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.

 First 20 Second 20 Difference 850 890 -40 740 840 -100 900 780 120 1070 810 260 930 760 170 850 810 40 950 790 160 980 810 170 980 820 160 880 850 30 1000 870 130 980 870 110 930 810 120 650 740 -90 760 810 -50 810 940 -130 1000 950 50 1000 800 200 960 810 150 960 870 90 Average=909 Average=831.5 Average=77.5 SD=104.9 SD=54.2 SD=109.8

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.

 Year Number of Year Number of deaths deaths 1875 3 1885 5 1876 5 1886 11 1877 7 1887 15 1070 9 1888 6 1879 10 1889 11 1880 18 1890 17 1881 6 1891 12 1882 14 1892 15 1883 11 1893 8 1884 9 1894 4 Total 92 104

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?

Solutions

Richard Lockhart
Tue Sep 3 19:16:15 PDT 1996