Question

In a study of government financial aid for college students, they need to estimate the percentage of students who graduate in four years. Find the sample size needed to estimate the percentage. Use a 4% margin of error, and 90% confidence level.

1. A previous study showed that 60% graduate in four years.

2. We don't know the percentages at all

Answer 1

Solution :

(A)

Given that,

= 0.60

1 - = 1 - 0.60 = 0.40

margin of error = E = 4% = 0.04

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.04)2 * 0.60* 0.40

=405.9

Sample size =406

(B)Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.04)2 * 0.5 * 0.5

=422.8

Sample size =423