Question

(A) Mrs. Smith took a random sample of students after winter break and asked if they enjoyed their break. She found that 70% of the 40 students she asked said yes. Estimate and interpret a 90% confidence interval for the proportion of all students who enjoyed their break.

(B) How large of a sample will allow Mrs. Smith to get a margin of error of 2.5% at a 95% confidence level? Remember to SHOW your work with the numbers plugged into the formula and answer in context.

Answer 1

a)

from above:

90% confidence interval for the proportion of all students who enjoyed their break =0.581 ;0.819

b)

here margin of error E =	0.025
for99% CI crtiical Z          =	2.580
estimated proportion=p=	0.700
required sample size n =	p*(1-p)*(z/E)2=	2237.00

( please try 2230 if z score is to be taken till 3 decimal places_