**5. Correct. The
answer is true**

Let _{}, _{},
and v=n-1. Then since X_{j} are normally
distributed with mean m and variance s^{2} we know that `X is
normally distributed with mean m and variance s^{2}/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.