The product manager for the new lemon-lime dessert topping Clear 'n Light was worried about the sales and future of the product. She was concerned that the marketing strategy had not correctly identified the attributes of the product, so she sampled 1200 customers and found that 780 of them thought that the product was a floor wax. Construct a .95 confidence interval for the true proportion of customers who held this misconception.

The Historic Trust is considering whether to buy a bunch of personal recording player devices for tourist to rent as they tour the historic Adams Castle. So they sampled 400 castle visitors and ask whether they would rent such a device. Assuming the 400 visitors tell the truth, and 52 of them say they would rent the device, then, what can the Trust conclude at the .90 confidence level about the proportion of all visitors who would use the device?

Assuming the visitors tell the truth, how many visitors do they need to sample to get a confidence interval for the true proportion within .03 (from lower bound to upper bound) at that .90 confidence level?

Dr G is using a new textbook in his statistics course. At the end of the course, he asks students to rate the new text as 1) excellent, 2) good, 3) poor, 4) horrible and he counts the number of students in each category. Assuming the students tell the truth, what can he conclude at the 95% confidence level about the real proportion of excellent ratings among all students who would ever take the course?

How many students does he need to sample to get a confidence interval for the proportion of excellent ratings within .03 (from lower bound to upper bound) at the 95% confidence level?