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

Please explain in the excel sheet

Answer 1

Null Hypothesis(H0):

The office vacancies were independent of the metropolitan area.

(There is no significant difference between the observed and expected frequencies).

Alternative Hypothesis(H1):

The office vacancies were not independent of the metropolitan area.

(There is a significant difference between the observed and expected frequencies).

Observed and expected frequencies for "Vacant":

So, the test statistic is: =6.4223

Degrees of freedom, df =n - 1 =4 - 1 =3

Given significance level (alpha) =0.05

At 0.05 alpha and at df =3, the critical value of Chi-square is: =7.8147

Conclusion:

Since the test statistic, of 6.4223 < of 7.8147, we failed to reject the null hypothesis(H0) at 0.05 significance level. Thus, we do not have enough evidence to claim that there is a significant difference between the observed and expected frequencies.

So, the given data suggest that the office vacancies were independent of the metropolitan area.