Question

# Data on the number of occurrences per time period and observed frequencies follow. Use α =...

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*1.3x/x!

from above:

applying goodness of fit test:

 relative observed Expected Chi square Category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei 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 X2= 8.334

option A is correct

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