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 0.02 margin of error and use a confidence level of 90​%.
Assume that nothing is known about the percentage to be estimated. n= ​(Round up to the nearest​ integer.)

Answer 1

Answer: 1692

Step-by-step explanation:

if prior estimate of proportion is not known , then the formula to find the sample size is given by:-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$  (1)

For 90% confidence interval , significance level =$\alpha=1-0.90=0.10$

Critical value =$z_{\alpha/2}=1.645$

Margin error =  0.02

Now, substitute all the above values in (1), we get

$n=0.25(\dfrac{1.645}{0.02})^2=1691.265625\approx1692$

Hence, the required minimum sample size should be 1692.

Answer 2

Answer:100.     Step-by-step explanation round to to nearest 10