Question

A university dean randomly selected 200 students and found that 102 of them were receiving financial aid.

a) Calculate the 80% confidence interval for the true rate of students who receive financial aid. Interpret the result.

b) Calculate the 90% confidence interval for the true rate of students who do not receive financial aids. Interpret the result.

c) How large a sample size needed with 95% confidence to estimate the true rate of students who receive financial aid within 0.05.

d) You will need to collect a smaller sample size if the dean: (choose one)

a	Increases the confidence level.
b	Decreases the sampling error.
c	Increases the sampling error.
d	None of these.

Answer 1

a)

b)

from above 90% CI:

for 90 % CI value of z=				1.645
margin of error E=z*std error                            =				0.058
lower confidence bound=sample proportion-margin of error				0.452
Upper confidence bound=sample proportion+margin of error				0.568

c)

here margin of error E =	0.050
for95% CI crtiical Z          =	1.960
estimated proportion=p=	0.510
required sample size n =	p*(1-p)*(z/E)2=	384.00

d)

Increases the sampling error.