Question

Independent random samples of newly completed apartments in four regions of a country yielded the data on monthly​ rents, in​ dollars and the summary statistics is given below:

Region	n	Mean	Std.deviation
MW	6	752.33	89.37
NE	5	1051	146.10
S	4	862.25	159.37
W	5	1055.60	122.62

Do the data provide sufficient evidence to conclude that a difference exists in mean monthly rents among newly completed apartments in the four​ regions?

A partially filled in ANOVA table is presented below

Source	SS	DF	MS	F
Between	359293.92
Within				XX
Total	620951.20		XX	XX

What is the value of the F critical value at the α=0.05α=0.05 level? Report 4 decimal places.

Answer 1

Source	SS	DF	MS	F
Between	359293.92	4 - 1 = 3	359293.92 / 3 = 119764.64	119764.64 / 16353.58 = 7.3234
Within	620951.20 - 359293.92 = 261657.28	19 - 3 = 16	261657.28 / 16 = 16353.58	XX
Total	620951.20	20 - 1 = 19	XX	XX

For critical value of F at α=0.05

F( 3, 16 ) at α=0.05 = 3.239

Do the data provide sufficient evidence to conclude that a difference exists in mean monthly rents among newly completed apartments in the four​ regions?

Since, F = 7.3234 > F( 3, 16 ) at α=0.05 = 3.239 therefore, we will reject the null hypothesis of equality

Yes, a difference exists in mean monthly rents among newly completed apartments in the four​ regions