Which statement best defines a Type I error in hypothesis testing?

Which statement best defines a Type I error in hypothesis testing?

• A. The probability of failing to reject a true null hypothesis.
• B. The probability of rejecting a true null hypothesis.
• C. The probability of failing to reject a false null hypothesis.
• D. The probability of observing the data under the null hypothesis.

Answer: (B)

Type I error is the false positive in hypothesis testing: it happens when you reject the null hypothesis even though it is true. In other words, you conclude there is an effect when there really isn’t one. That’s why the statement describing this error is “rejecting a true null hypothesis.” To connect the others: failing to reject a true null is a correct decision, not an error. failing to reject a false null is a Type II error (false negative). and observing data under the null hypothesis describes the sampling distribution under H0 rather than an error type. The probability of making a Type I error is controlled by the significance level, alpha.

Type I error is the false positive in hypothesis testing: it happens when you reject the null hypothesis even though it is true. In other words, you conclude there is an effect when there really isn’t one. That’s why the statement describing this error is “rejecting a true null hypothesis.”

To connect the others: failing to reject a true null is a correct decision, not an error. failing to reject a false null is a Type II error (false negative). and observing data under the null hypothesis describes the sampling distribution under H0 rather than an error type. The probability of making a Type I error is controlled by the significance level, alpha.