Question

(15pt) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following data are the rental vacancy rates in percentage (%) grouped by region for the first quarter of 2019 using a sample of 4 statistical metropolitan areas. Vacancy rates (%) Region northeast south west 1 6 12 8 2 5 9 10 3 9 11 8 4 4 8 6 sample mean 6 10 8 sample variance 4.7 3.3 2.7 a. (10pt) Perform an ANOVA test to find if there are vacancy rates differences among the regions. Allow 1% error on your test. b. (5pt) Do you think that the mean vacancy rate is the same for these regions? Why?

Answer 1

Answer:

Using One way ANOVA:

From the output,

F statistic = 4.5

P-value = 0.044

Since, p-value > 0.01 (alpha), we failed to reject the null hypothesis.

Hence, we conclude that there is no significant difference in vacancy rates among the regions.

Therefore, the mean vacancy rate is same for these regions.