2) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by

Question

2) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan tes in percentage (%) grouped b last quarter of 2016 using a sample of 4 statistical metropolitan areas. Vacancy rates (%) Region northeast south west 9 10 9 11 8 sample mean sample variance 6.58.5 7.5 3.3 3.3 4.8 a. (13pt)You are hired as statistician to test whether there are any differences among the regions regarding vacancy rates and you should allow for 5% error. I b. (5pt) Do you think that the mean vacancy rate is the same for these regions? Why?

Explanation / Answer

here applying one way ANOVA on abovedata:

nuill hypothesis: mean vacancy rate is same for all three regions.

alternative hypothesis:mean vacancy rate is different for at least 2 of given three regions

b) as p value for above test is very high high. therefore we can not reject null hypothesis

We do not have significant evidence to conclude that mean vacancy rate is different for at least 2 of given three regions .

i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 norhteast 4 6.5 10.890 4.000 32.670 south 4 8.5 10.890 4.000 32.670 west 4 7.5 23.040 0.000 69.120 Weighted mean 7.500 8.000 134.460 SSG SSE Source of variation SS df MS F P value F crit treatment 8.000 2 4.000 0.268 0.7710 4.2565 error 134.460 9 14.940 total 142.460 11

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