Sample surveys on sensitive issues can give different results depending on how t

Question

Sample surveys on sensitive issues can give different results depending on how the question is asked. A University of Wisconsin study divided 2700 respondents into three groups at random. All were asked if they had ever used cocaine. One group of 900 was interviewed by phone; 18% said they had used cocaine. Another 900 people were asked the question in a one-on-one personal interview; 24% said "Yes." The remaining 900 were allowed to make an anonymous written response; 26% said "Yes." Are there statistically significant differences among these proportions? State the hypotheses, convert the information given into a two-way table of counts, give the test statistic and its P-value, and state your conclusions. (Round your test statistic and P-value to three decimal places.)

H0:

All proportions are equal.

All proportions are different.    

Some proportions are different.

Ha:

All proportions are equal.

Some proportions are different.    

All proportions are different.

No

Yes

Phone

One-on-one

Anonymous

2

=

P-value

=

Conclusion

Reject H0. There is no evidence of differing proportions.

Fail to reject H0. There are statistically significant differences among these proportions.    

Fail to reject H0. There is no evidence of differing proportions.

Reject H0. There are statistically significant differences among these proportions.

No

Yes

Phone

One-on-one

Anonymous

Explanation / Answer

Ans:

H0:All proportions are equal.

Ha:Some proportions are different.   

df=(3-1)*(2-1)=2

p-value=CHIDIST(17.799,2)=0.000

As,p-value<0.0001,we reject null hypothesis.

Reject H0. There are statistically significant differences among these proportions.

Observed(O) Yes No Total Phone 162 738 900 one on one 216 684 900 anonymous 234 666 900 Total 612 2088 2700 Expected(O) Yes No Total Phone 204 696 900 one on one 204 696 900 anonymous 204 696 900 Total 612 2088 2700 (O-E)^2/E Yes No Phone 8.647 2.534 one on one 0.706 0.207 anonymous 4.412 1.293 Chi square test statistic=17.799

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