Interpreting Power Chantix (varenicline) tablets are used as...

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.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves formulating a null hypothesis, which represents the status quo or a baseline claim, and an alternative hypothesis, which represents the claim being tested against the null. In this context, the test is used to assess whether the proportion of users experiencing abdominal pain exceeds a specified level.

Significance Level (Alpha)

The significance level is the predetermined threshold for rejecting the null hypothesis, typically denoted by alpha (?). It represents the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. In the problem, a significance level of 0.05 means there is a 5% risk of incorrectly concluding that more than 8% of users experience abdominal pain.

Power of a Test

The power of a test is the probability that the test will correctly reject the null hypothesis when the alternative hypothesis is true. It reflects the test's sensitivity to detect an effect when one exists. In this scenario, having a power of 0.96 means there is a 96% chance of detecting that the true proportion of users experiencing abdominal pain is 18% rather than 8%, thereby reducing the likelihood of a Type II error.

Type II Error

A Type II error occurs when the test fails to reject the null hypothesis even though the alternative hypothesis is true. The probability of committing a Type II error is the complement of the test's power (1 - power). With a power of 0.96, the probability of a Type II error in this situation is 4%, indicating a low chance of missing a true effect.

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