Question

Interpreting Power Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.

Short answer

When the true proportion of Chantix users who suffer from abdominal pain is equal to 0.18, there is a 96% chance of making the right conclusion about supporting the claim that the proportion of Chantix users who suffer from abdominal pain is more than 8%.

Step-by-step solution

 Given information 

It is claimed that more than 8% of Chantix tablet users experience abdominal pain. The claim is supported at a 0.05 level of significance.

The alternative value of p=0.18 and the power of the test is equal to 0.96.

 Hypotheses 

The following hypotheses are noted for the given claim:

Null hypothesis: The proportion of Chantix users who experience abdominal pain is equal to 0.08.

That is, $H_0:p=0.08$.

Alternative hypothesis: The proportion of Chantix users who experience abdominal pain is more than 0.08.

That is, $H_A:p>0.08$.

It is mentioned that the claim of more than 8% or a proportion of 0.08 of Chantix users who suffered from abdominal pain is supported at a 5% level of significance. Thus, the null hypothesis is false here.

Power of the test

The value of the power of the test gives the probability value of rejecting a false null hypothesis. It stands for making the right conclusion of rejecting the null hypothesis that is not true.

An alternate value of the proportion is equal to 0.18. Also, the null hypothesis is false.

The power of the test has a value equal to 0.96.

This means that there is a 96% chance of rejecting the false null hypothesis that the proportion of Chantix tablet users who suffer from abdominal pain is equal to 0.08, but the actual proportion is equal to 0.18.

That is, when the true proportion of Chantix users who experience abdominal pain is equal to 0.18, there is a 96% chance of making the correct conclusion that the proportion of Chantix users who suffer from abdominal pain is more than 0.08.