MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A 14.2 Test Homogeneity and Indpi x b The data summarized in the acco x G screenshot screen on windows - X + A webassign.net/web/Student/Assignment-Responses/last?dep=25472461 The 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 or rarely eat three meals a day. Usually Eat 3 Meals a Day Rarely Eat 3 Meals a Day 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 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 counts Chi-3quare contributions are printed below expected count= Usually Rarely Total Male 25 22 47 21.43 25.57 0.596 0.499 Female 37 52 89 O Type here to search 12:17 AM A O 49) (a 12/10/2020 W 26 近
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Transcribed Image Text:A 14.2 Test Homogeneity and Indpi x b The data summarized in the acco x G screenshot screen on windows - X + A webassign.net/web/Student/Assignment-Responses/last?dep=25472461 The 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 or rarely eat three meals a day. Usually Eat 3 Meals a Day Rarely Eat 3 Meals a Day 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 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 counts Chi-3quare contributions are printed below expected count= Usually Rarely Total Male 25 22 47 21.43 25.57 0.596 0.499 Female 37 52 89 O Type here to search 12:17 AM A O 49) (a 12/10/2020 W 26 近
A 14.2 Test Homogeneity and Indpi x b 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 counts Chi-3quare contributions are printed below expected counts Usually Rarely Total Male 25 22 47 21.43 25.57 0.596 0.499 Female 37 52 89 48.43 40.57 0.315 0.264 Total 62 74 136 Chi-3g = 1.674, DF = 1, F-Value = 0.196 O 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, is the 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 z test lead to the same conclusion as in part (a)? Test for Two Proportions Sample Sample p Male 25 47 0.531915 Female 37 89 0.415730 Difference = p(1) - p (2) Test for difference = O (vs not = 0): z = 1.29 P-Value = 0.196 O 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 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 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. 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 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. 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 the proportions who usually eat three meals per day are the same for the two populations. Submit Answer P Type here to search 12:17 AM A O 49) (a 12/10/2020 W 26
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Transcribed Image Text:A 14.2 Test Homogeneity and Indpi x b 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 counts Chi-3quare contributions are printed below expected counts Usually Rarely Total Male 25 22 47 21.43 25.57 0.596 0.499 Female 37 52 89 48.43 40.57 0.315 0.264 Total 62 74 136 Chi-3g = 1.674, DF = 1, F-Value = 0.196 O 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, is the 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 z test lead to the same conclusion as in part (a)? Test for Two Proportions Sample Sample p Male 25 47 0.531915 Female 37 89 0.415730 Difference = p(1) - p (2) Test for difference = O (vs not = 0): z = 1.29 P-Value = 0.196 O 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 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 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. 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 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. 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 the proportions who usually eat three meals per day are the same for the two populations. Submit Answer P Type here to search 12:17 AM A O 49) (a 12/10/2020 W 26
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