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Independent Samples t-test


General Notes
 
Hypotheses:    H0:  mu2 - mu1 = delta     Ha:  mu2 - mu1 <> delta    (two-sided hypothesis)
                      Ha:  mu2 - mu1 > delta   or   Ha:  mu2 - mu1 < delta  (one-sided alternatives)
                      If delta = 0, then H0: mu1 = mu2
Test statistic:   t statistic 
P-value:           the one- or two-tailed probability of a t-value at least as large in absolute value as the observed
Conclusion:      Report P-value; reject H0 at alpha level if P <= alpha.
                       Also recommend reporting the standard error and the interval estimate. 
 

Assumptions
 
The observations from both samples are randomly drawn from normally distributed populations.
Diagnostic:  Normal probability plot with a test for normality.
 
The variances of both samples are equal.
Diagnostic:  Levene's test 


References