Question

In: Statistics and Probability

First National Bank employs three real estate appraisers whose job is to establish a property’s market...

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

House Type 1 2 3
Cape 424 413 429
Colonial 528 549 539
Ranch 387 403 378

a. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS", "p-value" to 4 decimal places and "F" to 3 decimal places.)

b. 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.)

Solutions

Expert Solution

a)

applying 2 way ANOVA without replication":

Source of Variation SS df MS F P-value
Rows 36978.6667 2 18489.3333 133.337 0.0002
Columns 120.6667 2 60.3333 0.435 0.6746
Error 554.6667 4 138.6667
Total 37654.0000 8

b)

MSE= 138.667
df(error)= 4
number of treatments = 3
pooled standard deviation=Sp =√MSE= 11.776
critical q with 0.05 level and k=3, N-k=4 df= 5.04
Tukey's (HSD) =(q/√2)*(sp*√(1/ni+1/nj)         = 34.265
Lower bound Upper bound differ
(xi-xj)-ME (xi-xj)+ME
μ1-μ2 -150.93 -82.40 significant difference
μ1-μ3 -1.60 66.93 not significant difference
μ2-μ3 115.07 183.60 significant difference

orchestra answered 1 year ago
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