91影视

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

a.

The observed frequencies are represented by O.

The expected frequencies are represented by E.

b.

The observed frequency (O) corresponding to the leading digit of 2 is equal to 62.

The formula to compute the expected frequency is as follows:

\(E = np\)where

n is the sum of all observed frequencies

p is the probability of occurrence of that outcome.

Here, the sum of all observed frequencies is computed below:

\(\begin{aligned}{c}n = 76 + 62 + ..... + 22\\ = 317\end{aligned}\)

The value of p for the leading digit of 2 is equal to:

\(\begin{aligned}{c}p = 17.6\% \\ = \frac{{17.6}}{{100}}\\ = 0.176\end{aligned}\)

Thus, the expected frequency of the leading digit of 2 is computed below:

\(\begin{aligned}{c}E = np\\ = 317\left( {0.176} \right)\\ = 55.792\end{aligned}\)

Therefore, the expected frequency of the leading digit of 2 is equal to 55.792.

c.

The contribution to thechi-squaretest statistic from the category representing the leading digit of 2 is computed below:

\(\begin{aligned}{c}\frac{{{{\left( {O - E} \right)}^2}}}{E} = \frac{{{{\left( {62 - 55.792} \right)}^2}}}{{55.792}}\\ = 0.6907\\ \approx 0.691\end{aligned}\)

Thus, the contribution to the chi-squaretest statistic from the category representing the leading digit of 2 is equal to 0.691.