Question

I WILL FAN AND MEDAL
A random sample of 100 undergraduate students at a university found that 78 of them had used the university library’s website to find resources for a class. What is the margin of error for the true proportion of all undergraduates who had used the library’s website to find resources for a class?

0.04
0.08
0.1
0.12

Answer 1

margin of error suggests a confidence interval, but no width has been suggested

Answer 2

if we wanted to be 99% confident that the true population proportion was within a given interval, we would use z=2.576 and use the standard error as a multiplier

Answer 3

the standard error is just a modification of the standard deviation.

in this case: and i dont really understand why, the binomial standard deviation is sqrt(npq) with a mean of np (the mean i get)

z=x−npnpq−−−√

z=x−npnnpq√n

z=xn−pnpqn2−−−√

z=xn−ppqn−−√

zpqn−−−√=xn−p

pmidpoint±zpqn−−−√margin of error=±xnend points

Answer 4

sorry dont know how to insert equations

Answer 5

my PC wont do it

Answer 6

Hint: use the central limit theorem, and use a maximum value for the standard deviation for a bernouli random variable.