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