BUS231
Chapter 15 Homework
1. (13 points) Are all disciplines in the University equally boring or there are
some more boring than others? To answer that question, a study performed
at Columbia University counted the number of times per 5-minute interval
professors from three different departments said “uh” or “ah” during lectures
to fill gaps between words. These counts were used as a proxy
(approximation) for the measure of class boredom. The data from observing
one hundred of 5-minute intervals from each of three departments’
professors were recorded in the file “Boring.jmp”.
a.
(4 points) Formulate null/alternative hypotheses H0/H1 that need to be
tested with these data to find if the departments offer equally boring
classes or not.
H0: All means are equal
Ha: At least one mean is different from the other
b.
(2 points) Report the p-value(s). Use 5% significance level.
(Independent Data)
P-value= 0.0006 < a=0.05
c.
(3 points) Check the conditions required and report findings.
(Normality)
H0: data =normal
Ha: data≠ normal
P-value for math=0.2697
p-value for English=0.6646
P-value for Poli Science=0.2981
All Data sets are > 0.05 so they are all normal
d.
(4 points) Is there sufficient evidence in the samples collected to
conclude that some departments offer more boring lectures than the
others?
With a p-value of 0.0006 less than a=0.05, we reject the null in favor of Ha. At least
one department mean is statistically different from another
1
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2. (17 points) Car manufacturer designed for different head lights, and would
like to compare them. One of the tests performed on headlights is how fat
away (in feet) a driver can read the road sign in the night conditions when
the headlights are on. Company equips four cars each with the one of the
four lamp designs, and selects 41 different drivers, aged between 20 and 60
years old. Each driver drives each one of the four test cars with different
headlight designs. When a driver can read a road sign in the dark,
illuminated by a headlight, distance is recorded (see the file
“Headlight.jmp”). A car company would like to compare the four designs
and test if they are any different in terms of night distance at which a road
sign can be recognized.
a. (3 points) Use a decision flowchart and decide which test is
appropriate for the data collected? Write the name of the test in the
space below.
Blocked, Two-way Anova
b. (2 points) Test the required conditions for the test selected in part
(a). (a.) Write down which hypotheses you tested, (b.) p-value, and
(c.) conclusion form the test.
a. H0: data =normal
Ha: data≠ normal
b. P-value= Design 1= 0.2658, Design 2= 0.3281 Design 3= 0.9538, Design
4=0.2043
c. With p-values all greater than 0.05, all data sets are normal
c. (8 points) Formulate all appropriate pairs of null and alternative
hypotheses that can be tested with this data. Report the hypotheses in
the space below.
Factor A (Design):
H0: All four means are the same
Ha: At least one mean is different from others
Factor B (Age):
H0: The mean distance of all ages is the same
Ha: At least one age has a different mean distance
d. (4 points) For each of the tests in part (c), report the p-value, and your
conclusion. Tables-> Stack (just the 4 designs), Data=Distance, Label=Design,
Analyze ->Fit Models, Y-Distance, Age & Design are for Construct Model Effects,
Factor A p-value< 0.0001 At least one mean is different
Factor B p-value= 0.5571 The average distance is the same for all ages
2
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