10.3 Testing and Estimating a Single Variance or Standard Deviation

Part 1: Testing

Testing • It is customary to talk about the variance instead

of standard deviation because out techniques employ the sample variance rather than the standard deviation.• Remember: the standard deviation is the square root of

the variance, therefore any discussion about the variance is easily converted to a similar discussion about the standard deviation.

• Testing is similar to testing the mean

Finding the P-Value in the Calculator

• Right-Tailed Testcdf (Test Stat, E99, d.f.)

• Left-Tailed Testcdf (0, Test Stat, d.f.)

• Two-Tailed Testcdf (0, Test Stat, d.f.)2

How to Test 1. Check Requirements• The variable must have a normal distribution and the sample

size

2. State the hypotheses and level of significance

3. Compute the sample test statistic

4. Find the P-Value• cdf (lower bound, upper bound, d.f.)

5. Conclude the Test6. Interpret the results