Question

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full time college students who earn a bachelors degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.05 margin of error and use a confidence level of 99%.

A. Assume that nothing is known about the percentage to be estimated

N =

B. Assume prior studies have shown that about 35% of full time students earn bachelors degrees in four years or less

C. Does the added knowledge in part b have much of an effect on the sample size?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.05

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.576 / 0.05)2 * 0.5 * 0.5

=663.57

Sample size = 664

(B)

Solution :

Given that,

= 0.35

1 - = 1 - 0.35 = 0.65

margin of error = E = 0.05

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.576 / 0.05)2 * 0.35 * 0.65

=603.8

Sample size = 604

(C) smaller sample size of the part b