In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.

R RRR D R D R RR D R RR D D R D D R R D R R D R D

Runs Test If we use a 0.05 significance level to test for randomness, what are the critical values from Table A-10? Based on those values and the number of runs from Exercise 2, what should be concluded about randomness?

A sequence of presidents corresponding to their political party affiliations is provided.

The level of significance\(\left( \alpha \right)\)is equal to 0.05.

Refer to Exercise 2 of Section 13-7. The sample values are \({n_1} = 17\) and \({n_2} = 10\).

Here,\({n_1} = 17\)and\({n_2} = 10\).

Since both\({n_1}\)and\({n_2}\)are less than 20, the critical value of G is noted from Table A-10.

The critical values of G corresponding to \(\alpha = 0.05\), \({n_1} = 17\), and \({n_2} = 10\) are 8 and 19.

The null hypothesis is as follows:

The two categories occur in random order.

The alternative hypothesis is as follows:

The two categories do not occur in random order.

The test statistic is G with a value equal to 16.

Since the value of G is not less than or equal to 8 and neither greater than or equal to 19,so the decision is fail to reject the null hypothesis.

There is not enough evidence to conclude that the sequence is not random.