Assignment for Monday, March 27 (M 358K, Spring 06, Smith)
I. Read pp. 448 through the middle of p. 459. Pay particular attention to the following:
- Be careful to distinguish between the following three
(related but distinct) concepts: The population standard deviation of
of x, the sample standard deviation of x, the standard deviation of the
samping distribution of x-bar, and the standard error of x-bar. Which
are parameters and which are statistics? What is the notation for each?
- The box on p. 452 tells you how to calculate the confidence interval, but to interpret what the confidence interval means, you need to go back to the ideas of Chapter 6.
- Note the Caution on p. 455.
- In using the tables in the book, be sure to note that Table D (for t-distributions, in the back of the book) gives right tailed probabilities, whereas Table A (for the standard normal distribution, in the front of the book) gives left tailed
probabilities. Moral: Be sure you know which type the table gives
before using it. (Note that the pictures with the tables tell you --
the shaded region is the one whose area is given.)
II. Read the handout "The Chi-Squared and t Distributions and
Degrees of Freedom" (to be handed out in class) for more
information on the t-distribution and degrees of freedom.
III. Do the following exercises to reinforce reading and for possible class discussion:
1. On p. 453, Example 7.1 ends with the sentence, "We are 95% conifdent
that the mean vitamin C content of the CSB for this run is between 16.5
and 28.5 mg/100g." Explain carefully and precisely what this means.
(Review Section 6.1 if needed.)
2. In Example 7.2 (pp. 454 - 455), the P-value is 0.0002, and the
authors say, "Clearly, these data are incompatible with a process
mean of µ = 40 mg/100g. We reject H0 and conclude that
the vitamin C content for this run is below the specifications." Would
you say the same thing if you got P-value 0.049? If not, what would you
say?
3. On p. 458 (after Example 7.5), the authors say, "The confidence interval suggests
that the broker's management of this account had a long-term mean
somewhere between a loss of 3.04% and a gain of 0.84% per month."
(Italics added for emphasis here.) Would it be correct to replace "suggests" by "tells us" or "says" or "shows"?
4. p. 471 #7.1 (but note that the answers in the back of the book are
pretty terse, so they are only hints rather than solutions.)
5. p. 472 #7.2 and 7.3
6. p. 475 #7.12 and 7.13
7. p. 476 and 477: #7.16, 7.17, and 7.23.