Question

An administrator in the Department of Power and Electrical Engineering needs to upgrade computers for the Department. She wants to know what sort of computer system employees prefer. She has three available choices: windows, mac, linux or no preference. The observed data is shown in table below:

Type of Computer	Observed
Windows	20
Mac	60
Linux	20

Using the chi-square test of significance:
a) State the hypotheses
b) Test the hypothesis or theory that an equal percentage of the employees prefers each type of computer system.

Answer 1

Chi square test of goodness of fit.

Null hypothesis (H0) : Pwin = PMac = PLinux

Alternate hypothesis (Ha:) : Proportion not same

Type of computer	observed Frequency(Oi)	Expected Frequency(Ei)	(Oi - Ei)^2	((Oi-Ei)^2)/Ei
Window	20	33.33	177.8	5.33
Mac	60	33.33	711.1	21.33
Linux	20	33.33	177.8	5.33
Total	100			32.00

Chi Square value = 5.33+21.33+5.33 = 32.00

Here P value =0.00000011

Here p value < 0.01 so we reject Ho.

So we can conclude that proportion not same for employee prefers each type of computer system.