I have a following problem: Let's have two sport teams, X and Y. X's score at world tournaments is 1., 6. and 1. place. Y's: 2,7,5,3,3. I want to calculate with 95% probability who's better. I have chosen students t-test of a hypothesis
H0: µ1 = µ2
and it's alternative
H1: µ1 < µ2
where µ1 is the mean "place" of team X and µ2 of Y. I chose the alternative because the arithmetic mean of team X is better than Y's.
I have calculated the test statistic as -0.938 and from tables t 0.975 (6) = 2.447
What next? I know that if alternative hypothesis was µ1 != µ2 the rejection region would be R - {-2.447, 2.447} but with my more specific alternative hypothesis I'm not sure.
A'd be thankfull for any advice..