1. Chapter 10 Chi-Square Tests and the F-Distribution

2. Section 10-1 – Goodness of Fit Goodness of Fit Multinomial Experiment – a fixed number of trials in which there are more than two possible outcomes for each independent trial. The probability of each outcome is fixed, and each outcome is classified into categories. Chi-Square Goodness of Fit Test Used to test whether a frequency distribution fits an expected distribution (claim). Two conditions that must be met in order to conduct a Chi-Square Goodness of Fit test 1)Samples must be randomly selected. 2)Each E must be ≥ 5. You may need to combine categories to achieve this.

3. Section 10-1 – Goodness of Fit Goodness of Fit Guidelines for conducting the test. 1)Write hypotheses and identify claim H 0 : Simply state the claimed percentages for each category. H a :State that the distribution is different from what is listed above. 2)Identify α. 3)Identify degrees of freedom (k-1) where k is the number of categories. 4)Find the critical value from the Chi-Square distribution table (page A19 in your book) 5)Find the rejection region (these will ALWAYS be right-tailed tests)

7. Section 10-1 – Goodness of Fit Guidelines for conducting the test. 1)Write the hypotheses and identify claim. H 0 : Simply state the claimed percentages for each category. H a :State that the distribution is different from what is listed above. 2)Identify α. 3)Identify degrees of freedom (k-1) where k is the number of categories. 4)Find the critical value from the Chi-Square distribution table (page A19 in your book) 5)Find the rejection region These will ALWAYS be right-tailed tests, so the rejection region will be to the right of the critical value.

8. Section 10-1 – Goodness of Fit Example 1 (Page 553) A marketing executive randomly selects 500 radio music listeners from the broadcast region and asks each whether he or she prefers classical, country, gospel, oldies, pop, or rock music. The results are shown in the table. Find the observed frequencies and the expected frequencies for each type of music. Survey Results (n = 500) Type of MusicClaimed %Observed Classical4%8 Country36%210 Gospel11%72 Oldies2%10 Pop18%75 Rock29%125

9. Section 10-1 – Goodness of Fit Example 1 (Page 553) The observed frequency for each type of music is the number of radio music listeners naming that particular type of music. This is what is given in the Observed column above. The expected frequency for each type of music is the claimed percentage for that music type times the total number in the sample (n). (Table above, far right column) Survey Results (n = 500) Type of MusicClaimed %ObservedExpected Classical4%8500(.04) = 20 Country36%210500(.36) = 180 Gospel11%72500(.11) = 55 Oldies2%10500(.02) = 10 Pop18%75500(.18) = 90 Rock29%125500(.29) = 145

13. Finding the Critical Value from the Chi-Square Chart Look in the row for degrees of freedom (k-1) Look in the column for the specified value for alpha. Where these intersect (15.086) is the critical value for this test.

15. Opinions on what is more important to save for. RetirementChildren’s CollegeNot sure Men44%40%16% Women41%46%13% Men’s Survey Results Retirement186 Children’s College143 Not sure71

18. ColorFrequency Brown80 Yellow95 Red88 Blue83 Orange76 Green78

21. Classwork:Page 560 #1-6 All Homework: Pages 560-563 #7-17 Odd