For testing the null hypothesis that X1,...,Xn are i.i.d. from a normal distribution with unknown mean µ and unknown variance σ2, show that the null distribution of (14.13) does not depend on (µ, σ) (but it does depend on n). Describe a simulation method to approximate this null distribution. How can you construct a test that is exact level α = 0.05 based on simulation? Generalize this problem to testing a general location-scale family.