1. Non parametric test - Sign test for the following data
7,5,2,3,8,2,4,4,3,7,6,2,10
2,1,0,1,3,2,3,5,1,4,4,3,4, Significance Level `alpha=0.05` and One-tailed test

Solution:
Step-1: The sign test with the null hypothesis:
`H_0: p=0.50`.

`H_1: p!=0.50`.

Step-2: In 4th column, we put + if difference is positive, - if difference is negative and n/a if difference is zero.

#	A	B	Sign
1	7	2	+
2	5	1	+
3	2	0	+
4	3	1	+
5	8	3	+
6	2	2	n/a
7	4	3	+
8	4	5	-
9	3	1	+
10	7	4	+
11	6	4	+
12	2	3	-
13	10	4	+

To perform the test, we count number of + sign and number of - sign.
Number of plus sign = 10
Number of minus sign = 2
n = 10 + 2 = 12
`mu=np=12xx0.5=6`

`sigma=sqrt(npq)=sqrt(12xx0.5xx0.5)=sqrt(3)=1.7321`

Applying the z-test statistic, we get
`z=(bar x-mu)/(sigma)=(10-6)/(1.7321)=2.3094`

Step-3:
At `alpha=0.05`, the critical value of `Z_(0.05)=1.6449`

As calculated `z=2.3094 > 1.6449`

So, `H_0` is rejected.