Goodness-of-Fit Test 10.1 526 CHAPTER 10 Chi-Square Tests and the F-Distribution What You Should Learn How to use the chi-square distribution to test whether a frequency distribution fits an expected distribution The Chi-Square Goodness-of-FitTest The Chi-Square Goodness-of-Fit Test A tax preparation company wants to determine the proportions of people who used different methods to prepare their taxes. To determine these proportions, the company can perform a multinomial experiment. A multinomial experiment is a probability experiment consisting of a fixed number of independent trials in which there are more than two possible outcomes for each trial. The probability of each outcome is fixed, and each outcome is classified into categories. (Remember from Section 4.2 that a binomial experiment has only two possible outcomes.) The company wants to test a retail trade association’s claim concerning the expected distribution of proportions of people who used different methods to prepare their taxes. To do so, the company could compare the distribution of proportions obtained in the multinomial experiment with the association’s expected distribution. To compare the distributions, the company can perform a chi-square goodness-of-fit test. A chi-square goodness-of-fit test is used to test whether a frequency distribution fits an expected distribution. DEFINITION To begin a goodness-of-fit test, you must first state a null and an alternative hypothesis. Generally, the null hypothesis states that the frequency distribution fits an expected distribution and the alternative hypothesis states that the frequency distribution does not fit the expected distribution. For instance, the association claims that the expected distribution of people who used different methods to prepare their taxes is as shown below. Distribution of tax preparation methods Accountant 24% By hand 20% Computer software 35% Friend or family 6% Tax preparation service 15% To test the association’s claim, the company can perform a chi-square goodness-of-fit test using these null and alternative hypotheses. H0:The expected distribution of tax preparation methods is 24% by accountant, 20% by hand, 35% by computer software, 6% by friend or family, and 15% by tax preparation service. (Claim) Ha:The distribution of tax preparation methods differs from the expected distribution. Study Tip The hypothesis tests described in Sections 10.1 and 10.2 can be used for qualitative data.
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