3. The chi-square test for goodness-of-fit - Reaching a conclusion Aa Aa A chi-square goodness-of-fit test is conducted to determine if the distribution of observed data among four possible categories is similar to a known distribution. The null hypothesis states that the population is distributed according to a known distribution with the following proportions: Category A B C D Proportion under Ho 35% 30% 25% 10% A random sample of N= 300 observations is obtained from the population. The resulting observed frequencies and the corresponding expected frequencies associated with the null hypothesis are shown in the following table. Category A B CD Observed frequency (0) 114 92 66 28 Expected frequency (E) 105 90 75 30 The chi-square test statistic for the preceding frequency data is x= 2.03. (See explanation for details.) Use the Distributions tool to answer the following questions. Chi-Square Distribution Degrees of Freedom = 3 0 1 -~ The value of the x test statistic is 2 -3 4 5 6 7 At the level of significance a .01, the critical value is ^^ If the null hypothesis is true, the test statistic has a chi-square distribution with df = 8 than the critical value. 9 10 11 12 13 14 15 16 degrees of freedom. rejected. Therefore, you The null hypothesis conclude that there are significant differences between the proportions for the population from which the sample was drawn and the proportions in the known distribution. 17 X