Download Section 4.8

STA220
4.8- Sampling Distributions
A _______________________________ is a numerical descriptive measure of a population. Its value is
almost always unknown.
A _______________________________is a numerical descriptive measure of a sample. It can be
calculated from the observations.
The _____________________________ of a sample statistic calculated from a sample of n
measurements is the probability distribution of the statistic.
Population Parameter
Sample Statistic
Mean
Variance
Standard Deviation
Binomial proportion
Neither the sample mean nor the sample Median will always fall closer to the population mean.
Example: The Concept of Sampling Distributions
Given the probability distribution
X
0
6
9
p(x)
1/3
1/3
1/3
Consider a random sample of n = 3 trails. Find the sampling distribution of mean and median of x
Possible Samples
x
m
Probability
0,0,0
0,0,6
0,0,9
0,6,0
0,6,6
0,6,9
0,9,0
0,9,6
0,9,9
6,0,0
6,0,6
6,0,9
6,6,0
6,6,6
6,6,9
6,9,0
6,9,6
6,9,9
9,0,0
9,0,6
9,0,9
9,6,0
9,6,6
9,6,9
9,9,0
9,9,6
9,9,9
0
2
3
2
4
5
3
5
6
2
4
5
4
6
7
5
7
8
3
5
6
5
7
8
6
8
9
0
0
0
0
6
6
0
6
9
0
6
6
6
6
6
6
6
9
0
6
9
6
6
9
9
9
9
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
1/27
Sampling distribution
of x
̅
𝑃(𝑥̅ )
𝒙
0
Sampling distribution
of M
M
P(M)
0
1
6
2
3
9
4
5
6
7
8
9
Using the following tables, find 𝐸(𝑥) = 𝜇. Then use the sampling distribution of 𝑥̅ to find the expected
value of 𝑥̅ , 𝐸(𝑥̅ ).