Data on the number of occurrences per time period and observed frequencies follow. Use α = .05 to perform the goodness of fit test to see whether the data fit a Poisson distribution. Calculate the the value of test statistic. Use the "Number of Occurences" as the categories.
Number of occurrences numbers of frequency
0 39
1 30
2 30
3 18
4 3
a) 8.334
b) 1.30
c) 3.142
d) 5
here weighted average mean=(39*0+30*1+30*2+18*3+3*4)/(39+30+30+18+3)=1.3
since P(x=x)=e^{-1.3}*1.3^{x}/x!
from above:
applying goodness of fit test:
relative | observed | Expected | Chi square | ||
Category | frequency(p) | O_{i} | E_{i}=total*p | R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} | |
0 | 0.2725 | 39 | 32.70 | 1.2122 | |
1 | 0.3543 | 30 | 42.51 | 3.6840 | |
2 | 0.2303 | 30 | 27.63 | 0.2024 | |
3 | 0.0998 | 18 | 11.98 | 3.0313 | |
4 | 0.0324 | 3 | 3.89 | 0.2044 | |
total | 0.99 | 120 | 118.72044 | 8.3343 | |
test statistic X^{2}= | 8.334 |
option A is correct
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