In: Math
) 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 Sample 6 10 8
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?
Using Minitab software, (Stat -> ANOVA -> One way),we get the following output :
Now,
The value of F statistic = 4.5
and P-value = 0.044
Since P-value > 0.01, so we fail to reject H0 at 1% level of significance and we can conclude that there is no significant difference in vacancy rates among the regions.