Can Dr. Easy Reject the Null Hypothesis in the EN-100 Test Analysis?

[lopram]

Statistic Help!

I need some help solving this problem...

Dr. Easy saw the scores from the EN-100 test and used the occasion to test the old adage that girls are smarter than boys on subjects tested by ACT. Assume the degrees of freedom for this problem is 28. Dr. Easy did the arithmetic and found the value of the test statistic was 2.69 (alpha equals .05). What is the critical value (3 decimal places of significance)? If the mean of the boys score was lower than the mean of the girls score can she reject her null hypothesis? Yes or No.

 

[benorin]

Put:
$$H_0 :\mu_g\leq \mu_b$$
$$H_A :\mu_g> \mu_b$$ (Claim: girls are smarter than boys)

We have a right-tailed test, and I found on a table of critical t-scores that for df=28 and $$\alpha =.05$$ we have $$t_{.05 ;28} =1.701$$, which puts the test statistic of $$t=2.69$$ in the critical region so that we reject the null hypothesis $$H_0$$, and conclude that the data supports the claim that girls are smarter than boys.

If "the mean of the boys score was lower than the mean of the girls score" had much to do with this, I don't know why, other than telling us the sign of the test stastic (but we knew that).