A university wants to renovate a building on campus, and wants to know how many of the 20,000 active members of the alumni association would be willing to contribute funds to this project. However, this is the first time alumni donations would be the sole financial source for such a project, and the university doesn't have an estimate of the proportion who would contribute toward the renovation.
A. If the university wanted to estimate, with a 95% confidence interval and a margin of error of 5%, the proportion of alumni who would be willing to donate to this project, what size sample would they need? (Hint: Do you remember how to estimate the minimum sample size when you don't have an estimate for the population proportion?) (1 point)
B. The university draws a sample of 385 alumni, and 120 of them say they'd be willing to donate to the building renovation. Construct a 95% confidence interval for the proportion of alumni who would donate to the project. (2 points)
C. Based on the sample size from part b, can you consider this situation binomial? Can you use a normal approximation here? (2 points)
D. The university postpones plans for the building renovations until the following year, when researchers take another sample of 385 alumni. This time, 262 alumni say they'd contribute to the project. Construct a 95% confidence interval for the proportion of alumni who would make donations. (2 points)
E. Use your graphing calculator to calculate a 99% confidence interval for the proportion of alumni who would donate to the building renovations (use
= 385and x = 262). (Show all work, functions, and inputs on your calculator too.