Unit 8 Section 7.5

7.5: Hypothesis Testing for Variance and Standard Deviation Three cases when finding critical values associated with chi-square. The test is right-tailed The test is left-tailed The test is two-tailed Recall…

Steps For Finding Critical Values for a Chi-Square Test Section 7.5 Steps For Finding Critical Values for a Chi-Square Test Specify the level of significance (α) Determine the degrees of freedom Use the Chi-Square Chart to find your critical value Right Tailed: Use the d.f and α Left Tailed: Use the d.f. and 1 – α Two-Tailed: Use the d.f. and 0.5α and 1 – 0.5α

Section 7.5 Example 1: a) Find the critical chi-square value for 15 degrees of freedom when α = 0.05 and the test is right tailed.

Section 7.5 Example 1: b) Find the critical chi-square value for 10 degrees of freedom when α = 0.05 and the test is left tailed.

Section 7.5 Example 1: c) Find the critical chi-square value for 22 degrees of freedom when α = 0.05 and the test is two tailed.

Section 7.5 Formula for the Chi-Square Test for a Single Variance Assumptions for the Chi-Square Test The sample must be randomly selected from a population The population must be normally distributed The observations must be independent of one another

Using the Chi-Square Test for Variance or Standard Deviation Section 7.5 Using the Chi-Square Test for Variance or Standard Deviation Verify that the sample is random and the population is normally distributed State the hypotheses and identify the claim. Specify the level of significance Identify the degrees of freedom. Determine the critical value(s) Determine the rejection region Find the standardized test statistic Make a decision Interpret your results

Section 7.5 Example 2: An instructor wishes to see whether the variation in scores of the 23 students in her class is less than the variance of the population. The variance of the class is 198. Is there enough evidence to support the claim that the variation of the students is less than the population variance (σ2 = 225) at α = 0.05? Assume the scores are normally distributed.

Section 7.5 Example 3: A hospital administrator believes that the standard deviation of the number of people using outpatient surgery per day is greater than 8. A random sample of 15 days is selected. The data is shown. At α = 0.10, is there enough evidence to support the administrator’s claim? Assume the variable is normally distributed. 25 30 5 15 18 42 16 9 10 12 12 38 8 14 27

Section 7.5 Example 4: A cigarette manufacturer wishes to test the claim that the variance of the nicotine content of its cigarettes is 0.644. Nicotine content is measured in milligrams, and assume that it is normally distributed. A sample of 20 cigarettes has a standard deviation of 1.00 milligrams. At α = 0.05, is there enough evidence to reject the manufacturer's claim?

Section 7.5 Homework: Pg 400-401: #’s 5 – 23 ODD