Question

 

The office occupancy rates were reported for four California metropolitan areas.
Do the following data suggest that the office vacancies were independent of the metropolitan area?
Run a hypothesis test at alpha of 0.05. What is your conclusion? Observed Frequencies           Occupancy Status/Metropolitan Area Los Angeles San Diego San Francisco San Jose Total Occupied 160 116 192 174 642 Vacant 40 34 33 26 133 Total 200 150 225 200 775

Answer 1

We use Chi-square Independence test.

Given: = 0.05

Hypothesis:

Ho: office vacancies were independent of the metropolitian area.

Ha: office vacancies were dependent of the metropolitian area.

Calculation

Expected Frequencies = (Corresponding row total * column total) / sample size

Where, sample size = 775

For First cell:

E1 = (642 * 200) / 775 = 165.68

Second cell:

E2 = (642 * 150) / 775 = 124.26

Third cell:

E3 = (642 * 225) / 775 = 186.39

.............

Computational table:

	Oi	Ei	(Oi-Ei)	(Oi-Ei)2	(Oi-Ei)2/Ei
	160	165.68	-5.68	32.23309	0.19
	116	124.26	-8.26	68.19563	0.55
	192	186.39	5.61	31.50468	0.17
	174	165.68	8.32	69.26535	0.42
	40	34.32	5.68	32.23309	0.94
	34	25.74	8.26	68.19563	2.65
	33	38.61	-5.61	31.50468	0.82
	26	34.32	-8.32	69.26535	2.02
Total	775	775.00			7.75

Test statistic:

Degrees of freedom = (r-1) * (c-1)

Where, r = Number of rows = 2

c = Number of columns = 4

Therefore, Degrees of freedom = (r-1)*(c-1) = (2-1)*(4-1) = 1*3 = 3

P-value: 0.051

Conclusion:

P-value > , 0.051 > 0.05, i.e Fail to Reject Ho at 5% level of significance.

Therefore, We can conclude that, the office vacancies were independent of the metropolitian area.