Question

In: Math

) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical...

) 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?

Solutions

Expert Solution

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.


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