Question

The President of the Student Affairs Office wants to estimate the percentage of students who favor a new student conduct policy. What (minimum) sample size is needed to form an 80% confidence interval to estimate the true percentage of students who favor the policy to within ± 3%?

Do not round intermediate calculations. Round up your final answer to the next whole number.

Sample size =  students

Answer 1

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5= 0.5

margin of error = E = ± 3% = 0.03

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z/2 = Z0.10 = 1.28 ( Using z table )

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

= (1.28 / 0.03)2 * 0.5 * 0.5

= 455.11

Sample size =456