Question

A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9. The frequencies of the observed integers were as follows. At the 0.05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?

Integer	0	1	2	3	4	5	6	7	8	9
Frequency	12	9	7	7	12	12	6	8	12	15

(a) Find the test statistic. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)


(b) State the appropriate conclusion.

Reject the null hypothesis. There is not significant evidence that the integers are not being generated uniformly. Fail to reject the null hypothesis. There is significant evidence that the integers are not being generated uniformly.     Reject the null hypothesis. There is significant evidence that the integers are not being generated uniformly. Fail to reject the null hypothesis. There is not significant evidence that the integers are not being generated uniformly.

Answer 1

a)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
0	0.1000	12.0000	10.00	0.63	0.400
1	0.1000	9.0000	10.00	-0.32	0.100
2	0.1000	7.0000	10.00	-0.95	0.900
3	0.1000	7.0000	10.00	-0.95	0.900
4	0.1000	12.0000	10.00	0.63	0.400
5	0.1000	12.0000	10.00	0.63	0.400
6	0.1000	6.0000	10.00	-1.26	1.600
7	0.1000	8.0000	10.00	-0.63	0.400
8	0.1000	12.0000	10.00	0.63	0.400
9	0.1000	15.0000	10.00	1.58	2.500
total	1.000	100	100		8.0000
test statistic X2 =		8.0000

ii)

degree of freedom =categories-1=

9

from excel p value =chidist(8,9)=

0.5341

Fail to reject the null hypothesis. There is not significant evidence that the integers are not being generated uniformly.