Question

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

Answer 1

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)	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