Wed April 5 assignment

Assignment for Wednesday, April 5 (M 358K, Sp 06, Smith)

I. Review and reading and exercises not yet discussed.

II. Read Section 7.3 (pp. 515 - 521)

The most important thing for you to get from pp. 516 - 518 is a little acquaintance with the F-distribution, which we will encounter again later.
Pay particular attention to the discussion of robustness (pp. 518 - 519)
You can just skim the part on power of the two-sample t-test (pp. 519 - 521)

(No exercises on today's reading; we will mainly spend class time discussing distributions and catching up.)

III. Hand in: Note: You will need to use software for some of these, so be sure to allow enough time. If you use Minitab, be sure to consult the handout Using Minitab in M 358K as needed.
1. #7.6 (p. 473)
  2. # 7.10 (p. 474-475) (Remember that part (a) can be done by computer.) Added 4/2/06: In part (e), remember to explain why you have chosen the null and alternate hypotheses that you specify. Remember that the appropriate choice depends on the context explained in the paragraph before the data, so you need to say what in the context tells you what hypotheses are appropriate.
3. #7.20 (p. 476) (Be sure to include part (g).)
4. a. A certain brand of toothpaste claims that on average, one gram of their toothpaste contains 1mg of fluoride. Alek and Becca have analyzed the fluoride content of twenty tubes of that brand of toothpaste and tested the null hypothesis
    H₀: µ = 1 mg/g
versus the alternative
    H_a: µ > 1 mg/g.
(They have chosen this one-sided alternative because they believe that consistent exposure to concentrations of fluoride higher than 1 mg/g may be harmful to young children.) They obtained p-value 0.064. Alek says that they have proved, at the alpha = 0.05 level, that H₀ is true. Becca says that there is some evidence against H₀, and that a study using a larger sample size may be worthwhile. Is Alek right? Becca? Both? Neither? Explain your answer.
    b. If instead, Alek and Becca had used a sample of 100 tubes of the toothpaste, and had obtained the same sample mean and standard deviation as they did in the study with 20 tubes, how would their p-value compare with the one they obtained using 20 tubes: Would it be smaller, larger, the same, or is it impossible to say which it would be? Explain.