consider the case of two iid samples. X..... X and Y..... Ya. with common variance o...

 

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consider the case of two iid samples. X..... X and Y..... Ya. with common variance o and under a null hypothesis they have a common mean, say . Then the two-sample pooled / statistic is where X-Y (+1) (m-1)s+ (n-1)s m+n-2 and = ---- It can be shown that p 1=1 N(0, 1) as min(m, n) . However, the proof is fairly tricky. Instead it is common to assume that both sample sizes go to oo at a similar rate, i.e., Amn = m/(m + n) > 0 as min(m, n) c. Under this assumption prove that tp d N(0, 1). Hint: show that tp = { (x-1) semnn ( H)}/sp. consider the case of two iid samples. X..... X and Y..... Ya. with common variance o and under a null hypothesis they have a common mean, say . Then the two-sample pooled / statistic is where X-Y (+1) (m-1)s+ (n-1)s m+n-2 and = ---- It can be shown that p 1=1 N(0, 1) as min(m, n) . However, the proof is fairly tricky. Instead it is common to assume that both sample sizes go to oo at a similar rate, i.e., Amn = m/(m + n) > 0 as min(m, n) c. Under this assumption prove that tp d N(0, 1). Hint: show that tp = { (x-1) semnn ( H)}/sp.