Question

Sample surveys on sensitive issues can give different results depending on how the question is asked. A University of Wisconsin study divided 2400 respondents into 3 groups at random. All were asked if they had ever used cocaine. One group of 800 was interviewed by phone; 158 said they had used cocaine. Another 800 people were asked the question in a one-on-one personal interview; 199 said "Yes." The remaining 800 were allowed to make an anonymous written response; 233 said "Yes."

Are there statistically significant differences among these proportions?

Carry out a chi-square test for association. Test H0:H0: the proportion of people who admit cocaine use is the same for all three interview methods versus Ha:Ha: the proportions are not the same (interview type makes a difference). Use α=0.01α=0.01.

χ2(±0.0001)=χ2(±0.0001)=

P(±0.0001)=P(±0.0001)=0.0001

There is no evidence that interview type makes a difference

There is evidence that interview type makes a difference

Answer 1

Applying chi square test of homogeneity

Expected	Ei=row total*column total/grand total	1st group	2nd group	3rd group	Total
	used	196.67	196.67	196.67	590
	not used	603.33	603.33	603.33	1810
	total	800	800	800	2400
chi square    χ2	=(Oi-Ei)2/Ei	1st group	2nd group	3rd group	Total
	used	7.602	0.028	6.712	14.3424
	not used	2.478	0.009	2.188	4.6751
	total	10.0803	0.0367	8.9005	19.0175
test statistic X2=		19.0175
p value =	0.0001	from excel: chidist(19.0175,2)

since p value <0.01

There is evidence that interview type makes a difference