Stat. 5303, Spring 2024 Problem Set 1

发布时间：2024-01-22

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Problem Set 1

Stat. 5303, Spring 2024

Due: In Canvas by 12:00pm on Tuesday, Jan. 23

The goal of problems 1 and 2 is to encourage you to start thinking about experimental design. You will necessarily have to search the literature (books, internet) for answers, but the words you turn in must be your own. Please provide the reference you used to formulate your responses.

Problems 1 and 2 will be graded S/N. Problems 3 and 4 are intended as review.

Problem 1. Section 1.5 makes reference to a uniformity trial. What is a uniformity trial and what is its purpose?

Problem 2. Brieﬂy describe an experimental design from the literature that makes use of Ran-domization, Replication or Blocking. Identify:

1. The goal of the experiment

2. The outcome variable(s) of interest

3. The experimental factors(s)

4. Any control and/or nuisance factors identiﬁed in the design

5. The set of treatments

6. The experimental unit

7. The nature of the randomization employed

8. The blocking scheme, if the design was blocked

9. The method of analysis used

Problem 3. Technical Note Panel 1.1 is based a sample from a normal distribution. Is the result of the panel altered if we drop drop the normality condition and require instead only that Y1 , . . . , Yn is a sample with E(Yi ) = μ, var(Yi ) = σ2 , i = 1, . . . , n?

Problem 4. Let denote the usual estimator of σ2. Under the setting described in Technical Note Panel 1.1,

(a) Why might this result be important? Hint: Recall how var() is usually estimated.

(b) When deriving result (1), we use that

where Yi is an arbitrary single member of the sample. Show that this result is true. Hint: write