Final answer:
When the significance level alpha decreases from 0.05 to 0.01, the probability of Type I error decreases. The probability of Type II error remains the same.
Step-by-step explanation:
When the significance level alpha decreases from 0.05 to 0.01, the probability of Type I error decreases. Type I error, also known as a false positive, occurs when we reject the null hypothesis when it is actually true. By reducing alpha, we are making it less likely to mistakenly reject the null hypothesis.
Therefore, option b. the probability of Type I error increases is incorrect.
Option a. the probability of Type II error decreases is also incorrect. Type II error, also known as a false negative, occurs when we fail to reject the null hypothesis when it is actually false. Changing alpha does not directly affect the probability of Type II error.
So, the correct answer is option c. the error probabilities stay the same. Changing alpha does not impact the probability of Type II error.