1. Hypothesis Testing for Variance and Standard Deviation
The chi-square Test

2. -test for a population variance or standard deviation
The test statistic is s2 and the standardized test statistic is:
Assumption: The population is normally distributed

3. Guidelines Degrees of freedom is d.f. = n – 1
The critical values for the distribution are found in Table 6 of Appendix B.
Right-tailed test, use the value that corresponds to d.f. and
Left-tailed test, use the value that corresponds to d.f. and 1 –
Two-tailed test, use the values that correspond to d.f. and ½ and – ½

4. Example #1
Find the critical value for a right-tailed test when n = 18 and = 0.01.
Answer:

5. Example #2
Find the critical value for a left-tailed test when = 0.05 and n = 30.
Answer:

6. Example #3 Find the critical values for a two-tailed test when n = 19 and
Answer: and 8.231

7. Example # 4
A police chief claims that the standard deviation in the length of response times is less than 3.7 minutes. A random sample of nine response times has a standard deviation of 3.0 minutes. At = 0.05, is there enough evidence to support the police chief’s claim? Assume the population is normally distributed.

8. Answer to #4
Fail to reject the null, there is NOT enough evidence at the 5% level to support the claim that the standard deviation in the length of response times is less than 3.7 minutes.