1. THE RUNS TEST FOR RANDOMNESS
Determine the number of runs, V, for each of these sequences:
(a) A B A B B A A A B B A B
(b) H H T H H H T T T T H H T H H T H T
2. Twenty-five individuals were sampled as to whether they liked or did not like a product (indicated by Y and N, respectively). The resulting sample is shown by the following sequence:
Y Y N N N N Y Y Y N Y N N Y N N N N N Y Y Y Y N N
(a) Determine the number of runs, V.
(b) Test at the 0.05 significance level whether the responses are random.
3. Use the runs test on sequences (10) and (11) in this chapter, and state any conclusions about randomness.
4. (a) Form all possible sequences consisting of two a’s and one b, and give the number of runs, V, corresponding to each sequence.
(b) Obtain the sampling distribution of V and its graph.
(c) Obtain the probability distribution of V and its graph.
5. In Problem 17.58, find the mean and variance of V (a) directly from the sampling distribution and (b) by formula.
6. Work Problems 17.58 and 17.59 for the cases in which there are (a) two a’s and two b’s, (b) one a and three b’s, and (c) one a and four b’s.
7. Work Problems 17.58 and 17.59 for the case in which there are two a’s and four b’s.