Posted by Kate on .
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:
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?
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.