A researcher tested the idea that being part of a support group that meets regul

Question

A researcher tested the idea that being part of a support group that meets regularly would help people who are wearing the nicotine patch quit smoking. He split smokers randomly into two groups. Group 1 were given the patch and attended a weekly support group meeting. Group 2 were given the patch but did not attend the meeting. He wants to test if the proportion of those who quit smoking in Group 1 is higher than the proportion of those who quit smoking in group 2. Set up the hypothesis for this test.

After Crunching the numbers the researcher found a z-score of 2.42. With this, find the p-value and determine if he can determine if he can make his claim at a 95% level of significance.

Explanation / Answer

Solution:-

As given that the researcher wants to test if the proportion of those who quit smoking in Group 1 is higher than the proportion of those who quit smoking in group 2.

Null hypothesis: P1 >= P2
Alternative hypothesis: P1 < P2

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the proportion of those who quit smoking in Group 1 (p1) is sufficiently smaller than the proportion of those who quit smoking in group 2 (p2).

Since we have a one-tailed test, the P-value is the probability that the z-score is less than 2.42.

We use the Normal Distribution Calculator to find P(z < 2.42) = 0.00776.

Thus, the P-value = 0.00776.

Interpret results. Since the P-value (0.00776) is smaller than the significance level (0.05), we can reject the null hypothesis. Thus, accepting the alternate hypothesis which states that proportion of those who quit smoking in Group 1 (p1) is sufficiently smaller than the proportion of those who quit smoking in group 2 (p2).

Conclusion. From the above test it is proved that being part of a support group that meets regularly would help people who are wearing the nicotine patch quit smoking.

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