Question

1. 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. 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. Do you think that the mean vacancy rate is the same for these regions? Why

Answer 1

1. 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.

The hypothesis being tested is:

H₀: Mean vacancy rate is the same for these regions

H_a: Mean vacancy rate is not the same for these regions

The output is:

SUMMARY	Count	Sum	Average	Variance
Row 1	3	20	6.666667	2.333333
Row 2	3	25	8.333333	4.333333
Row 3	3	28	9.333333	2.333333
Row 4	3	23	7.666667	0.333333
Column 1	4	29	7.25	1.583333
Column 2	4	33	8.25	6.25
Column 3	4	34	8.5	1
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	11.33333	3	3.777778	1.494505	0.308436	4.757063
Columns	3.5	2	1.75	0.692308	0.536377	5.143253
Error	15.16667	6	2.527778
Total	30	11

Since the p-value (0.536377) is greater than the significance level (0.10), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there are any differences among the regions regarding vacancy rates.

1. Do you think that the mean vacancy rate is the same for these regions? Why

Since the p-value (0.536377) is greater than the significance level (0.10), we cannot reject the null hypothesis.

Therefore, we can conclude that the mean vacancy rate is the same for these regions.