Question

1.Quit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment. In this experiment researchers randomly assigned smokers to treatments.

We conducted a hypothesis test to determine if the side effect rates are significantly different for nicotine patches versus bupropion at a 5% level of significance. (The normality conditions are met by the data.) The P-value is 0.04.

What does a P-value of 0.04 mean?

a.There is a 4% chance there is no difference in side effect rates for these two treatments.

b.If the side effect rates are the same for the two treatments, there is a 4% chance that future experiments will show differences in side effect rates greater than observed in this experiment.

c.If the side effect rates are the same for the two treatments, there is a 4% that the rates will be different in future experiments.

d.If the side effect rates are different for the two treatments, there is a 4% chance that future experiments will show the same differences in side effect rates observed in this experiment.

2.Quit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment. In this experiment researchers randomly assigned smokers to treatments.

Of the 244 smokers taking the antidepressant bupropion, 74 stopped smoking by the 8th day. Of the 244 smokers using the nicotine patches, 40 stopped smoking by the 8th day. A hypothesis test supports the conclusion that “quit smoking” rates are significantly higher for smokers taking bupropion compared to smokers using nicotine patches. (P-value=0.0001)

In statistics what does the phrase “significantly higher” mean?

a.In this experiment the difference observed in the success rates from the two treatment groups is large. One treatment had a much higher success rate than the other.

b.In this experiment the difference observed in the success rates from the two treatment groups is larger than we expect in random sampling if the treatments had the same success rates.

c.In this experiment the difference observed in the success rates from the two treatment groups is larger than we expect in random sampling if neither treatment is effective.

3. In 2013, psychology researchers conducted an experiment featuring 40 undergraduate college students, each of whom took a 20-question general-knowledge test on a computer. Participants were given four possible answers and instructed to pick the correct one. Before doing so, half the students were told that just before each question was asked, the correct answer was momentarily flashed onto the screen. They were informed that this happened too quickly for them to process the information consciously, but assured that it would register in their brains. This was the placebo treatment. In the control treatment participants were not told this.

The researchers write that: “Participants in the placebo condition who believed they had been exposed to the correct answers subliminally scored higher than participants in the control condition.”

The researchers conducted a hypothesis test to determine if the proportion of correct answers is significantly different for participants in the placebo condition and participants in the control condition (placebo proportion minus control proportion). The P-value is 0.02. What can the researchers conclude?

A.Researchers reject the null hypothesis. The proportion of correct answers for participants in the placebo condition is no different than the proportion of correct answers for participants in the control group.

B.Researchers reject the null hypothesis. The proportion of correct answers is significantly different for the placebo condition and the control group.

C.Researchers reject the null hypothesis. The proportion of correct answers for participants in the placebo condition is significantly higher than the proportion of correct answers for participants in the control group.

D.Researchers fail to reject the null hypothesis. The proportion of correct answers is different, but not significantly different.

4. Quit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment. In this experiment researchers randomly assigned smokers to treatments.

A hypothesis test supports the conclusion that “quit smoking” rates are significantly higher for smokers taking bupropion compared to smokers using nicotine patches. (P-value=0.0001)

We have seen that statistically significant differences can sometimes be too small to make a practical difference in decision-making. The 95% confidence interval to estimate the difference in “quit smoking” rates for these two treatments is (0.065, 0.213). What course of action is best supported by the confidence interval?

A.Doctors should recommend buproprion over nicotine patches. Why? We are 95% confident that buproprion has a 6.5% success rate compared to a 21.3% success rate for the nicotine patches.

B.Doctors should recommend buproprion over nicotine patches. Why? We are 95% confident that buproprion has anywhere between a 6.5% and a 21.3% higher success rate than nicotine patches.

C.Doctors should not recommend buproprion over nicotine patches. Why? We are 95% confident that the difference is somewhere between 0.065% and 0.213%. This is less than 1% which may be statistically significant, but it is not large enough to affect a doctor’s recommendations for treatment.

D.Doctors should not recommend buproprion over nicotine patches. Why? We are 95% confident that the difference is not statistically significant.

Answer 1

1) If the side effect rates are different for the two treatments, there is a 4% chance that future experiments will show the same differences in side effect rates observed in this experiment.

Option- (d)

2) In this experiment the difference observed in the success rates from the two treatment groups is large. One treatment had a much higher success rate than the other.

Option- (a)

3) Researchers reject the null hypothesis. The proportion of correct answers is significantly different for the placebo condition and the control group.

Option- (B)

4) Doctors should not recommend buproprion over nicotine patches. Why? We are 95% confident that the difference is somewhere between 0.065% and 0.213%. This is less than 1% which may be statistically significant, but it is not large enough to affect a doctor’s recommendations for treatment.

Option- (C)