The use of t, whenx(bar)is estimated is based on the underlying

assumption of a normally distributed variable when sigma is known; ifx

isN(mui,sigma^2)thenis

x - mui/sigmaN(0; 1). It follows that ifs^2is an estimate for

sigma^2, then

x - mui/sigma

istdistributed with some degree of freedomv. What

can you say aboutsasvtends to infnity? What is the distribution

of

x - mui/sigma

asvtends to infnity?