Q. 37 - The Practice of Statistics for AP

Question

How to quit smoking It’s hard for smokers to quit. Perhaps prescribing a drug to fight depression will work as well as the usual nicotine patch. Perhaps combining the patch and the drug will work better than either treatment alone. Here are data from a randomized, double-blind trial that compared four treatments. A “success” means that the subject did not smoke for a year following the beginning of the study. 

Group Treatment           Subjects  Successes 

1          Nicotine patch     244          40 

2         Drug                     244          74 

3         Patch plus drug   245          87 

4         Placebo                160          25

(a) Summarize these data in a two-way table. 

(b) Make a graph to compare the success rates for the four treatments. Describe what you see.

(c) Explain in words what the null hypothesis H0: p1 = p2 = p3 = p4 says about subjects’ smoking habits. 

(d) Find the expected counts if H0 is true, and display them in a two-way table similar to the table of observed counts. 

Step-by-Step Solution

Answer

(a) The summary of the data is :

Group	Success	Failure	Subjects
1	40	204	244
2	74	170	244
3	87	158	245
4	25	135	160
Total	226	667	893

(b)  

(c) In words we can say that the null hypothesis asserts that all the groups have same proportions of smokers.

(d) 

Group	Success	Failure
1	61.7514	182.2486
2	61.7514	182.2486
3	62.00448	182.9955
4	40.49272	119.5073

Given :

The table,

Group  Treatment           Subjects  Successes 

1           Nicotine patch     244          40 

2          Drug                     244          74 

3          Patch plus drug   245          87 

4          Placebo                160          25

Part(a) :

The summary of the data in two way table is as follows:

Group	Success	Failure	Subjects
1	40	204	244
2	74	170	244
3	87	158	245
4	25	135	160
Total	226	667	893

Part(b) :

The graph compairing the success rate of different groups are as follows

Part(c) :

In words we can say that the null hypothesis asserts that all the groups have same proportions of smokers.

Step(d) :

The expected count is as follows:

Group	Success	Failure
1	61.7514	182.2486
2	61.7514	182.2486
3	62.00448	182.9955
4	40.49272	119.5073