Graduate Statistics

Question

Does computer-assisted instruction help community college health science students with reading difficulties to learn reading skills at a faster than normal rate? A researcher arranged for one of these students to have access to a set of computer-learning programs instead of the normal reading curriculum for one term. At the end of the term, the researcher tested her on a standardized reading ability test on which the mean for students with reading difficulties is 36 with a standard deviation of 6. The test participant scored 55. What would you conclude? Explain. 8 points

a. Yes, the students scored significantly different because they are more than 2 standard deviations to the right of the mean..

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

Answer 1

It seems that the answer should be a, because 55 is 19 points above 36, and that is about 3.17 (19/6) standard deviations above the mean, and that's greater than 2. But there are 2 things that make me a little less sure. One is that this is categorized as graduate statistics, and this looks like a basic statistics question. The other is that one student scoring well does not appear to be sufficient evidence of the effectiveness of the curriculum. It would seem that a larger sample size would be necessary to rule out this score being an outlier.

But the only choices are based on a comparison based on how many standard deviations above the mean. So based on that, I'm going with a.