67 of students enrolled in college or trade school within 12

67% of students enrolled in college or trade school within 12 months of graduating high shcool. in a random sample of 160 students, 102 students were found to be in college or trade school

a. construct a 90% confidence interval to calculate the actual proportion of students enrolled in college or a trade school

b. what is the margin of error for this sample

Solution

b)

z for 90 % = 1.645

p^ = 102/160 = 0.6375

Margin of error = z * sqrt (p^ (1-p^)/n)

= 1.645 * sqrt (102/160 * ( 1 -102/160)* 1/160)

= 0.0625 Answer

a)

90% Confidence Interval :

( p^ - Margin of Error , p^ + Margin of error)

= ( 0.6375-0.0625 , 0.6375 + 0.0625)

= ( 0.575 ,0.7 ) Answer