Question

Cybersecurity When using the data from Exercise 1 to test for goodness-of-fit with the distribution described by Benford’s law, identify the null and alternative hypotheses.

Short answer

The null hypothesis and the alternative hypothesis is

\(\begin{aligned}{l}{H_0}:{p_1} = 0.301,{p_2} = 0.176,{p_3} = 0.125,{p_4} = 0.097,{p_5} = 0.079,{p_6} = 0.067,{p_7} = 0.058,\\\;\;\;\;\;{p_8} = 0.051,{p_9} = 0.046\end{aligned}\)

\({H_1}:\)At least one of the proportions will differ from the others.

Step-by-step solution

Given information

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

Identify the hypotheses

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.

\(\begin{aligned}{l}{H_0}:{p_1} = 0.301,{p_2} = 0.176,{p_3} = 0.125,{p_4} = 0.097,{p_5} = 0.079,{p_6} = 0.067,{p_7} = 0.058,\\\;\;\;\;\;{p_8} = 0.051,{p_9} = 0.046\end{aligned}\)

Alternative Hypothesis:

The alternative hypothesis is that in which at least one of the proportions should not be equal to the claimed value.