This problem concerns course scores (on a 0–100 scale) for a large undergraduate computer programming course. The class is composed of both underclassmen (freshmen and sophomores) and upperclassmen (juniors and seniors). Also, the students can be categorized according to their previous mathematical background from previous courses as “low” or “high” mathematical background. The data for these students are in the file P09_75.xlsx. The variables are:
• Score: score on a 0–100 scale
• Upper Class: 1 for an upperclassman, 0 otherwise
• High Math: 1 for a high mathematical background, 0 otherwise
For the following questions, assume that the students in this course represent a random sample from all college students who might take the course. This latter group is the population.
a. Find a 90% confidence interval for the population mean score for the course. Do the same for the mean of all upperclassmen. Do the same for the mean of all upperclassmen with a high mathematical background.
b. The professor believes he has enough evidence to “prove” the research hypothesis that upperclassmen score at least five points better, on average, than lowerclassmen. Do you agree? Answer by running the appropriate test.
c. If a “good” grade is one that is at least 80, is there enough evidence to reject the null hypothesis that the fraction of good grades is the same for students with low math backgrounds as those with high math backgrounds? Which do you think is more appropriate, a one-tailed or two-tailed test? Explain your reasoning.