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 statistical areas. The following data are the rental vacancy rates in percentage (%) grouped by region for the last quarter of 2016 using a sample of 4 statistical metropolitan areas Vacancy rates (%) northea Regio st south west 2 69 10 4 4 sample mean 6.5 8.5 7.5 sample variance 3.3 3.3 4.8 1. 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. 2. Do you think that the mean vacancy rate is the same for these regions? Why?

Explanation / Answer

here null hypothesis: there is no difference in mean vacancy rate among all regions.

alternate hypothesis : there is difference in  mean vacancy rate among at least 2 regions.

from above given data:

2) as p value is greater then 0.05 level we can not reject null hypothesis. we do not have suffiicent evidence to conclude that mean vacancy rate is different.

therefore we go along with the notion that mean vacancy rate is same for these regions

i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 northeast 4 6.5 4.333 4.000 13.000 south 4 8.5 4.333 4.000 13.000 west 4 7.5 6.333 0.000 19.000 Weighted mean 7.500 8.000 45.000 SSG SSE Source of variation SS df MS F P value F crit treatment 8.000 2 4.000 0.800 0.4789 4.2565 error 45.000 9 5.000 total 53.000 11

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