The Education Testing Service conducted a study to investigate differences between the scores of males and females on the SAT. The study identified a random sample of 562 females and 852 males that had achieved the same high score on the math portion of the test. That is, both females and males were viewed as having similar high abilities in Math. The SAT verbal scores for the two samples are:

Question

The Education Testing Service conducted a study to investigate differences between the scores of males and females on the SAT.  The study identified a random sample of 562 females and 852 males that had achieved the same high score on the math portion of the test.  That is, both females and males were viewed as having similar high abilities in Math.  The SAT verbal scores for the two samples are:
Females	Males
X1 = 547	X2 = 525
S1 = 83	        S2 = 78

Do the data support the conclusion that give a population of females and a population of males with similar high mathematical abilities, the females will have a significantly higher verbal ability?  Test at a 0.02 level of significance.  What is your conclusion?

Anonymous · Accepted Answer

wow I wish you actually solved the problem out

PsyDAG · Answer

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to your Z score.