Graduate Statictics

Question

Do college students from private schools have higher than average test-taking skills? A researcher administered a standard measure of test-taking skills to a randomly chosen student from a private university and found him to have a score of 68. The average on this measure for the population in general is 60 with a standard deviation of 10. What should you conclude about whether this student from a private university has higher test-taking ability? Explain. 8 points

a. Yes, the students scored significantly different because they are to the right of the mean.

b. No, the students did not scored significantly different because they are less than 2 std. deviation from the mean.

Answer 1

This student is above the mean, but not by much. We know that because he/she is only 8 points above the mean, which is less than 1 standard deviation (10) above. If this was normally distributed (and if it's a large enough group of test takers, we generally assume that it is), then 68% of the test takers will be within 1 standard deviation (in this case, the 50-70 range), and 34% will be in the 60-70 range. That may not seem like a lot, but the percentage would have to be much lower for this to be significantly above the mean.

In any caae, the only choices given to us are "yes, because the student is above the mean" or "no, because they are less than 2 standard deviations above the mean." So, given these options, we have to say no, this is not significantly different or better, because they are less than 2 std. deviation from the mean.