Independent samples T test & T critical

[jefgif]

If given the following hypotheses :

Ho: mean1 >or equal to mean2 or mean1 - mean2 >or equal to 0

Ha: mean1<mean2 or mean1 - mean2 < 0

How do you know if T critical should be negative or positive ??

 

[royhaas]

The critical point is in the "direction" of the alternative hypothesis. Note that the critical point comes from assuming a specific value for the null distribution; thus, the null hypothesis is really a test of equality.

\(\displaystyle H_a: \mu_1 > \mu_2\) implies a positive critical value;
\(\displaystyle H_a: \mu_1 < \mu_2\) implies a negative critical value.