At a Certain University, 16% of Students Fail General Chemistry $\mathrm { z }$

Essay

At a certain university, 16% of students fail general chemistry on their first
attempt. Professor Brown teaches at this university and believes that the rate of
first-time failure in his general chemistry classes is 33%. He samples 96 students
from last semester who were first-time enrollees in general chemistry and finds
that 15 of them failed his course. i). State the appropriate null and alternate hypotheses.
ii). Compute the test statistic $\mathrm { z }$ .
iii). Using $\alpha = 0.05$ , can you conclude that the percentage of failures differs from $33 \%$ ?