The data in the accompanying table are from a paper. Suppose that each person in a random sample of 46 male students and

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The Data In The Accompanying Table Are From A Paper Suppose That Each Person In A Random Sample Of 46 Male Students And 1 (269.28 KiB) Viewed 17 times

The data in the accompanying table are from a paper. Suppose that each person in a random sample of 46 male students and in a random sample of ez temale students at a particular college was classified according to gender and whether they usually or rarely cat three meals a day Usually Eat 3 Meals a Day Rarely Eat 3 Meals a Day Male 24 22 Female 38 54 I USE SALT (a) Is there evidence that the proportions who would fall into each of the two response categories are not the same for maics and females? Use the x statistic to test the relevant hypotheses with a significance level of r = 0.05. Stzte the appropriate null and alternative hypotheses HoThe proportions falling into the two response categories are 0.5 for both males and females 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 not 0.5 for both males and females ,: The proportions falling into the two response categories are 0.5 for both males and females. HoThe proportions falling into the two response categories are not the same for males and females. M. The proportions falling into the two response categories are the same for meles and fernales, Ho The proportions falling into the two response categories are the same for males and females. ,: The proportiors falling into the two response categories are not the same for males and fernales. Find the test statistic and P-value. (Use SALT. Round your test statistic to three decimal places and your P-value to four decimal places.) X- puvalue - State the conclusion in the problem context. Reject. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females. Fail to reject. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. Refect H. There is not 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 convincing evidence that the proportions falling into the two response categories are not the same for males ard females. (b) Are your calculations and conclusions from part (a) consistent with the accompanying Minitab outnut7 Fxper-ed counts are prin ad belev shred courts CI.-- Luibalionas pilsduon EXP CL La Jally Bay Tulal 24 22 25.33 9.439 Ecoalc 38 92 50.82 0.26 Ictal 62 128 ChL-- 1.464, DE 2-V-0.226 26 - -. - The calculations and conclusions from part (a) are consistent with the accompanying Minitab outout. 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 Ho: P1 – P2 = 0 versus Ha: P1 - P2 = 0, where P1 is the proportion who usually eat three meals a day for males and P2 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 z test lead to the same conclusion as in part (a)? Test for Two Proportions Sample X N Sample p Male 24 46 0.521739 Female 38 92 0.413043 Difference = p(1) - p (2) Test for difference = 0 (vs not = 0): Z = 1.21 P-Value = 0.226 The large-sample z test leads to the same conclusion as in part (a). 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. 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 from the exp cted 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 expected proportions than what was observed, given that the proportions who usually eat three meals per day are the same for the two populations. 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 the 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 the expected proportions than what was observed, given that the proportions who usually eat three meals per day are the same for the two populations. 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 the proportions who usually eat three meals per day are the same for the two populations. 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 what was observed, given that the proportions who usually eat three meals per day are the same for the two populations.