Question

2. The Dean of Students at the University of Waterloo wanted to estimate the proportion of students who are willing to report cheating by fellow students. So, her staff surveyed the 172 students currently enrolled in the introduction to biology class. The students were asked, “Imagine that you witness two students cheating on a quiz. Would you tell the professor?” 19 of the surveyed students responded “yes.” (11 points total)
a. Using these data, calculate the 90% confidence interval for the proportion of all students at the University of Waterloo that would report cheating. (4 points)
b. Interpret the confidence interval from part “a” in a sentence. Interpret in terms of percentages, rather than proportions. (4 points)
c. Is it appropriate to use these data to estimate the proportion of all students at the university that would report cheating? Why or why not? (3 points)

Answer 1

Let p denotes the true proportion of all students at the University of Waterloo that would report cheating.

b) Interpretation : We are 90% confident that the true percentage of all students at the University of Waterloo that would report cheating lies within the interval (8%, 14.1%).

c) The Dean of Students at the University had done convenience sampling to choose students, it was not a random sample, so it is not appropriate to use these data to estimate the proportion of all students at the university that would report cheating.