=+the value of the noncentrality parameter ( 5 0 gives the central t distribution). The key result is that the variable t 5 x 2 

y1n 2 (zpercentile)1n sy

has a noncentral t distribution with df 5 n 2 1 and

 5 (2zpercentile)1n. Let t.025.v, and t.975,v, denote the critical values that capture lower tail area