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

1. The null hypothesis H0H0 is given by

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

2. The null hypothesis H1H1 is given by

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

3. If α=.05,n1=17,n2=32 and G=12α=.05,n1=17,n2=32 and G=12, then the test statistic is

A. z=−0.393388341965073z=−0.393388341965073.
B. z=+3.57742668080986z=+3.57742668080986.
C. G=−12G=−12.
D. z=−3.57742668080986z=−3.57742668080986.
E. z=0.393388341965073z=0.393388341965073.
F. G=12G=12.
G. z=+1.11661165803493z=+1.11661165803493.
H. z=−1.11661165803493z=−1.11661165803493.
I. z=−0.606611658034927z=−0.606611658034927.
J. z=+0.606611658034927z=+0.606611658034927.
K. None of the above.

4. If α=.01,n1=17,n2=32 and G=12α=.01,n1=17,n2=32 and G=12, then the test statistic is

A. z=0.393388341965073z=0.393388341965073.
B. z=−1.11661165803493z=−1.11661165803493.
C. z=−3.57742668080986z=−3.57742668080986.
D. z=−0.393388341965073z=−0.393388341965073.
E. z=+0.606611658034927z=+0.606611658034927.
F. z=−0.606611658034927z=−0.606611658034927.
G. G=−12G=−12.
H. G=12G=12.
I. z=+3.57742668080986z=+3.57742668080986.
J. z=+1.11661165803493z=+1.11661165803493.
K. None of the above.

Answer 1

We wish to test a claim that a sequence of sample data was produced in a random manner

Thus

1. The null hypothesis H0 is given by

G. H0 : The data are in a random order

2. The null hypothesis H1 is given by

E.   H1 :The data are in an order that is not random

3.If α=.05,n1=17,n2=32 and G=12, then the test statistic is

Fisrt we will calculate mean and variance

Mean E(G) = u = + 1 = + 1 = 22.20408 +1 = 23.20408

Standard Devitaion SD(G) = =

After calculation  SD(G) = = 3.131883

test statistic is given by

z = = =    -3.577426

Thus test statistic is z = -3.577426

So correct option is

D. z=−3.57742668080986

4. If α=.01,n1=17,n2=32 and G=12 , then the test statistic is

Mean E(G) = u = + 1 = + 1 = 22.20408 +1 = 23.20408

SD(G) = =

After calculation  SD(G) = = 3.131883

Test statistic is given by

z = = =    -3.577426

Thus test statistic is z = -3.577426

So correct option is

C. z=−3.57742668080986

Note that Question 3 and Question 4 are same i.e same questions are repeated twice . So we were only asked about test Statistics which will be same for both question .