## probaility type 1 error

Suppose that 100 students each draw a sample from a normal distribution
with unknown population mean μ and and population variance σ2. Each student then
uses Student’s 1-sample t-test to test H0 : μ = 0 versus H0 : μ 6= 0 at significance level
α = 0.05. Unbeknownst to the students, the null hypothesis is correct, i.e., it actually
is the case that μ = 0. What is the probability that at least two students will commit
Type I errors?