Name:____________________________ Section:____

Include your name, section number, and homework number on every page that you hand in. Enter ``Section 1'' for the morning class (10-11AM) and ``Section 2'' for Professor Sawyer's class (12-1PM).

Begin the exposition of your work on this page. If more room is needed, continue on sheets of paper of exactly the same size (8.5 x 11 inches), lined or not as you wish, but not torn from a spiral notebook. You should do your initial work and calculations on a separate sheet of paper before you write up the results to hand in.

SHOW ALL STEPS in your calculation of confidence intervals, starting from the appropriate ``magic number'' (like 1.960 or 1.645, technically called a quantile) for a normal or Student's t-distribution. In particular, DO NOT just enter the numbers into a calculator, press a button, and write down the results. (However, you are free to check your results using a calculator. It is OK to use a calculator to find the sample mean Xbar and the sample standard deviation s.)

1. (10 points) Do exercise 6.70 on page 288. (This asks you to find a 95% confidence interval for the population standard deviation of a normal population.)

2. (10 points) Do exercise 7.6 on page 301. (This asks you to find
H_{0} and H_{1} in several settings.)

3. (15 points) A lamb farmer is considering whether to add antibiotics to his lamb feed. Specifically, he or she wants to carry out a statistical test to see whether the use of antibiotics increases lamb weight.

4. (15 points) A teacher gives an exam to a class of n=16 students. The sample mean of the n=16 scores was Xbar=74.7 with sample standard deviation s=12.3 In every previous year in which the exam was given, the mean was exactly 70.0. The teacher wants to test whether this year's exam was easier than the tests of previous years (or else that this year's class was more gifted). The alternative would be that the apparently higher class average of 74.7 was just sampling error.

5. (10 points) (Suggested by exercise 7.36 on page 324.) When negotiating with an insurance company, the owner of a pizza delivery service asserts that at least 75% of his drivers wear seat belts at any given time. However, in a random sample of n=8 of his drivers, only two were wearing seat belts. Is this sufficient evidence to reject the hypothesis that 75% of the drivers wear seat belts at any given time? Find the P-value using a lower one-tailed test. Find the P-value exactly from the binomial distribution, for example from Table A1.