Tutorial Exercise You may need to use the appropriate technology to answer this question. Test the following hypotheses by using the y' goodness of fit test. Hot PA = 0.40, Pp - 0.40, and Pc = 0.20 H: The population proportions are not PA - 0.40, Pp - 0.40, and Pc = 0.20. A sample of size 200 yielded 160 in category A, 20 in category B, and 20 in category C. Use a = 0.01 and test to see whether the proportions are as stated in Ho (a) Use the p-value approach. (b) Repeat the test using the critical value approach. Step () Use the p-value approach. Agoodness of fit test will be conducted for the following hypotheses. This type of test is always an upper tall test. The p-value approach will be used, mea ning that the given level of significance, a = 0.01, will be compared to the area under the curve to the right of the calculated test statistic. HotPA = 0.40, Pa = 0.40, and Pc = 0.20 He: The population proportions are not PA = 0.40, P. = 0.40, and Pc = 0.20. The goal of the hypothesis test Is to determine d proportions are significantly different from the given proporti ins. A sample size of 200 vielded 160 in category A, 20 in category B, and 20 in category C. Assuming the hypothesized proportions are true, then the expected frequencies I expected frequency = category proportion(sample size) The proportion for category A is assumed to be 0.40. Use the sample size of 200 to find the expected frequency for this category, ex- expected frequency = category proportion(sample size) A = 0.4 7 0.40 (200) The proportion for category B is assumed to be 0.40. Use the sample size of 200 to find the expected frequency for this category, es expected frequency = category proportion(sample size) "B - 0.4 0.40 (200) (No Response) 80 The proportion for category C Is assumed to be 0.20. Use the sample size of 200 to find the expected frequency for this category, ec expected frequency = category proportion(sample size) "c = 0.2 4 0.20 (200) - 40 40 Step 2 The x test statistic for a goodness of hit follows where f, is the observed or category I, e, is the expected frequency for category (, and & is the number of categories. The appropriate x has k - 1 degrees of freedom. The observed and exper ted frequencies nmarized in the table below Category Observed Frequency / Expected Frequency ey Difference fy - ey Squared Difference (fg - cy) |Squared Difference Divided by Expected Frequency -1) 160 160 - 80 - 80 (80)2 - 6,400 6,400 20 80 20 40 400 10 The sum of the final column will be the y? test statistic. Thus, the test statistic is x- There are k # 3 categories, so the degrees Submal Skip (you.cannot come back) Submil