A program for generating random numbers on a computer is to be tested. The progr

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 .05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?

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


(ii) Find the p-value. (Give your answer bounds exactly.)
__ < p < __

Integer 0 1 2 3 4 5 6 7 8 9 Frequency 5 12 10 14 14 4 4 11 6 20

Explanation / Answer

test stat chi square =25

and p vlaue =0.0030

observed Expected Chi square Integers Probability O E=total*p =(O-E)^2/E 0 0.100 5.00 10.00 2.50 1 0.100 12.00 10.00 0.40 2 0.100 10.00 10.00 0.00 3 0.100 14.00 10.00 1.60 4 0.100 14.00 10.00 1.60 5 0.100 4.00 10.00 3.60 6 0.100 4.00 10.00 3.60 7 0.100 11.00 10.00 0.10 8 0.100 6.00 10.00 1.60 9 0.100 20.00 10.00 10.00 100 100 25.000

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