Hypothesis Testing for Variance and Standard Deviation The
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Hypothesis Testing for Variance and Standard Deviation The chi-square Test
-test for a population variance or standard deviation The test statistic is s 2 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. a. Right-tailed test, use the value that corresponds to d. f. and b. Left-tailed test, use the value that corresponds to d. f. and 1 – c. Two-tailed test, use the values that correspond to d. f. and ½ and 1–½
Example #1 Find the critical -value for a righttailed test when n = 18 and = 0. 01. Answer: 33. 409
Example #2 Find the critical tailed test when Answer: 17. 708 value for a left= 0. 05 and n = 30.
Example #3 Find the critical values for a twotailed 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.