Question: Submission deadline: Wednesday, April 26, 5:00pm
Instructions: This project will be completed and turned in individually, not as a team. You will submit a write-up of your solutions (hand written is fine). You can use any computational device you like (calculator, Excel, R,...), there is no need to electronically submit your computational files.
However, on your write up you should show enough work so that your results could be replicated by someone else. In addition to your work, please fill in the point estimate and confidence intervals in the space provided below. (Staple your work to this document.)
It is fine to have general conversations about this project with others, but you should make a good faith effort to work out the answers independently. In particular, you should write up your own solutions - don't copy others! Please include the pledge at the end to indicate that you have followed these instructions.
The Setting: There are 3 buildings under consideration. All that is known prior to sampling is the location of the buildings, not the internal layout or the number or type of classrooms.
1. Building 1: Made up of wing A (6 large classrooms, 8 medium rooms) and wing B (4 large classrooms, 8 seminar rooms)
2. Building 2: Made up of wing A (8 medium classrooms, 4 seminar rooms) and wing B (10 large classrooms)
3. Building 3: Made up of 4 large classrooms, 16 medium classrooms, and 2 seminar rooms The Objective: Find a 95% confidence interval for the total number of wheelchair accessible seats in these 3 buildings. If the design information given does not make it possible to find the confidence interval, then state that and explain why.
Design 1: Selected a SRS with replacement of 3 buildings with equal probability. For each selected building, select a single room with equal probability. (Number of wheelchair accessible seats in each room given in parentheses.)
Data:
Sample 1: Building 2; Room B5 (16)
Sample 2: Building 2; Room A4 (10)
Sample 3: Building 1; Room B2 (6)
Point estimate: Confidence Interval:
Design 2: Selected a SRS with replacement of 4 buildings with equal probability. For each selected building, select a simple random sample without replacement of 2 rooms.
Data:
Sample 1: Building 3; Room 7 (8), Room 9 (10)
Sample 2: Building 2; Room A4 (6), Room B1 (12)
Sample 3: Building 3; Room 7 (8), Room 17 (18)
Sample 4: Building 1; Room A3 (14), Room B6 (4)
Point estimate: Confidence Interval:
Design 3: For each building, choose an equal probability SRS with replacement of 3 rooms.
Building 1; Room A3 (14), Room B2 (6), Room A5 (10)
Building 2; Room A9 (20), Room B3 (8), Room B3 (8)
Building 3; Room 1 (8), Room 5 (4), Room 21 (5)
Point estimate: Confidence Interval:
Design 4: Choose 3 buildings at random with replacement, each with probabilities prob(1) = 0.5, prob(2) = 0.3, and prob(3) = 0.2. Within each building, select a SRS without replacement of size 2 from each room type.
Data:
Sample 1: Building 1; Room A1 (10; large), Room B3 (16, large), Room A7 (8, medium),
Room A13 (4, medium), Room B5 (10, seminar), Room B9 (8, seminar)
Sample 2: Building 3; Room 2 (18; large), Room 3 (16, large), Room 11 (8, medium),
Room 14 (10, medium), Room 21 (6, seminar), Room 22 (8, seminar)
Sample 3: Building 1; Room B1 (20; large), Room B3 (16, large), Room A10 (8, medium),
Room A12 (14, medium), Room B6 (4, seminar), Room B10 (14, seminar)
Point estimate:____________ Confidence Interval:_____________
Pledge:___________________