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

Question

3) (Spt) 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 Vacancy rates(%) Source of SDegreesMean F variation of Square (SS) freedom (MS) Region Northeast South West 3.27 9 81.22 Error sample mean Total 19 a(5pt) Conduct a Eisher 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

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/2 ( critical value ) , we reject Ho at alpha (level of significance) or if calculated F statistic < Tabulated F1-alpha/2 ( critical value ) , we reject Ho at alpha (level of significance)

From the given ANOVA table,

Calculated F statistic = 3.27

Tabulated F alpha/2(2,9) = 4.2565 at alpha = 0.10

Tabulated F 1-alpha/2(2,9) = 0.05158 at alpha = 0.10

Since, Calculated F statistic = 3.27 < 4.2565 Tabulated F ( critical value ) , we do no reject Ho at alpha = 0.10 (level of significance).

(b)  Since we do not reject Ho , we can conclude that  there is no significant difference in vacancy rates in the regions.

Reason : The test statistic value we computed does not lie in the critical region of rejection.

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