Statistics 4C03/6C03 - Test #1

2006-02-08 17:30-19:30

This test is to be written in the BSB Student Technology Centre. 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.
When no particular method is specified and there is a choice, you are free to use any method you like.

Part A.

Analyse the following two examples. Include an appropriate graph, an ANOVA table and a 99% confidence interval for the residual variance. State your assumptions and your conclusions.

  1. The following data resulted from an experiment to investigate whether yield from a certain chemical process depended on either the formulation of a particular input or the mixer speed.

    Speed
    60 70 80
    Formulation 1 189.7, 188.6, 190.1 185.1, 179.4, 177.3 189.0, 193.0, 191.1
    2 165.1, 165.9, 167.6 161.7, 159.8, 161.6 163.3, 166.6, 170.3

  2. The following data come from a paper “Cotton square damage by the plant bug, Lygus hesperus, and abcission rates.”

    age of a cotton plant (days): 9 12 12 15 18 18 21 21 27 30 30 33
    percent damaged squares: 11 12 23 30 29 52 41 65 60 72 84 93

Part B.

Here are 20 independent observations from an inverse Gaussian distribution.

 9.589359 46.853136  3.241903 26.681170 24.020465  6.851572
 6.463341  8.290286  3.425824  4.843495 13.809297  4.212797
 8.309223  8.464925  3.576289 37.117973 16.066626  3.028943
 4.602975  5.758892
  1. Plot 90%, 95% and 99% joint confidence regions for the inverse Gaussian parameters mu and lambda.
  2. Test the hypothesis that mu = 10, assuming (a) inverse Gaussian data, (b) gamma data, (c) normal data, giving a P-value for each test.
  3. Test the hypothesis that mu = 20, assuming (a) inverse Gaussian data, (b) gamma data, (c) normal data, giving a P-value for each test.
  4. In this example, was it worthwhile to develop an inverse Gauussian test, or was the t-test good enough?
Statistics 4C03/6C03