Q. 5.2 - The Practice of Statistics for AP

Question

Sample surveys on sensitive issues can give different results depending on how the question is asked. A University of Wisconsin study randomly divided 2400 respondents into three groups. All participants were asked if they had ever used cocaine. One group of 800 was interviewed by phone; 21% said they had used cocaine. Another 800 people were asked the question in a one-on-one personal interview; 25% said “Yes.” The remaining 800 were allowed to make an anonymous written response; 28% said “Yes.”

2. Make a two-way table of responses about cocaine use by how the survey was administered 

Step-by-Step Solution

Answer

The two way table is :

Category	Yes	No
Direct	0.21	0.79
One on one	0.25	0.75
Anonymous	0.28	0.72

Given information

In a study, 2400 respondents into three groups. All participants were asked if they had ever used cocaine. One group of 800 was interviewed by phone; 21% said they had used cocaine. Another 800 people were asked the question in a one-on-one personal interview; 25% said “Yes.” The remaining 800 were allowed to make an anonymous written response; 28% said “Yes.”

Solution

We need to test the hypothesis that:

$H_0:p_1=p_2=p_3$

Against the alternative

$H_0:p_1\ne p_2\ne p_3$

where $p_i$ is the proportion of people who take consume cocain in $i^{th}$ process.

The following is a two-way table for cocain consumers obtained using different methods :

 

Category	Yes	No
Direct	0.21	0.79
One on one	0.25	0.75
Anonymous	0.28	0.72