Question

Let X equal the number of chocalate chips in a chocalate chip cookie. Sixty-two oberservations of X yielded the following frequencies for the possible outcomes of X:

Outcome (x)	0	1	2	3	4	5	6	7	8	9	10
Frequency	0	0	2	8	7	13	13	10	4	4	1

(a) Use this data to graph the relative frequency histogram and the Poisson probability with

lamda = 5.6 on the same figure.

(b) Do these data seem to be observations of a Poisson random variable with

lamda = 5.6 ?

Answer 1

x	f(x)	Relative frequency=f(x)/sum(f(x))	Poisson probbaility
0	0	0.000	0.003697864
1	0	0.000	0.020708037
2	2	0.032	0.057982503
3	8	0.129	0.108234006
4	7	0.113	0.151527608
5	13	0.210	0.169710921
6	13	0.210	0.15839686
7	10	0.161	0.126717488
8	4	0.065	0.088702241
9	4	0.065	0.055192506
10	1	0.016	0.030907803
sum(f(X))=	62

note: To calculate poission probbailities we use the following formula:

b) To test whether the observations are from the poisson distribution we use the chi square goodness of fit test which is given as:

Where:

~

Where n= no. of observations=11

Oi	Ei	(Oi-Ei)^2/Ei
0	0.003698	0.004
0	0.020708	0.021
0.032258	0.057983	0.011
0.129032	0.108234	0.004
0.112903	0.151528	0.010
0.209677	0.169711	0.009
0.209677	0.158397	0.017
0.16129	0.126717	0.009
0.064516	0.088702	0.007
0.064516	0.055193	0.002
0.016129	0.030908	0.007
	=	0.100

Since calculated (4.57) at 5% level of significance we conclude that the data seem to be observations of poission random variable with lamda =5.6