1. Test the following sequence for randomness at = 0.05. A A A A B B B A A A B B
ID: 3437299 • Letter: 1
Question
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
Value of
n1
Value of n2Explanation / Answer
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.
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