1. HYPOTHESIS TESTING FOR VARIANCE AND STANDARD DEVIATION Section 7.5

2. Uses the Chi-Square Test To find critical value(s) 1. Specify level of significance, alpha 2. Find degrees of freedom 3. Use the Chi-Square table. (#6) ◦ For a right tailed test, use α ◦ For a left tailed test, use (1 – α) ◦ For a 2-tailed test, use ½ α and (1 – ½ α)

3. Find the critical value(s) 6. Right tailed test, α = 0.10, n = 10 8. Left tailed test, α = 0.05, n = 24 10. Two tailed test, α = 0.01, n = 61

4. Finding the Test Statistic

5. Guidelines for the X 2-Test 1. find H 0 and H a 2. identify alpha 3. find the critical value(s) 4. shade the rejection region(s) 5. find X 2 6. make decision to reject or not reject the null hypothesis 7. interpret decision in context

6. Test each claim 16. Claim: σ 2 > 8.5; α = 0.05 s 2 = 7.45, n = 23 17. Claim: σ = 24.9; α = 0.10 s = 29.1, n = 51

7. 20. An auto manufacturer believes that the variance of the gas mileages of its hybrid vehicles is 1.0. You work for an energy conservation agency and want to test this claim. You find that a random sample of the gas mileages of 25 of the manufacturer’s hybrid vehicles has a variance of 1.65. At α = 0.05, do you have enough evidence to reject the manufacturer’s claim?

8. 22. A state school administrator says that the standard deviation of test scores for 8 th grade students who took a US history test is less than 30 points. You work for the administrator and are asked to test this claim. You randomly select 18 tests and find the standard deviation to be 33.6 points. At α = 0.01, is there enough evidence to support the administrator’s claim?