Question

Suppose that we wish to test a claim that a sequence of sample data was produced in a random manner, and suppose that each data value belongs to one of two categories. Let n1n1 be the number of elements in the sequence that belong to the first category, n2n2 be the number of elements in the sequence that belong to the second category, and GG be the number of runs in such a sequence.

Answer each of the following questions

(a) The null hypothesis H0H0 is given by

A. β=0β=0
B. n1=n2n1=n2
C. ρ=0ρ=0
D. G=0G=0
E. The data are in a random order
F. r=0r=0
G. The data are in an order that is not random
H. Median=0=0
I. None of the above.

(b) The null hypothesis H1H1 is given by

A. The data are in an order that is not random
B. G≠0
C. n1≠n2n
D. The data are in a random order
E. Median ≠0
F. β≠0
G. r≠0
H. ρ≠0
I. None of the above.

(c) If α=.05,n1=11,n2=10 and G=11α=.05,n1=11,n2=10 and G=11, then the test statistic is

A. z=−1.73818884141813
B. z=+0.213735725267969
C. z=−1.77383808744063
D. z=0.786264274732031
E. z=+1.73818884141813
F. z=−0.213735725267969
G. G=11.
H. G=−11
I. z=+1.77383808744063
J. z=−0.786264274732031
K. None of the above.

(d) If α=.01,n1=10,n2=11 and G=11α=.01,n1=10,n2=11 and G=11, then the test statistic is

A. z=−1.78626427473203
B. z=−0.786264274732031
C. z=0.786264274732031
D. G=11G=11.
E. z=0.276264274732031
F. G=−11
G. z=−0.276264274732031
H. z=+0.213735725267969
I. z=1.78626427473203
J. z=−0.213735725267969
K. None of the above.

Answer 1

In this question we want to test a claim that a sequence of sample data was produced in a random manner. In other words it is a question of non parametric run test for randomness.

Answer (a) we want to test the randomness of data so the statement of null hypothesis will negate any deviation from this this claim.

so, the null hypothesis H0 is given by

Correct option: E. The data are in a random order

Answer (b)

we want to test the randomness of data so the statement of alternative hypothesis will give an indication of deviation from this this claim.

so, the alternative hypothesis H1 is given by

Correct option: A. The data are in an order that is not random

Answer (c)

Given

G=11

α=.05,

n1=11,

n2=10

Here, n1 and n2 both are less than 20. Hence we will use small sample run test for randomness.

for small sample run the test statistics is given by number of runs.

So test statistics is G=11

Correct option: G. G=11

Answer (d)

Given

G=11

α=.01,

n1=11,

n2=10

Here, n1 and n2 both are less than 20. Hence we will use small sample run test for randomness.

for small sample run the test statistics is given by number of runs.

So test statistics is G=11

Correct option: D. G=11