STAT 330

Assignment 3

1. From text (3rd ed in parentheses): Chapter 9, Q 59(58), 60(59), 66(62), 70(66), 74(71), 75(72).

2. In 1879, over the period from June 5 to July 2, Michelson carried out a number of measurements of the speed of light. The first 20 measurements and last 20 measurements (minus 299000 km/sec) and several summary statistics are recorded below.

   

   Has the bias of the measurements changed between the first 20 and the last 20?

3. Annual records were kept in the Prussian army for the number of deaths by horsekick.

   

   1. Use a Poisson model and obtain a 95% confidence interval for the long run average mean number of deaths per year.
   2. Develop a test of the hypothesis that there has been no change in this underlying death rate over the time period in question as follows. Let N be the number of deaths in the first 10 years and M the number in the second 10 years. If the Poisson model with constant death rate is credible then M and N have the same mean. What is the standard error of N-M in terms of the Poisson parameter? How can you estimate this standard error? How can you use this to test the hypothesis that there is no change in mean?

DUE: Wednesday, 28 January