A local college recently made the news by offering foreign language-speaking dorms to its students. At another school, 50 randomly selected students from each class were asked if they favored foreign language-speaking dorms. The results are shown below. At αα =0.10, is there sufficient evidence to conclude that the proportions of students favoring foreign language-speaking dorms are not the same? Freshmen Sophmores Juniors Seniors Yes (favor) 6 11 22 20 No 44 39 28 30 What are the expected numbers? (round to 3 decimal places) Freshmen Sophmores Juniors Seniors Yes (favor) No The hypotheses are H0:p1=p2=p3=p4H0:p1=p2=p3=p4 HA:HA: At least one of the proportions is different. (claim) Since αα = 0.10 the critical value is 6.251 The test value is: (round to 3 decimal places) The p-value is (round to 3 decimal places) So the decision is to reject H0H0 do not reject H0H0 Thus the final conclusion is There is not enough evidence to support the claim that at least one of the proportions is different. There is enough evidence to reject the claim that at least one of the proportions is different. There is enough evidence to support the claim that at least one of the proportions is different. There is not enough evidence to reject the claim that at least one of the proportions is different.

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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A local college recently made the news by offering foreign language-speaking dorms to its students. At another school, 50 randomly selected students from each class were asked if they favored foreign language-speaking dorms. The results are shown below. At αα =0.10, is there sufficient evidence to conclude that the proportions of students favoring foreign language-speaking dorms are not the same?

	Freshmen	Sophmores	Juniors	Seniors
Yes (favor)	6	11	22	20
No	44	39	28	30

What are the expected numbers? (round to 3 decimal places)

	Freshmen	Sophmores	Juniors	Seniors
Yes (favor)
No

The hypotheses are

H0:p1=p2=p3=p4H0:p1=p2=p3=p4

HA:HA: At least one of the proportions is different. (claim)

Since αα = 0.10 the critical value is 6.251

The test value is: (round to 3 decimal places)

The p-value is (round to 3 decimal places)

So the decision is to

reject H0H0
do not reject H0H0

Thus the final conclusion is

There is not enough evidence to support the claim that at least one of the proportions is different.
There is enough evidence to reject the claim that at least one of the proportions is different.
There is enough evidence to support the claim that at least one of the proportions is different.
There is not enough evidence to reject the claim that at least one of the proportions is different.

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