Question

For the data in the table below, assume a uniform distribution. Estimate the parameters for this distribution, and perform a Chi Squared goodness of fit test on what is assumed to be a uniform distribution.

6.40	4.39	6.86	5.24	4.01
5.54	4.50	5.69	5.85	5.42
5.94	6.78	6.52	5.82	6.46
4.65	4.20	5.25	6.58	4.73
6.53	4.99	5.90	5.51	6.50

Answer 1

The null hypothesis

H0: the data follow uniform distribution

Test statistic

where

Oi : observed frequency

Ei : expected frequency

First we find sample mean = (6.40+.....+6.50)/25 = 5.61

For Uniform distribution ,each observation has a equal probability and therefore equal expected frequency

Calculation

	Oi	Ei	(Oi-Ei)^2/Ei
	4.01	5.6104	0.45652363
	4.2	5.6104	0.35456084
	4.39	5.6104	0.26546702
	4.5	5.6104	0.21976832
	4.65	5.6104	0.16440328
	4.73	5.6104	0.13815488
	4.99	5.6104	0.06860405
	5.24	5.6104	0.0244539
	5.25	5.6104	0.02315132
	5.42	5.6104	0.0064616
	5.51	5.6104	0.00179669
	5.54	5.6104	0.00088339
	5.69	5.6104	0.00112936
	5.82	5.6104	0.00783049
	5.85	5.6104	0.01023245
	5.9	5.6104	0.0149487
	5.94	5.6104	0.01936335
	6.4	5.6104	0.11112722
	6.46	5.6104	0.12865752
	6.5	5.6104	0.14105735
	6.52	5.6104	0.14747115
	6.53	5.6104	0.15073153
	6.58	5.6104	0.16756812
	6.78	5.6104	0.24382649
	6.86	5.6104	0.27832243
total			3.14649508

Therefore ,

degrees of freedom = 25-1=24

P value = 1.000

Since P value > 0.05

The result is not significant

We fail to reject H0

There is not sufficient evidence to conclude that the sample data do not follow uniform distribution .