In hypothesis testing, what does the alpha value represent?

• A. The probability of failing to reject the null when it is false.
• B. The observed significance level of the test.
• C. The probability of rejecting the null hypothesis when the null hypothesis is true.
• D. The power of the test

Answer: (C)

Alpha is the pre-specified significance level that represents the chance of making a Type I error—rejecting the null hypothesis when it is actually true. It’s set before collecting data, commonly at 0.05, which means you’re willing to accept up to a 5% risk of a false positive. This threshold defines the rejection region for the test statistic: if the observed data yield a p-value at or below alpha, you reject the null. It’s not the probability of rejecting when the null is false (that’s the test’s power), and it’s not the observed p-value itself. Lowering alpha lowers the risk of false positives but can reduce power; increasing alpha raises power but increases the chance of a false-positive conclusion.