1 Test the following sequence for randomness at 005 A A A A

1. Test the following sequence for randomness at = 0.05.

A A A A B B B A A A B B

Table of Critical Values for the Number of Runs, = 0.05

Value of

n1

2

9

3

10

3

11

3

12

2

10

3

11

3

12

3

13

3

10

3

11

3

12

4

13

a. Do not reject the hypothesis that the sequence is random, because the test value 4 is between the critical values 3 and 11.

b. Do not reject the hypothesis that the sequence is random, because the test value 3 is between the critical values 3 and 10.

c. Do not reject the hypothesis that the sequence is random, because the test value 5 is outside

d. Reject the hypothesis that the sequence is random, because the test value 3 is between the critical values 3 and 11.

2. How many runs are in the following sequence?
A A A A B B B B B A B A

a. 5

b.6

c. 7

d.8

Solution

1.

n1 -number of A\'s = 7

n2 - number of B\'s = 5

Corresponding critical values from table are 3 and 11.

Number of runs = 4

d. Reject the hypothesis that the sequence is random, because the test value 3 is between the critical values 3 and 11.

2.

Each bracket represents one run.

(AAAA)(BBBBB)(A)(B)(A)

Thus in the given sequence there are 5 runs.