3) (8pt) The U.S. Census Bureau computes quarterly vacancy and homeownership rat

Question

3) (8pt) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following table shows the rental vacancy rates in percentage (%) grouped by region for the last quarter of 2017 using a sample of 4 statistical metropolitan areas ANOVA TABLE Source ofSum of Degrees Mean variation ! Squares | of | Square freedom(MS) Vacancy rates (% ) Region Northeast SouthWest Treatment Error Total 4 3.27 1.22 4 sample mean 7 19 a(5pt) Conduct a Fisher test allowing for 10% error. b.(3pt) According to the result of your test, did you find differences in vacancy rates in these regions? WHY?

Explanation / Answer

Sol:

a. Fisher test

Null hypothesis Ho : There is no significant difference in vacancy rates in the regions.

Alternate hypothesis H1 : There is significant difference in vacancy rates in the regions.

Decision criteria : If calculated F statistic > Tabulated Falpha ( critical value ) , we reject Ho at alpha (level of significance) or if calculated F statistic < Tabulated F1-alpha ( critical value ) , we reject Ho at alpha (level of significance)

From the given ANOVA table,

Calculated F statistic = 3.27

Tabulated F alpha(2,9) = 3.006452 at alpha = 0.10

Tabulated F 1-alpha(2,9) = 0.106604 at alpha = 0.10

Since, Calculated F statistic = 3.27 > 3.006472 Tabulated F ( critical value ) , we reject Ho at alpha = 0.10 (level of significance).

(b)  Since we reject Ho , we can conclude that  there is significant difference in vacancy rates in the regions.

Reason : The test statistic value we computed lies in the critical region of rejection.

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