1. Since everything is a reflection of our minds,
everything can be changed by our minds.

2. Inferences about Population Variances
Sections 7.1 to 7.3
The distribution of s^2
Tests for equal variances

3. The Distribution of S^2
Let Y1, Y2, …, Yn be a random sample from a normal population with mean m and variance s^2.
The definition of s^2:
The distribution of s^2:

4. Estimation and Tests for s^2
(Chi-square) Confidence Interval: p.364
Chi-square Test: p.366
Normal population is required.

5. F Test for Equal Variances
Consider two independent (random) samples from two NORMAL populations
Ho: s1=s2
T.S.:

6. F Test for Equal VariancesHa
R.R: Reject Ho if
s1=s2
s1>s2
s1<s2

7. Example: Minitab Lab Key in the data
Sample1
8.1
7.4
9.3
7.5
7.1
8.7
9.1
7.9
8.4
8.8
Sample2
3.9
4.4
3.6
4.1
4.6
3.5
4.0
4.2
4.7
Key in the data
Check the normality assumption on both samples
Calculate a 95% confidence interval of variance for each population
Conduct a test for equal variances