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​ bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.03 margin of error and use a confidence level of 99​%. Complete parts​ (a) through​ (c) below. . Assume prior studies have shown that about 45​% of​ full-time students earn​ bachelor's degrees in four years or less

n=?

Answer 1

Solution:

Given that,

= 0.45

1 - = 1 - 0.45 = 0.55

margin of error = E = 0.03

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.03)² * 0.45 * 0.55

=1824.60

= 1825

n = sample size = 1825