Question

1) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following data last quarter of 2018 using a sample of 4 statistical metropolitan areas. the rental vacancy rates in percentage (%) grouped by region for the are Vacancy rates (% Northeast Region South West 8 1 7 5 2 6 9 10 9 11 8 4 7 8 8 sample mean sample variance 7.3 8.3 8.5 1.2 4.7 0.8 statistician to test whether there are any differences among the regions You are hired regarding vacancy rates and you should allow for 10% error b. 2. as Do you think that the mean vacancy rate is the same for these regions? Why?

Answer 1

Solution -From the given data, >here, in this Case, we need to Compate the bental Vacancy rates In this Case we will use the one way ANOVA to Compane the means oL the tental va cany by tegion by region. the at lo/ evio (i-e, =0.10) mangin ob Hy polthesis; a Significant difeence betueen the e, There is no meanat the legion eaual ane Ha: Not all means formula to Calculale ANOVA Ms S S Source df mean Square Rogions (betuon) k-1 En( SR- SSR k-) M SSR s MSSE Enor n-klni-)si SSE SSE (oilhin) h-k Total n-I where, k no.o roups (Regions h Total no o obsenvation >2(- Sumot Squares betoeen negions Sum of the Sauanes within the Yegion

22(i- Total Sum of Sauane get Now pulting the values in ANOVA table We f odf Source MSS S S Regions O.S94 3.5 2 St.l 26.5 2.94 Total 30.0 3 1 have by dif the Regions then the O.1o and ue 2 tale Value oh fis 3.006 0:594 <0.36 e, f<ft we accept the null hypothesis Ho Yes, the mean Vacancy aate is the Same for these 1egiens, becaut Sianiticance in the table value of the f is the at the o.lo level of the reaten than the Calculaled f.. statis ticaly accept the null >Therebore, we pothesis.