When the sample size is large, some people treat the sample standard deviation s as if it were the population standard deviation σ, and use the standard normal distribution rather than the Student’s t distribution, to find a critical value. Assume that a right-tailed test will be made with a sample of size 100 from a normal population, using the α = 0.05 significance level.

a. Find the critical value under the assumption that σ is known.

b. In fact, σ is unknown. How many degrees of freedom should be used for the Student’s t distribution?

c. What is the probability of rejecting H0 when it is true if the critical value in part (a) is used? You will need technology to find the answer.