Question

Does being part of a support group affect the ability of people to quit smoking? A county health department enrolled 300 smokers in a randomized experiment. 150 participants were assigned to a group that used a nicotine patch and met weekly with a support group; the other 150 received the patch and did not meet with a support group. At the end of the study, 40 of the participants in the patch plus support group had quit smoking while only 30 smokers had quit in the other group. Answer each of the following questions under the null hypothesis that being part of a support group does not affect the ability of people to quit smoking, and think about whether the expected values are higher or lower than the observed values. a) How many subjects in the "patch + support" group would you expect to quit? b) How many subjects in the "patch only" group would you expect to not quit?

Answer 1

Under the null hypothesis, the expected number of subjects to quit smoking is similar in both the 'patch + support' and 'patch only' groups.

Step-by-step explanation:

Under the null hypothesis that being part of a support group does not affect the ability of people to quit smoking, we would expect the same proportion of participants to quit smoking in both the 'patch + support' group and the 'patch only' group. Therefore, the number of subjects in the 'patch + support' group that we would expect to quit is the same as the number in the 'patch only' group that we would expect to quit.

Since 40 participants in the 'patch + support' group actually quit smoking, we would expect a similar number of participants in the 'patch only' group to quit. Therefore, we would expect around 40 subjects in the 'patch + support' group to quit.

Similarly, since 30 participants in the 'patch only' group actually quit smoking, we would expect a similar number of participants in the 'patch + support' group to not quit. Therefore, we would expect around 30 subjects in the 'patch only' group to not quit.

Answer 2

Under the null hypothesis, we expect 20 subjects in the 'patch + support' group to quit smoking and 130 subjects in the 'patch only' group to not quit.

Step-by-step explanation:

The questions can be answered as -

a) Under the null hypothesis that being part of a support group does not affect the ability of people to quit smoking, the expected number of subjects in the 'patch + support' group who would quit can be calculated by multiplying the total number of participants in that group (150) by the rate of quitting in the entire study (40/300). So the expected number would be (150 * 40/300) = 20.

b) Under the null hypothesis, we would expect the same percentage of subjects in the 'patch only' group to quit as in the 'patch + support' group. So the expected number of subjects in the 'patch only' group who would not quit can be calculated by subtracting the expected number of subjects who would quit from the total number of participants in that group (150 - 20) = 130.