Question

A study conducted at a major university indicates that the tendency among undergraduates to seek the assistance of helper differs by ethnic group. You select 25 subjects each from two different ethnic groups or business majors and count the number who sought help. In ethic group A, 11 sought out helpers at some point. In ethnic group B, 17.

1. What are the frequency expected values for each group?
2. Do results support the earlier study?
3. What does the alternate hypothesis suggest about the relationship between ethnicity and help-seeking?

Answer 1

following tabulated information is generated from the given data

		Ethnicity
		group A	group B	total
help-seeking	Yes	11	17	28
	No	14	8	22
total		25	25	50

(a) E(11)=28*25/50=14 and E(17)=28*25/50=14

(b) Yes, results support the earlier study of  tendency among undergraduates to seek the assistance of helper differs by ethnic group. as observed frequency differs .

(c) here we use chi-square test

with null hypothesis H0:  there is no relationship between ethnicity and help-seeking

alternate hypothesis Ha:  there is relationship between ethnicity and help-seeking

and chi-square=sum((O-E)²/E)=2.9211 with (r-1)(c-1)=(2-1)(2-1)=1 df

and typical critical chi-square(0.05,1)=3.84 is more than observed chi-square=2.9211, so we fail to reject the null hypothesis and conclude that  there is relationship between ethnicity and help-seeking at 5% level of significance.

	observed(O)	Expected(E)	(O-E)	(O-E)2/E
	11	28*25/50=14	-3	0.6429
	17	28*25/50=14	3	0.6429
	14	22*25/50=11	3	0.8182
	8	22*25/50=11	-3	0.8182
sum=	50	50	0	2.9221