stat310

# Homework 10

This homework follows the standard late penalty: 0% if in the stat310 mailbox by Thursday 12 Apr 4pm, 10% by 5pm the following day, 100% otherwise. Please read the syllabus for other homework policies.

1. Despite what it says on the bottle, the amount of beer in a bottle actually varies a little (in line with a normal distribution). I picked a 12 pack beer and measured amount of beer in each bottle: 12.54 13.40 10.41 12.36 12.06 11.42 12.76 11.91 13.19 11.73 10.70 12.24.

1. (6 pts) Find a 95% confidence interval for $$\sigma^{2}$$.

2. (2 pts) Find another 95% confidence interval for $$\sigma^{2}$$.

3. (6 pts) Find a 90% confidence interval for $$\mu$$.

2. Following is the number of beer bike titles won by Will Rice College each year from 2000 to 2012: 2, 1, 1, 1, 2, 0, 1, 1, 2, 3, 2, 2, 2.

1. (8 pts) Assuming a binomial distribution, find a 99% confidence interval for p, the probability that Will Rice claims one title. Comment on the quality of the approximation.

2. (2 bonus points) What is the probability of Will Rice sweeping next beer bike? What assumptions do you make?

3. Assume the waiting time for the Rice bus is exponentially distributed. Here are 10 waiting times (in minutes) I observed when waiting for the bus: 1.50 8.52 0.50 0.73 2.36 17.64 8.01 2.54 17.78 20.76.

1. (6 pts Find a 95% confidence interval for $$\theta$$.