6 A large university has a college algebra enrollment of 500

6. A large university has a college algebra enrollment of 5000 students each semester. Because of space limitations, the university decides to offer the course in a self-study format where students have access to tutors and other help in a lab setting, but students learn independently. Historically students in traditional college algebra courses scored 73.2 points on the final exam, and the coordinator of the course is afraid that scores will drop with the new format. At the end of the first semester using the new format, 3851 students took the final exams and had a mean score of 72.8 and a standard deviation of 12.3. Show all work, especially calculator functions.

(a) Treating those students as a simple random sample of all students, find a 90% confidence interval for the mean score of all students on the final.

(b) Use your confidence interval from part (a) to explain why there is statistically significant evidence at the level of = 0.05 that the scores have decreased.

(c) Do you think the decrease in scores you found in part (b) has practical significance? Would you recommend to the administration that they spend 4 million dollars on a new classroom building so they can go back to the old format of the class? Why or Why not?

Solution

alpha = 1 - 0.90 = 0.10

alpha / 2 = 0.05

Z = 1.64

I : 72.8 +/- 1.64 * 12.3 / srqt (3851)

I : 72.8 +/- 0.325

I : [72.475 , 73.125 ]

b)

there is statistically significant evidence at the level of = 0.05 that the scores have decreased.

because as you can see the interval does not contain the mean of 73.2 that was the scored average historically