Question

A stats class was interested in determining the percentage of students on their campus who are opposed to a new policy eliminating all paper books from the campus bookstore in favor of ebooks. After surveying 176 students, the class finds that 35% are opposed to the policy. The margin of error is 7.2%.If surveying more students keeps the percentage at 35% , how many more would need to be surveyed in order to be 95% confident that the correct percentage for the entire student body is between 32% and 38% ? Don't forget to consider the number of students that have already been surveyed. Round up to the nearest student, if necessary. (Hint: What would the margin of error be in this case?)

In order to be 95% confident that the correct percentage for the entire student body is between 32% and 38%, the class needs to survey more students.

Answer 1

Here the 95% confidence interval for the the correct percentage for the entire student body is (32%,38%)

The width of the confidence interval is 6%

which means that the margin of error required is 3% =0.03

for 95% confidence

p=0.35

students are required

176 students have already been taken in the sample so we are left with 972-176=796 more students