Question

If alpha is changed from 0.01 to 0.05....

a. the probability we will retain a false H0 increases
b. the probability of Type II error decreases
c. the probability of Type I error increases
d. the error probabilities stay the same
e. b and c

Answer 1

When the significance level alpha is increased from 0.01 to 0.05, the probability of Type I error increases and the probability of Type II error decreases, leading to the correct answer being e. b and c.

Step-by-step explanation:

When the significance level, denoted as alpha (α), is changed from 0.01 to 0.05, the probability of making certain types of errors in hypothesis testing changes. Specifically:

• The probability of Type I error (incorrectly rejecting a true null hypothesis) increases, because the threshold for rejecting the null hypothesis is now higher.
• The probability of Type II error (failing to reject a false null hypothesis) decreases, as there is a larger chance of rejecting the null hypothesis which may actually be false.

Therefore, the correct answer to this question is e. b and c:

• b. the probability of Type II error decreases
• c. the probability of Type I error increases