Question

These numbers have been drawn from a uniform distribution with range 1-40.

4, 6, 16, 12, 23, 19, 16 26, 14, 12, 12, 10, 3, 26, 35, 8, 30, 11, 14, 34, 37, 16, 36, 30, 18, 39, 24, 18, 39, 5, 12, 28, 4, 12, 34, 16, 35, 27, 15, 1

Test the sample for randomness using:

1. a graphical method.
2. a Chi-square tests.
3. a Kolmogorov—Smirnov test.

Answer 1

These numbers have been drawn from a uniform distribution with range 1-40.

4, 6, 16, 12, 23, 19, 16 26, 14, 12, 12, 10, 3, 26, 35, 8, 30, 11, 14, 34, 37, 16, 36, 30, 18, 39, 24, 18, 39, 5, 12, 28, 4, 12, 34, 16, 35, 27, 15, 1

b. Chi Square test for goodness

These numbers converted into continuous frequency distribution.

Here range 1- 40

The continuous uniform distribution.

X~CU(a=1,b=50)

f(x)=1/(b-a)

Distribution function

F(X)=(x-a)/(b-a)

=( X-1)/(40-1)

= (X-1)/39

Class	f	ul X	F(X)	p(X)	Ei	(Oi-Ei)^2/Ei
0-10	07	10	0.2307	0.2307	9.228	0.5379
10-20	17	20	0.4871	0.2307	9.228	6.5457
20-30	06	30	0.7435	0.2307	9.228	1.1291
30-40	10	40	1	0.2307	9.228	0.0645
-	total fi=40					Total= 8.2772

Ho: The given sample fit for continuous uniform distribution.

H1: The given sample does not fit for continuous uniform distribution.

Calculated value=8.2772

Tabulated value= chi square tab( n-1;5%)

= chi square tab (4-1;0.05)

=7.81

Chi square calculated greater than chi square table.

The sample does not fit for uniform distribution.