STATISTICS 4C03/6C03

TEST #1 * 2005-02-10

Instructions

This test is to be written in the BSB Computer Lab. The duration of the test is 2 hours.

Any aids and resources are permitted. You may consult any web pages but you may not use e-mail or communicate with anyone other than the instructor.

Question 1

Here are 20 observations from a Beta(a, b) distribution.

  0.2691 0.8532 0.8898 0.5609 0.4778 0.5847 0.3129
  0.1773 0.2394 0.3885 0.3794 0.5598 0.6687 0.4766
  0.4856 0.2827 0.6765 0.3996 0.4395 0.6841
  1. Find the maximum likelihood estimates of a and b.
  2. Draw a 95% confidence region for a and b jointly.
  3. Test the hypothesis that a = b.
  4. Assuming that a = b, find the MLE of the common value a and give a 95% confidence interval.
Question 2

The current necessary to produce a certain level of brightness of a television tube was measured for two different types of glass and three different types of phosphor. Some of the replicate observations were lost, leaving the design unbalanced. Analyse the following data as a two-factor design with interaction, by (a) using the statistical software of your choice and (b) computing the general linear model matrix formulas directly.

Phosphor type

A

B

C

Glass type

1

280, 290

300

270, 285, 290

2

230

260, 240

220, 225, 230
Statistics 4C03/6C03