Question

Runs Test/G:

Consider the following sequence:

DDD EE DDD EE DD E DD EEE DD E DDDD EEEEE DD

With a 0.05 significance level, we wish to test the claim that the above sequence was produced in a random manner. Answer each of the following questions

(a) The null hypothesis H0 is given by

A. Median=0
B. ρ=0
C. The data are in a random order
D. The data are in an order that is not random
E. β=0
F. G=0
G. r=0
H. n1=n2
I. None of the above.

(b) The null hypothesis H1 is given by

A. ρ≠0
B. The data are in an order that is not random
C. Median ≠0
D. n1≠n2
E. G≠0
F. β≠0
G. r≠0
H. The data are in a random order
I. None of the above.

(c) The number of runs G is

A. 32
B. 24
C. 18
D. 34
E. 14
F. 13
G. None of the above.

(d) What kind of test should you conduct

A. Runs test for randomness and the test statisc is a z-score
B. Sign test
C. Goodness of fit test
D. Runs test for randomness and the test statistic is G
E. Independence Test
F. Both sign and goodness of fit tests
G. None of the above.

(e) What is/are the critical(s) value(s)

A. The only critical value is 23
B. The smallest one is 10 and the largest one is 23
C. The only critical value is 10
D. The negative one is -1.96 and the positive one is 1.96
E. The only critical value is 1.96
F. The only critical value is -1.96
G. The smallest one is -1.96 and the largest one is 1.96
H. None of the above.

(f) The conclusion:

A. We reject H0 and then there isn't enough evidence to support the claim that the above sequence was in a random order
B. We fail to reject H0 and then there isn't enough evidence to reject the claim that the above sequence was in a random order.
C. We reject H0 and then there is enough evidence to reject the claim that the above sequence was in a random order
D. We fail to reject H0 and then there is enough evidence to support the claim that the above sequence was in a random order
E. We fail to reject H0 and then there is enough evidence to reject the claim that the above sequence was in a random order
F. We reject H0 and then there is enough evidence to support the claim that the above sequence was in a random order
G. We fail to reject H0 and then there isn't enough evidence to support the claim that the above sequence was in a random order
H. We reject H0 and then there isn't enough evidence to reject the claim that the above sequence was in a random order
I. None of the above.

Answer 1

a) ans
C. The data are in a random order

b) ans
B.The data are in an order that is not random

c)ans F. 13

d)ans
D.Runs test for randomness and the test statistic is G

e) ans
B. The smallest one is 10 and the largest one is 23
Explanation :
DDD EE DDD EE DD E DD EEE DD E DDDD EEEEE DD
n1 : number of D =18
n2 : number of E =14
G : number of runs = 13
We can find the lower and upper critical value from statistical run table
Lower critical value = 10
Upper critical value = 23

d) ans
B. We fail to reject H0 and then there isn't enough evidence to reject the claim that the above sequence was in a random order.

Explanation : number of runs lies between lower critical value & upper critical value.
So we fail to reject Ho.

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