Example 16-8 Section
This is how I used Minitab to help with the calculations of the alpha particle example on the Unspecified Probabilities page in this lesson.
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Use Minitab's Calc >> Probability distribution >> Poisson command to determine the Poisson(5.6) probabilities:
Poisson with mean = 5.6 x P (X = x) 0 0.003698 1 0.020708 2 0.057983 3 0.108234 4 0.151528 5 0.169711 6 0.158397 7 0.126717 8 0.088702 9 0.055193 10 0.030908 11 0.015735 12 0.007343 -
Enter the observed counts into one column and copy the probabilities (collapsing some categories, if necessary) into another column. Use Minitab's Calc >> Calculator command to generate the remaining necessary columns:
Poisson with mean = 5.6 Row Obsd p_i Expd Chisq 1 5 0.082389 8.2389 1.27329 2 15 0.108234 10.8234 0.43772 3 19 0.151528 15.1528 0.97678 4 16 0.169711 16.9711 0.05557 5 15 0.158397 15.8397 0.04451 6 9 0.126717 12.6717 1.06390 7 12 0.088702 8.8702 1.10433 8 7 0.055193 5.5193 0.39724 9 4 0.053986 5.3986 0.36233 Sum up the "Chisq" column to obtain the chi-square statistic Q.
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Example 16-9 Section
This is how I used Minitab to help with the calculations of the IQ example on the Continuous Random Variables page in this lesson.
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The sorted data:
Sample 54 66 74 74 75 78 79 80 81 82 82 82 83 84 87 88 88 88 88 89 89 89 89 89 90 90 90 91 92 93 93 93 94 96 96 97 97 98 98 99 99 99 99 99 100 100 100 102 102 102 102 102 103 103 104 104 104 105 105 105 105 106 106 106 107 107 108 108 108 109 109 109 110 111 111 111 111 112 112 112 114 114 115 115 115 116 118 118 120 121 121 122 123 125 126 127 127 131 132 139 -
The working table:
Row CProb Z Sample Obsd Expd Chisq 1 0.1 -1.28155 79.495 7 10 0.9 2 0.2 -0.84162 86.534 7 10 0.9 3 0.3 -0.52440 91.610 14 10 1.6 4 0.4 -0.25355 95.946 5 10 2.5 5 0.5 0.00000 100.000 14 10 1.6 6 0.6 0.25355 104.054 10 10 0.0 7 0.7 0.52440 108.390 12 10 0.4 8 0.8 0.84162 113.466 11 10 0.1 9 0.9 1.28155 120.505 9 10 0.1 10 11 10 0.1
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The chi-square statistic:
