I only need help with b, c, and d. I did however attach the rest of the problem for reference. A 14.2 Test Homogeneity and Indpi xb The data summarized in the acco x G screenshot screen on windows - X +A webassign.net/web/Student/Assignment-Responses/last?dep=25472461The data in the accompanying table are from a paper. Suppose that each person in a random sample of 47 male students and in a random sample of 89 female students at a particular college was classified according to gender and whether they usually orrarely eat three meals a day.Usually Eat3 Meals a DayRarely Eat3 Meals a DayMale2522Female3752(a) Is there evidence that the proportions who would fall into each of the two response categories are not the same for males and females? Use the x? statistic to test the relevant hypotheses with a significance level of a = 0.05.State the appropriate null and alternative hypotheses.O H,: The proportions falling into the two response categories are the same for males and females.H: The proportions falling into the two response categories are not the same for males and females.O H: The proportions falling into the two response categories are not the same for males and females.H: The proportions falling into the two response categories are the same for males and females.O H: The proportions falling into the two response categories are 0.5 for both males and females.H: The proportions falling into the two response categories are not 0.5 for both males and females.: The proportions falling into the two response categories are not 0.5 for both males and females.Ho:H: The proportions falling into the two response categories are 0.5 for both males and females.Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)x =P-value =State the conclusion in the problem context.O Reject Hn. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females.O Fail to reject Hg. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Fail to reject H,. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females.O Reject H. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.(b) Are your calculations and conclusions from part (a) consistent with the accompanying Minitab output?Expected counts are printed below observed countsChi-3quare contributions are printed below expected count=UsuallyRarelyTotalMale25224721.4325.570.5960.499Female375289O Type here to search12:17 AMA O 49) (a 12/10/2020W26近 A 14.2 Test Homogeneity and Indpi xb The data summarized in the acco x G screenshot screen on windows - X +A webassign.net/web/Student/Assignment-Responses/last?dep=25472461(b) Are your calculations and conclusions from part (a) consistent with the accompanying Minitab output?Expected counts are printed below observed countsChi-3quare contributions are printed below expected countsUsuallyRarelyTotalMale25224721.4325.570.5960.499Female37528948.4340.570.3150.264Total6274136Chi-3g = 1.674, DF = 1, F-Value = 0.196O The calculations and conclusions from part (a) are consistent with the accompanying Minitab output.O The calculations and conclusions from part (a) are not consistent with the accompanying Minitab output.(c) Because the response variable in this exercise has only two categories (usually and rarely), you could have also answered the question posed in part (a) by carrying out a large-sample z test of H: P, - P, = 0 versus H: P, - P, + 0, where p, isthe proportion who usually eat three meals a day for males and p, is the proportion who usually eat three meals a day for females. Minitab output from the large-sample z test is shown. Using a significance level of a = 0.05, does the large-sample ztest lead to the same conclusion as in part (a)?Test for Two ProportionsSampleSample pMale25470.531915Female37890.415730Difference = p(1) - p (2)Test for difference = O (vs not = 0): z = 1.29 P-Value = 0.196O The large-sample z test leads to the same conclusion as in part (a).O The large-sample z test does not lead to the same conclusion as in part (a).(d) How do the P-values from the tests in parts (a) and (c) compare? Does this surprise you? Explain.O The two P-values are equal when rounded to three decimal places. It is not surprising that the P-values are at least similar, since both measure the probability of getting sample proportions at least as far from the expected proportions as whatwas observed, given that the proportions who usually eat three meals per day are the same for the two populations.O The two P-values are equal when rounded to three decimal places. It is surprising that the P-values are so similar, since the P-value from the chi-square test is measuring the probability of getting sample proportions at least as far from theexpected proportions as what was observed, given that the proportions who usually eat three meals per day are the same for the two populations, and the z test is measuring the probability of getting sample proportions closer to the expectedproportions than what was observed, given that the proportions who usually eat three meals per day are the same for the two populations.O The two P-values are not equal when rounded to three decimal places. It is not surprising that the P-values are different, since the P-value from the chi-square test is measuring the probability of getting sample proportions at least as far fromthe expected proportions as what was observed, given that the proportions who usually eat three meals per day are the same for the two populations, and the z test is measuring the probability of getting sample proportions closer to theexpected proportions than what was observed, given that the proportions who usually eat three meals per day are the same for the two populations.O The two P-values are very different. It is quite surprising that the P-values are this different, since both measure the probability of getting sample proportions at least as far from the expected proportions as what was observed, given that theproportions who usually eat three meals per day are the same for the two populations.Submit AnswerP Type here to search12:17 AMA O 49) (a 12/10/2020W26

The observed values table is Usually Rarely Row totals Male 25 22 r1=47 Female 37 52 r2=89 Column totals c1=62 c2=74 Total=136 The formula of expected value isEi=ri×ciTotalwhere ri is the row total and ci is the column total. Then, the expected value table is Usually Rarely Male 62×47136=21.43 74×47136=25.57 Female 62×89136=40.57 74×89136=48.4389 The degree of freedom=r-1c-1=2-12-1=1 The chi-square test statistic isχ2=∑Oi-Ei2Ei=0.595+0.314+0.498+0.263=1.674 Then, from the chi-square table, the p-value is 0.1957. Therefore, the calculations and conclusions are consistent with the accompanying output.c)Here, p value is 0.196 which is greater than 0.05, thus do not reject the null hypothesis. d)Option b) is correct.

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rarely eat three meals a day. Usually Eat 3 Meals a Day| 3 Meals a Day Rarely Eat Male 25 22 Female 37 52 (a) Is there evidence that the proportions who would fall into each of the two response categories are not the same for males and females? Use the x statistic to test the relevant hypotheses with a significance level of a - 0.05. State the appropriate null and alternative hypotheses. O H,: The proportions falling into the two response categories are the same for males and females. H: The proportions falling into the two response categories are not the same for males and females. O Ho: The proportions falling into the two response categories are not the same for males and females. H: The proportions falling into the two response categories are the same for males and females. O H: The proportions falling into the two response categories are 0.5 for both males and females. H: The proportions falling into the two response categories are not 0.5 for both males and females. O Ho: The proportions falling into the two response categories are not 0.5 for both males and females. H: The proportions falling into the two response categories are 0.5 for both males and females. Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.) Prvalue State the conclusion in the problem context. O Reject Ho. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. O Fail to reject Ho. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females. O Fail to reject Ho. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. O Reject Ho. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females. (b) Are your calculations and conclusions from part (a) consistent with the accompanying Minitab output? Expected counts are printed below observed counts Chi-Square contributions are printed below expected counte Total 47 Rarely 22 25.57 25 21.43 Male 0.596 0.499 Female 37 52