13 Consider the following frequency table of observation on

13. Consider the following frequency table of observation on the random variable X. (a)Based on these 100 observations, is a Poisson distribution with a mean of 2.4 an appropriate model? Perform a goodness-of-fit procedure with a = 0.05. (b)Calculate the P-value for this test.

Solution

Data

Mean/Expected number of events of interest:

2.4

POISSON.DIST Probabilities Table

Observed

X

P(X)

Expected=p*100

8

0

0.0907

9.0718

25

1

0.2177

21.7723

23

2

0.2613

26.1268

21

3

0.2090

20.9014

16

4

0.1254

12.5408

7

5

0.0602

6.0196

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

8

9.072

-1.072

0.127

25

21.772

3.228

0.478

23

26.127

-3.127

0.374

21

20.901

0.099

0.000

16

12.541

3.459

0.954

7

6.020

0.980

0.160

100

96.433

3.567

2.094

Warning: sums should be equal.

2.094

chi-square

5

df

.8360

p-value

Chi square value at 0.05 level with 5 DF =11.070

Calculated chi square =2.094 < 11.070 the table value

The null hypothesis is not rejected

We conclude that this distribution is a Poisson with mean 2.4.

b).

P value =0.8360

Data
Mean/Expected number of events of interest:				2.4
POISSON.DIST Probabilities Table
Observed	X	P(X)	Expected=p*100
8	0	0.0907	9.0718
25	1	0.2177	21.7723
23	2	0.2613	26.1268
21	3	0.2090	20.9014
16	4	0.1254	12.5408
7	5	0.0602	6.0196