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.

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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 6 8 8 14 10 6 12 13 11

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

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

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.

Integer 0 1 2 3 4 5 6 7 8 9
Frequency 12 6 8 8 14 10 6 12 13 11

We have to test if there is sufficient reason to believe that the integers are not being generated uniformly .

Thus H0 and H1 are:

H0: the integers are  being generated uniformly

Vs

H1: the integers are not being generated uniformly

Part a) Find the test statistic

\chi ^{2}=\sum \frac{O_{i}^{2}}{E_{i}}-N