Question

Different colors of floor tiles are going to be installed in a random pattern with the frequency of each color being same. A sample of 200 tiles laid exactly as they were packaged was observed and the following was found: Color and number of tiles orange-32, white-36, blue-48, green-50, violet-34.Test the hypothesis at the 5 percent level of significance for the uniform color distribution.  

Answer 1

We need to check whether the color distribution so uniform so hypotheses are:

H0: The color distribution is uniform.

Ha: The color distribution is not uniform.

If all the five colors are equally likely then expected frequency for each color is 200 /5 = 40.

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
32	40	1.6
36	40	0.4
48	40	1.6
50	40	2.5
34	40	0.9
Total		7

Following is the test statistics:

Degree of freedom: df =5-1=4

The p-value is: 0.1359

Since p-value is greater than 0.05 so we fail to reject the null hypothesis. That is we can conclude that the color distribution is uniform.

Excel function used for p-value: "=CHIDIST(7,4)"