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 0.04 margin of error and use a confidence level of 95​%. Complete parts​ (a) through​ (c) below.  

Answer 1

Solution :

Given that,

= 0.50

1 - = 0.50

margin of error = E = 0.04

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

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

= (1.96/0.04)² *0.50*0.50

= 600

sample size = n = 600