Solve This: Statistic Help for EN-100 Test

[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).

 

[tacman]

To solve this problem, we need to use the t-test for independent samples. The null hypothesis (H0) states that there is no significant difference between the mean scores of boys and girls on the EN-100 test. The alternative hypothesis (H1) states that there is a significant difference between the mean scores of boys and girls on the EN-100 test.

To find the critical value, we need to look at the t-table for a two-tailed test with 28 degrees of freedom and a significance level of 0.05. The critical value is 2.048. Since the test statistic (2.69) is greater than the critical value, it falls in the rejection region. This means that we can reject the null hypothesis and accept the alternative hypothesis.

Since the mean of the boys' scores is lower than the mean of the girls' scores, this supports the alternative hypothesis, which states that there is a significant difference between the mean scores of boys and girls. Therefore, we can reject the null hypothesis and conclude that girls are, on average, smarter than boys on subjects tested by the ACT.

In conclusion, the critical value for this problem is 2.048 and we can reject the null hypothesis. The answer to the question "Can she reject her null hypothesis?" is Yes.