Let X1,X2,X3,...Xn be random variables with Xi∼N(μ,σ²) and define the usual sample mean (i.e. X =1/n∑i= Xi). We know that if
Z=X−μσ/n then Z∼N(0,1). If we now define
W=X−μS/n where S comes from the usual estimator of σ, i.e. S²=1/n−1 ∑i=(X1−X)² then what distribution does W follow?
a. N(0,1.6)
b. tn−1 (i.e. a t-distribution with n−1 degrees of freedom)
c. N(0,1)
d. tn (i.e. a t-distribution with n degrees of freedom)
