Question

Questions: 1/Suppose that the data resulted from classifying each person in a random sample of 48 male students and each person in a random sample of 91 female students at a particular college. Rarely eat 3 meals a day Usually eat 3 meals a day 16 Male 32 65 Female 26 Is there any evidence that the proportions falling into each of the 2 categories are not the same for males or females? Test the relevant hypotheses with a = 0.05.

Answer 1

1)

Claim: The proportions fallings into each of the 2 categories are not the same for males and females.

The null and alternative hypothesis is

H0: The proportions fallings into each of the 2 categories are not the same for males and females.

H1: The proportions fallings into each of the 2 categories are the same for males and females.

Level of significance = 0.05

Test statistic is

$\chi ^{2}=\sum \frac{(O-E)^{2}}{E}$

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	Usually	Rarely	Total
Male	32	16	48
Female	26	65	91
Total	58	81	139

O	E	(O-E)	(O-E)^2	(O-E)^2/E
32	20.02878	11.97122	143.3102	7.155214
16	27.97122	-11.9712	143.3102	5.123486
26	37.97122	-11.9712	143.3102	3.774179
65	53.02878	11.97122	143.3102	2.702498
			Total	18.755

$\chi ^{2}=\sum \frac{(O-E)^{2}}{E}=18.755$

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (2 - 1) = 1 * 1 = 1

Critical value = 3.841

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

The proportions fallings into each of the 2 categories are the same for males and females.

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