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.

Option B is correct.

The term 'significantly higher' mean that: 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.

Step-by-step explanation:

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

For this question, we want to verify that "quit smoking" rates are significantly higher for smokers taking bupropion compared to smokers using nicotine patches.

So, the null hypothesis would be that the two rates aren't significantly different.

Alternative hypothesis would be that the two rates are significantly different.

If the 'quit smoking' rate for smokers taking bupropion is p₁

And the 'quit smoking' rate for smokers using nicotine patches. is p₂

And the difference between them is μ₀

μ₀ = p₁ - p₂

Mathematically,

Null Hypothesis is

H₀: p₁ = p₂

Or

H₀: μ₀ = 0

Alternative hypothesis

H₀: p₁ ≠ p₂

Or

H₀: μ₀ ≠ 0

And the quantity that helps to make the right conclusion as to which hypothesis is the correct one is the p-value.

The p-value is defined as the probability of obtaining results as extreme as the observed results in the statistical analysis provided that the null hypothesis is true.

On occasions when the p-value is lower than the significance level at which the test was performed, it means results as extreme as that stated in the alternative hypothesis are true and the conclusion is that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in the statement of the alternative hypothesis.

So, a conclusion arrived at with p-value less than the significance level like in this problem, it means that the the very less likely result/the extreme result/the result that shouldn't happen if random chance was in play, has happened.

For this question, thay extreme result that random chance wouldn't be able to explain is that the difference observed in the success rates from the two treatment groups is larger, way larger than if random chance was in control of the result. Random chance would have resulted in the treatments having the same success rates.

So, option B is correct.

Hope this Helps!!!