Prep Courses? Scores for men (nationwide) on the verbal portion of the SAT test are normally distributed with a mean of 509 and a standard deviation of 112. Randomly selected men are given the Columbia review course before taking the SAT test. After the course, a sample of 49 men revealed an average of 535 points and a standard deviation of 90 points. Using a significance level of 0.05, test the claim that the review course students have a mean score greater than or equal to the normal population. (use the 5-step method).

Question

Prep Courses?  Scores for men (nationwide) on the verbal portion of the SAT test are normally distributed with a mean of 509 and a standard deviation of 112.  Randomly selected men are given the Columbia review course before taking the SAT test.  After the course, a sample of 49 men revealed an average of 535 points and a standard deviation of 90 points. Using a significance level of 0.05, test the claim that the review course students have a mean score greater than or equal to the normal population.  (use the 5-step method).

PsyDAG · Answer

I don't know what your 5-step method is. Here is what I do.

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

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√(n-1)

If can only calculate one SEm, 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 related to that Z score.