Question

The significance level is 5%. the p-value was 0.014. what is the probability of a type i error for this hypothesis test (assuming that the null hypothesis is true)?

A. 0.05
B. 0.014
C. it is impossible to tell from the information given.

Answer 1

The correct answer is option A. The probability of making a Type I error in a hypothesis test, given a significance level of 5% (0.05) and a p-value of 0.014, remains at the predetermined significance level, which is 5% or 0.05.

Step-by-step explanation:

The question asks about the interpretation of statistical hypothesis testing results, particularly in relation to Type I error and p-values. Given a significance level (alpha) of 5% (0.05) and a p-value of 0.014, we want to determine the probability of making a Type I error. A Type I error occurs when the null hypothesis is true, but is incorrectly rejected. The significance level itself represents the probability of a Type I error if the null hypothesis is true. Therefore, regardless of the p-value, if we decide to reject the null hypothesis when the p-value is less than the significance level, the probability of committing a Type I error is the significance level.

Since the p-value (0.014) is indeed less than the significance level (0.05), we would typically reject the null hypothesis. However, the probability of making a Type I error is still determined by the predefined significance level, not the p-value. In this case, the correct answer is A. 0.05, which is the given significance level and the maximum risk of making a Type I error we are willing to accept to reject the null hypothesis.