Question

First National Bank employs three real estate appraisers whose job is to establish a property’s market value before the bank offers a mortgage to a prospective buyer. It is imperative that each appraiser values a property with no bias. Suppose First National Bank wishes to check the consistency of the recent values that its appraisers have established. The bank asked the three appraisers to value (in $1,000s) three different types of homes: a cape, a colonial, and a ranch. The results are shown in the accompanying table. (You may find it useful to reference the q table.)

	Appraiser
House Type	1	2	3
Cape	425	415	430
Colonial	530	550	540
Ranch	390	400	380 If average values differ by house type, use Tukey’s HSD method at the 5% significance level to determine which averages differ. (If the exact value for nT − c is not found in the table, use the average of corresponding upper & lower studentized range values. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Answer 1

Here in this problem we have to do One factor ANOVA (factor is house type)

Data Table

	Appraiser
House type	1	2	3
Cape	425	415	430
Colonial	530	550	540
Ranch	390	400	380

Hypothesis

H₀ = All the means of house types are equal

H₂ = Arleast one mean of house type differ.

ANOVA table (using excel data analysis pack)

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Cape	3	1270	423.3333	58.33333
Colonial	3	1620	540	100
Ranch	3	1170	390	100
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	37222.22	2	18611.11	216.129	2.57E-06	5.143253
Within Groups (Error)	516.6667	6	86.11111
Total	37738.89	8

From the ANOVA table we can find tha test statistic F is grater than F_critical Hence we reject null hypothesis and we conclude that there is a significant difference between the mean price of house type.

Tukeys HSD multiple comparision test

Q_{^{α=0.05,k=3,ν=6}critical} = 4.33

Tukey HSD Q-statistic,

=

are treatment means of huse types

Q_i,j>Q_critical for all relevant pairs of treatments result is significant.

Tukey HSD multiple comparison results are as follows

treatments	Tukey HSD	Tukey HSD	Tukey HSD
pair	Q statistic	p-value	inferfence
Cape vs Colonial	21.78	0.001005	p<0.01
Cape vs Ranch	6.22	0.010801	p<0.05
Colonial vs Ranch	28.00	0.001005	p<0.01

from the above results wilth level of significance 0.05 we can conclude that all the pairs are significantly different.