Elementary Statistics and Computer Application

Test for equality of two Means ( Independent Samples)

 
• Given two sets of sample observation x11,x12,x13…x1n , and x21,x22,x23…x2n of sizes n1 and n2 respectively from the normal population.
• 1.Using F-Test , test their variances
• (i)Variances are Equal
• Ho:., µ1=µ2
• H1 µ1≠µ2 (or µ1<µ2 or µ1>µ2)

Test statistic

where the combined variance

The test statistic t follows a t distribution with (n1+n2-2) d.f.


(ii)Variances are unequal and n1=n2

It follows a t distribution with


(i)Variances are unequal and n1≠n2

• This statistic follows neither t nor normal distribution but it follows Behrens-Fisher d distribution. The Behrens – Fisher test is laborious one. An alternative simple method has been suggested by Cochran & Cox. In this method the critical value of t is altered as tw (i.e) weighted

• where t1is the critical value for t with (n1-1) d.f. at a dspecified level of significance and
• t2 is the critical value for t with (n2-1) d.f. at a dspecified level of significance and