A realtor wants to compare the mean sales-to-appraisal ratios of residential pro
ID: 3234185 • Letter: A
Question
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Neighborhood A
Neighborhood B
Neighborhood C
Neighborhood D
1.2
2.5
1.0
0.8
1.1
2.1
1.5
1.3
0.9
1.9
1.1
1.1
0.4
1.6
1.3
0.7
State the null and alternative hypotheses below.
H0: ____________________________
H1: ____________________________
b)List the formula for the degrees of freedom among groups, the degrees of freedom within groups, and total degrees of freedom below.
Among groups df ________________
Within groups df ________________
Total df ________________
c)List values for the degrees of freedom among groups, the degrees of freedom within groups, and total degrees of freedom in the table below.
d)List values for the total, among groups, and within groups sum of squares in the table below.
e)List the formula for the mean square among groups, the mean square within groups, and the total mean square below.
Mean Square Among groups _______________________
Mean Square Within groups _______________________
Total Mean Square _______________________
f)List values for the mean square among groups, the mean square within groups, and the total mean square in the table below.
g)List the formula for the one-way ANOVA F test statistic. _______________________
h)Estimate the F statistic for the problem. List this value in the table below.
_______________________________________________________________________________
i)List the critical F value when testing the null hypothesis at the 0.05 level of significance in the table below.
j)Do you accept or reject the null hypothesis. _______________________
Source
Degrees of Freedom
Sum of Squares
Mean Square
F
F Critical
Among Neighborhoods
Within Groups
Total
k)State your conclusion. ____________________________________________________________
_______________________________________________________________________________
Neighborhood A
Neighborhood B
Neighborhood C
Neighborhood D
1.2
2.5
1.0
0.8
1.1
2.1
1.5
1.3
0.9
1.9
1.1
1.1
0.4
1.6
1.3
0.7
Explanation / Answer
null hypothesis: all neighbourhood has same mean of ratios.
alternate hypothesis: at least 2 neighbourhood has different mean of ratios.
from above table at 0.05 level critical value of F =3.4903
as F stat is greater then critical value we reject null hypothesis and conclude that at least 2 of neighbourhood has diffferent mean of ratios
Groups Count Sum Average Variance Neighborhood A 4 3.6 0.9 0.126667 Neighborhood B 4 8.1 2.025 0.1425 Neighborhood C 4 4.9 1.225 0.049167 Neighborhood D 4 3.9 0.975 0.075833 ANOVA Source of Variation SS df MS F P-value Between Groups 3.181875 3 1.060625 10.76321 0.001016 Within Groups 1.1825 12 0.098542 Total 4.364375 15