Question: Some college professors make bound lecture notes available to students in an effort to improve teaching effectiveness. Two groups of students were surveyed - 86 students enrolled in an eco100 class that required the purchase of the lecture notes and 60 students in an eco100 class that did not offer lecture notes. In both classes the instructors used lectures as the main method of delivery. At the end of the semester students were asked to respond to the statement "having a copy of the lecture notes was [would be] helpful in understanding the material"

Reponses were measured on a 9 point scale where 1 = "strongly disagree" and 9 = "strongly agree". The results can be summarized as follows:

Students buying notes

\(\begin{aligned} & {{n}_{1}}=86 \\ & {{{\bar{X}}}_{1}}=8.48 \\ & {{s}_{1}}=0.94 \\ \end{aligned}\)


students not buying notes

\(\begin{aligned} & {{n}_{2}}=35 \\ & {{{\bar{X}}}_{2}}=7.80 \\ & {{s}_{2}}=2.99 \\ \end{aligned}\)

a) Describe the populations involved in the comparison

b) Do the samples provide sufficient evidence to conclude that there is a difference in the mean responses of the two groups of students? Test \(\alpha =0.01\).
c) Construct and interpret a 99% confidence interval for the difference in the population means.
d) Would a 95% confidence interval for the difference in the population means be wider or narrower than the one you found in part c)? Why?