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.

검증된 단계별 안내

Step 1: Understand the concept of 'power of a test'. The power of a statistical test is the probability that the test correctly rejects the null hypothesis (H₀) when the alternative hypothesis (H₁) is true. It is calculated as 1 - β, where β is the probability of a Type II error (failing to reject H₀ when H₁ is true).

Step 2: Identify the context of the problem. In this case, the null hypothesis (H₀) is that the proportion of Chantix users experiencing abdominal pain is 8% (p = 0.08). The alternative hypothesis (H₁) is that the proportion is greater than 8% (p > 0.08).

Step 3: Recognize the significance of the power value provided. A power of 0.96 means that there is a 96% probability of correctly rejecting the null hypothesis (H₀) when the true proportion of Chantix users experiencing abdominal pain is 18% (p = 0.18).

Step 4: Interpret the practical implication. A high power (0.96) indicates that the test is very effective at detecting a true difference (i.e., when the true proportion is 18%, the test will almost always reject the null hypothesis that the proportion is 8%).

Step 5: Conclude the interpretation. The power of 0.96 suggests that the test is highly reliable in identifying that the proportion of Chantix users experiencing abdominal pain is greater than 8% if the true proportion is indeed 18%.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0. In this context, the null hypothesis would state that 8% or fewer Chantix users experience abdominal pain, while the alternative suggests that the proportion is greater than 8%.

Power of a Test

The power of a test is the probability that it correctly rejects the null hypothesis when the alternative hypothesis is true. It is calculated as 1 minus the probability of a Type II error (failing to reject H0 when H1 is true). A power of 0.96 indicates a very high likelihood of detecting a true effect (in this case, that more than 8% of users experience abdominal pain) if it exists.

Significance Level

The significance level, denoted as alpha (α), is the threshold for determining whether to reject the null hypothesis. In this scenario, a significance level of 0.05 means there is a 5% risk of concluding that a difference exists when there is none (Type I error). It sets the standard for how strong the evidence must be to support the claim that more than 8% of users experience abdominal pain.