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Would being part of a support group that meets regularly help people who are wearing the nicotine patch actually quit smoking? A department that deals with health matters in the county conducted an   experiment using a sample of several hundred volunteers who are planning to use the patch. The subjects were randomly
divided into two groups.
– People in Group 1 were given the patch and attended a weekly discussions meeting with
counselors and others trying to quit. People in Group 2 also used the patch but did not
participate in the counseling groups.
– After six months 46 of the 143 smokers in Group 1 and 30 of the 151 smokers in Group 2
had successfully stopped smoking.
Do these results suggest that such support groups could be an effective way to help people
stop smoking.Use the test of proprtions to address the claim. 

Take the people in group 1 to be the ones given the new treatment condition,  therefore hypotheses will be constructed as follows.

Hypotheses.

H0: p1 - p2  = 0

Ha: p1 - p2 > 0

Apply the formula for the normaly distributed data for proportions.

2.42

 

Z =  2.42

Minitab Output for this test of proportions.

Test and CI for Two Proportions

Sample   X    N  Sample p
1       46  143  0.321678
2       30  151  0.198675


Difference = p (1) - p (2)
Estimate for difference:  0.123003
95% CI for difference:  (0.0234449, 0.222561)
Test for difference = 0 (vs ≠ 0):  Z = 2.42  P-Value = 0.015

Fisher’s exact test: P-Value = 0.017


The on-sided p-value is 0.015/2  =  0.0075, which implies that the null hypothesis is rejected. There is sufficient evidence to support the claim that the treatment that has been introduced is effective. 

 

 

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