 3

The mean of the sampling distribution just equals the mean of the population (what you want- refer to slides to see how it simplifies to this)

Question 4

How do you get the variance and standard deviation of a sampling distribution of the means?

Answer 4

Variance= variance of population/ n
Standard deviation= standard deviation of population/ square root of n

(remember standard deviation is just the square root of variance)

To see how math simplifies down look at slides

Question 5

What is the special name for standard deviation in a sampling distribution of means?

Answer 5

Standard error. It is measure of the precision with which we have estimated the mean.

Question 6

With an increased sample size (n) how does variance and therefore SD/standard error alter?

Answer 6

Less variation

Question 7

Suppose we know that adult female heights have values which are
normally distributed with mean 169cm and standard deviation 3.20cm.
Find:
(I) Pr(X > 172)
(II) Pr(X > 172) where X is the distribution of means for samples of size
n = 9.

Answer 7

(I) Pr(X > 172)= 0.1743
(II) Pr(X > 172)= 0.0025

Use slides to see working/ what to enter into r