(due Friday, September 12, by 3:00 p.m.)
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 Hw02_1.csv.
The data set is available at
To create a data frame in R, use
Hw02_1 <- read.table("http://www.stat.uiuc.edu/~stepanov/Hw02_1.csv", sep=",", header=T)
indicates that the data in the data file are separated by a comma,
indicates that the first line of the data file contains the names for the variables
(as opposed to
You can then access individual variables in the data frame
For example, to combine the four 30-component data sets (one for each form) into one
120-component data set, use
Time <- c(Hw02_1$Form1, Hw02_1$Form2, Hw02_1$Form3, Hw02_1$Form4)
Form <- c(rep(1,30), rep(2,30), rep(3,30), rep(4,30))
Test for differences in average time required to fill these four forms using the ANOVA
Specify the null and the alternative hypotheses.
What are the required conditions (assumptions) for this test?
Show the calculations leading to your conclusion in the form of an ANOVA table.
What conclusions can be drawn from these data? Use