91Ó°ÊÓ

The observed frequencies and the expected frequencies of the leading digits of inter-arrival traffic times are tabulated.

The following hypotheses are set up to test for the goodness of fit test of the given distribution:

Null Hypothesis:

The null hypothesis is that in which the proportions of all the leading digits should be equal to the claimed value. In other words, thedistribution of the leading digits fits well with Benford’s law.

Alternative Hypothesis:

The alternative hypothesis is that in which thedistribution of the leading digits does not fit well with Benford’s law.

The test statistic value\(\left( {{\chi ^2}} \right)\)is equal to 20.9222.

The corresponding p-value is equal to 0.0074.

The critical chi-square value is 15.5073.

Assume the significance level is 0.05.

Since the test statistic is greater than the critical value, so the null hypothesis is rejected.

Since the p-value is less than 0.05, the null hypothesis is rejected.

Thus, there is enough evidence to warrant rejection of the claim that the leading digits have a distribution that fits well with Benford’s law.