Hypothesis Testing for Variance and Standard Deviation

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(Hypothesis test for small sample sizes)

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Presentation transcript:

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

-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

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 1 – ½

Example #1 Find the critical -value for a right-tailed test when n = 18 and = 0.01. Answer: 33.409

Example #2 Find the critical value for a left-tailed test when = 0.05 and n = 30. Answer: 17.708

Example #3 Find the critical values for a two-tailed test when n = 19 and Answer: 31.526 and 8.231

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.

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.