In the context of hypothesis testing, what does the $\mathrm{level of significance}$ represent?

• A. The probability of making a $\mathrm{Type II error}$
• B. The probability of rejecting the $\mathrm{null hypothesis}$ when it is actually true
• C. The probability that the $\mathrm{sample mean}$ equals the $\mathrm{population mean}$
• D. The probability of accepting the $\mathrm{alternative hypothesis}$ when it is false

Answer: (B)

Verified step by step guidance

1. Understand that the level of significance, often denoted by \(\alpha\), is a threshold set by the researcher before conducting a hypothesis test.
2. Recognize that the level of significance represents the probability of making a Type I error, which occurs when the null hypothesis is rejected even though it is actually true.
3. Recall that a Type I error means falsely concluding there is an effect or difference when there isn't one, so \(\alpha\) quantifies how willing we are to risk this error.
4. Note that the level of significance is not related to the probability of a Type II error (which is failing to reject a false null hypothesis), nor does it represent probabilities about the sample mean equaling the population mean.
5. Summarize that the level of significance is the probability of rejecting the null hypothesis when it is actually true, guiding the decision rule for hypothesis testing.