Homework #8, Math 320, Spring 2001

Name:____________________________      Section:____

## Math 320 Homework #8 --- Due 3/23

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.

1. (Similar to exercise 7.28 on page 313.) A company is concerned about a machine that fills cans with ground coffee. The machine is tested each day by weighing all of the cans filled by the machine during the first hour of production, which is always n=29 cans. The machine is assumed to be working properly if the sample standard deviation of the weights of the cans is not too large. The company will repair the machine only if there is convincing evidence that the standard deviation is greater than 2.6. Otherwise, it is assumed that the standard deviation equals 2.6 and that the machine is working properly. Assume that the weights of the coffee cans are normally distributed with the same mean.

(a) State the hypotheses H0 and H1.
(b) Suppose that the production manager measures T=3.08 for the sample standard deviation of the n=29 coffee cans on one day. Does he or she accept H0 or reject H0? What is the P-value? (Hint: It may be easier to work with sample variances rather than sample standard deviations.)
(c) Find the critical value lambda0 for the test at level of significance alpha=0.10 based on the sample standard deviation T. Is the observed value T=3.08 below or above that value? In this way, if the manager decides to become concerned about the machine only when the P-value is 0.10 or less, then he or she just has to check whether the observed sample standard deviation T is greater or less than lambda0 without having to calculate a new P-value each day.

2. Do exercise 7.44 on page 325. (This asks you to find the level of significance and the power for a test based on a binomial distribution. Warning:``Greater than'' means ``strictly greater than'' and not ``greater than or equal to''.)

3. Do exercise 7.48 on page 335. What test statistic are you using? What is its distribution given H0? Is this a one-sided or a two-sided test? How does that affect the P-value?

4. Do exercise 7.72 on page 346.

5. Do exercise 8.6 on page 360. Is this a one-sided or a two-sided P-value?

6. Do exercise 8.14 on page 375.