Question

A random number generator in an ESP experiment is supposed to produce digits one through five with equal frequency. In 900 trials, the results were 170 ones, 210 twos, 163 threes, 175 fours and 182 fives. The researcher wishes to run a statistical test.

Answer 1

The researcher wishes to conduct a goodness of fit test, where his null hypothesis would be that probability of producing any one of 1 to 5 is 1/5. with the alternative is they are different. So, the expected frequency for producing any of the digits is 900/5 = 180. Let

Then, the test-statistic is given by

By, calculation we get the observed value of test statistic as

p-value of the test is given by

Which means we fail to reject H₀. We conclude that the random number generator produces random digits with equal probability