5. Incorrect. The answer is true.

Let , , and v=n-1. Then since X_j are normally distributed with mean m and variance s² we know that `X is normally distributed with mean m and variance s²/n, so that Y is normally distributed with mean 0 and variance 1. Also, from Theorem 5-6, page 161, Z is chi-square distributed with v=n-1 degrees of freedom.

It follows from Theorem 4-6, page 117, that

has the t distribution with n-1 degrees of freedom.