Question

A University president has become exceptionally interested in determining whether her faculty members are engaging in scholastic misconduct by not teaching their classes. To check on her faculty she installs cameras in the university's classrooms. How many videos with the president need to review to achieve the results below?

a. She is uncertain of the distribution of faculty who are engaged in misconduct (i.e.,50/50) and wants to be 95% certain she is within 0.02 of the true population proportion. How many videos should she review?

b. Research suggests that 10% of faculty admit to not teaching their classes as assigned during the semester. If the president used this result and wanted to be 99% sure she was within 0.01 of the true population proportion how many videos should she review?

c. The president also thinks that her faculty are pretty good for the most part and think that there is a 5% chance that her faculty are not teaching their classes appropriately and she wants to be 95% certain she is within 0.01 of the true population proportion. How many video should she review here?

Answer 1

(a)

= 0.05

From Table, critical values of Z = 1.96

p = 0.5

e = 0.02

Substituting, we get:

So,

Answer is:

2401

(b)

= 0.01

From Table, critical values of Z = 2.576

p = 0.10

e = 0.01

Substituting, we get:

So,

Answer is:

5973

(c)

(a)

= 0.05

From Table, critical values of Z = 1.96

p = 0.05

e = 0.01

Substituting, we get:

So,

Answer is:

1825