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

 

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: Office vacancies and metropolitan area are independent.
H_a: Office vacancies and metropolitan area are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (4 - 1)
D.F = 3
E_r,c = (n_r * n_c) / n


Χ² = 7.753

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 7.753.

We use the Chi-Square Distribution Calculator to find P(Χ² > 7.753) = 0.051

Interpret results. Since the P-value (0.051) is greater than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between Office vacancies and metropolitan area.