The data summarized in the accompanying table is from a paper. Suppose that the data resulted from classifying each person in a random sample of 50 male students and each person in a random sample of 94 female students at a particular college according to their response to a question about whether they usually eat three meals a day or rarely eat three meals a day. Usually Eat 3 Meals a Day Rarely Eat 3 Meals a Day Male 27 23 Female 38 56 (a) Is there evidence that the proportions falling into each of the two response categories are not the same for males and females? Use the ?2 statistic to test the relevant hypotheses with a significance level of 0.05. Calculate the test statistic. (Round your answer to two decimal places.) ?2 = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? Fail to reject H0. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Reject H0. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. Reject H0. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Fail to reject H0. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. (b) Are the 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 counts Usually Rarely Total Male 27 23 50 22.57 27.43 0.870 0.716 Female 38 56 94 42.43 51.57 0.463 0.381 Total 65 79 144 Chi-Sq = 2.43, DF = 1, P-Value = 0.1191 YesNo (c) Because the response variable in this exercise has only two categories (usually and rarely), we could have also answered the question posed in part (a) by carrying out a two-sample z test of H0: 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 two-sample z test is shown below. Using a significance level of 0.05, does the two-sample z test lead to the same conclusion as in part (a)? Test for Two Proportions Sample X N Sample p Male 27 50 0.540000 Female 38 94 0.404255 Difference = p(1) − p(2) Test for difference = 0 (vs not = 0): Z = 1.56 P-Value = 0.1191 YesNo

The data summarized in the accompanying table is from a paper. Suppose that the data resulted from classifying each person in a random sample of 50 male students and each person in a random sample of 94 female students at a particular college according to their response to a question about whether they usually eat three meals a day or rarely eat three meals a day. Usually Eat 3 Meals a Day Rarely Eat 3 Meals a Day Male 27 23 Female 38 56 (a) Is there evidence that the proportions falling into each of the two response categories are not the same for males and females? Use the ?2 statistic to test the relevant hypotheses with a significance level of 0.05. Calculate the test statistic. (Round your answer to two decimal places.) ?2 = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? Fail to reject H0. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Reject H0. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. Reject H0. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Fail to reject H0. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. (b) Are the 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 counts Usually Rarely Total Male 27 23 50 22.57 27.43 0.870 0.716 Female 38 56 94 42.43 51.57 0.463 0.381 Total 65 79 144 Chi-Sq = 2.43, DF = 1, P-Value = 0.1191 YesNo (c) Because the response variable in this exercise has only two categories (usually and rarely), we could have also answered the question posed in part (a) by carrying out a two-sample z test of H0: 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 two-sample z test is shown below. Using a significance level of 0.05, does the two-sample z test lead to the same conclusion as in part (a)? Test for Two Proportions Sample X N Sample p Male 27 50 0.540000 Female 38 94 0.404255 Difference = p(1) − p(2) Test for difference = 0 (vs not = 0): Z = 1.56 P-Value = 0.1191 YesNo

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

	Usually Eat 3 Meals a Day	Rarely Eat 3 Meals a Day
Male	27	23
Female	38	56

(a)

Is there evidence that the proportions falling into each of the two response categories are not the same for males and females? Use the

?²

statistic to test the relevant hypotheses with a significance level of 0.05.

Calculate the test statistic. (Round your answer to two decimal places.)

?² =

Use technology to calculate the P-value. (Round your answer to four decimal places.)

P-value =

What can you conclude?

Fail to reject H₀. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Reject H₀. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females. Reject H₀. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females.Fail to reject H₀. There is not convincing evidence that the proportions falling into the two response categories are not the same for males and females.

(b)

Are the 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 counts
	Usually	Rarely	Total
Male	27	23	50
	22.57	27.43
	0.870	0.716
Female	38	56	94
	42.43	51.57
	0.463	0.381
Total	65	79	144
Chi-Sq = 2.43, DF = 1, P-Value = 0.1191

YesNo

(c)

Because the response variable in this exercise has only two categories (usually and rarely), we could have also answered the question posed in part (a) by carrying out a two-sample z test of

H₀: p₁ − p₂ = 0

versus

H_a: 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 two-sample z test is shown below. Using a significance level of 0.05, does the two-sample z test lead to the same conclusion as in part (a)?

Test for Two Proportions

Sample	X	N	Sample p
Male	27	50	0.540000
Female	38	94	0.404255
Difference = p(1) − p(2)
Test for difference = 0 (vs not = 0): Z = 1.56
P-Value = 0.1191

YesNo

(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-squared 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 equal when rounded to three decimal places. It is surprising that the P-values are at least similar, since the P-value from the chi-squared 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 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.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.

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