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STAT 420
Spring 2008
Homework #9
(10 points)
(due Friday, April 11, by 4:00 p.m.)
1.
The friendly folks at the Internal Revenue Service (IRS) are always looking for ways to
improve the wording and format of its tax return forms. Three new forms have been
developed recently. To determine which, if any, are superior to current form, 120
individuals were asked to participate in an experiment. Each of the three new forms and
the currently used form were filled out by 30 different people. The amount of time (in
minutes) taken by each person to complete the task was recorded and stored in columns 1
through 4 (forms Form1 through Form4, respectively) in file Hw09_1.csv.
The data set is available at
http://www.stat.uiuc.edu/~stepanov/Hw09_1.csv
a)
Test for differences in average time required to fill these four forms using the ANOVA
F
test.
(i)
Specify the null and the alternative hypotheses.
(ii)
What are the required conditions (assumptions) for this test?
(iii)
Show the calculations leading to your conclusion in the form of an ANOVA table.
(iv)
What conclusions can be drawn from these data? Use
α
= 0.05.
b)
Plot the residuals by Form on the same plot, make four sidebyside boxplots for the
residuals (one for each sample), and compare the spreads. Make a histogram of the
residuals and a normal Q–Q plot of the residuals. Comment on the assumptions made in
part (a).
c)
Use a 95% confidence level and Scheffé’s multiple comparison procedure to compare
the average time required to fill forms Form1, Form2, and Form3 with the average time
required to fill the current form (Form4).
F
0.05
(
3
, 116
) = 2.6828
[ R:
qf(0.95,3,116)
]
[ EXCEL:
=
FINV
(
0.05
,
3
,
116
)
]
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View Full Document a)
(i)
Y
i
j
=
μ
i
+
ε
i
j
,
j
= 1, 2, … , 30,
i
= 1, 2, 3, 4,
where
ε
i
j
’s are
i.i.d. N
(
0,
σ
2
).
H
0
:
μ
1
=
μ
2
=
μ
3
=
μ
4
, where
μ
i
= the average time required to fill Form
i
.
H
a
: at least two of
μ
i
’s are different.
OR
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This note was uploaded on 02/10/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 STEPANOV
 Statistics

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