Mathematical Statistics—Homework Assignment #4

Due Monday, February 8 (beginning of class)

Important Reminders

Please respect me, your classmates, and yourself by taking the Honor Code very seriously. Your grade will depend on both the content and exposition of your answers. That is, be sure your logic is clear, you defend all your steps (unless they are, for example, obvious algebra steps), your solutions read smoothly (even if using symbols—they should still read like an English sentences), and that one of your peers could read and understand your solutions without asking any additional questions.

Okay-to-work-together Problems (5 problems)

Chapter 8:

28 (since n is very large in this problem, you can use a confidence interval based on the z-distribution rather than the t-distribution)

43

50 (use R for this problem—enter in the data yourself; as part of your solution, include the R code for your bootstrap program; also, be sure to read Section 8.5 of the textbook, so you understand the book’s difference between a bootstrap confidence interval based on standard methods and a bootstrap percentile confidence interval)

Chapter 9:

7

32 (for part a, be sure to work through all the steps of the significance test: i) statement of hypotheses, ii) check of conditions, iii) calculation of test statistic, iv) calculation of p-value, and v) interpretation of the results, including a check for practical significance; you can use Minitab—data file is in the share folder—to check the normality condition and to determine numerical summaries, but determine the test statistic and p-value “by hand”; for part b, do not use the textbook formulas for computing the Type-II error rate—work through these problems fully on your own; also, additionally suppose the data come from a normal population, so you can use a z-test)

Work-alone Problems (5 problems)

Chapter 8:

20 (this problem has a very large sample size; compute both the “standard” confidence interval and the “score” confidence interval—given on page 388 of the textbook; how do the intervals compare? Be sure to include an appropriate interpretation of the interval)

34 (use Minitab—data file is in the share folder—to check the normality condition and find numerical summaries, but calculate the confidence interval “by hand”)

76 (for part d, when determining the t-interval, use Minitab—data file is in the share folder—to check the normality condition and find numerical summaries, but calculate the confidence interval “by hand”)

Chapter 9:

25 (be sure to work through all the steps of the significance test: i) statement of hypotheses, ii) check of conditions, iii) calculation of test statistic, iv) calculation of p-value, and v) interpretation of the results, including a check for practical significance; you can use Minitab—enter the data yourself—to determine numerical summaries, but determine the test statistic and p-value “by hand”)

27 (for part a, be sure to work through all the steps of the significance test: i) statement of hypotheses, ii) check of conditions, iii) calculation of test statistic, iv) calculation of p-value, and v) interpretation of the results, including a check for practical significance; you can use Minitab—enter the data yourself—to check the normality condition and to determine numerical summaries, but determine the test statistic and p-value “by hand”; for parts b and c, do not use the textbook formulas for computing the Type-II error rate—work through these problems fully on your own)