When I Was a Student at the University of Michigan

Essay

When I was a student at the University of Michigan, we had a little saying that we liked to use with students who attended other universities: "We're not snobs-we're just better than you." To prove it, I collected data from 61 randomly selected undergrads at Michigan and 61 randomly selected undergrads at Boston University (BU). The Michigan sample had a mean SAT verbal score of 600 with a standard deviation of 200. The BU sample had a mean SAT verbal score of 565 with a standard deviation of 150.
a. What kind of test should I use to examine whether the difference between these means is statistically significant?
b. Is this a 1-tailed or a 2-tailed test? Why do you think so?
c. What would your alternative hypothesis be? Tell me why.
d. Report the critical value for this test. Why do you think that is the correct critical value
e. So perform the necessary calculations and tell me whether the difference between the means is statistically significant using an alpha level of .05. Be sure to wrap words around your results. Tell me all that you know
f. Give me one plausible explanation for your results. Why do you think the results turned out this way. (Note: I am not looking for the technical, mathematical answer here-nothing about probabilities or formulas. I just want you to give me a reasonable explanation for why Michigan students may have higher SAT scores, or not, depending on what your results were.)