Question

When the probability of Type I error (\(\alpha\)) is 0.05 and the maximum acceptable probability of Type II error (\(\beta\)) is 0.20, the researcher is willing to accept that Type I error is ........ (answer in integer) times more serious than a Type II error.

Hint:

Type I error represents a false positive (rejecting a true null hypothesis), and Type II error represents a false negative (failing to reject a false null hypothesis). Understanding the trade-off between these errors is crucial in statistical hypothesis testing.

Answer 1

In this case, the researcher is willing to accept that the Type I error is 4 times more serious than the Type II error. This is calculated by dividing the probability of Type II error (\(\beta = 0.20\)) by the probability of Type I error (\(\alpha = 0.05\)): \[ \frac{\alpha}{\beta} = \frac{0.05}{0.20} = 4 \] Thus, the researcher considers a Type I error to be 4 times more serious than a Type II error. Therefore, the correct answer is: \[ \boxed{4} \]