Question

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1. (13pt) 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 2018 using a sample of 4 statistical metropolitan areas.

                                     Vacancy rates (%)

Region	Northeast	South	West
1	7	5	8
2	6	9	10
3	9	11	8
4	7	8	8
sample mean	7.3	8.3	8.5
sample variance	1.2	4.7	0.8

1. 1. (10pt) You are hired as statistician to test whether there are any differences among the regions regarding vacancy rates and you should allow for 10% error.
2. 2. (3pt) Do you think that the mean vacancy rate is the same for these regions? Why?

Answer 1

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 0.10 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