Chapter 10 Analysis of Variance 425teaching method. The two factors are
region (East, Midwest, South, or West)
and teaching method (standard or ex-
perimental). Schools are entered into
the study, and their average test scores
are recorded. There are fi ve replicates
for each combination of the region and
method factors.
a. Using the information about the de-
sign of the study, complete the follow-
ing ANOVA table:Term SS df MS F
Region 9,305???
Method 12,204???
Interaction 6,023???
Error???
Total SS 60,341?
b. What is the R^2 value of the ANOVA
model?
c. Use Excel’s FDIST function to calcu-
late the p values for each of the factors
and the interaction term in the model.
d. State your conclusions. What factors
have a signifi cant impact on the test
scores? Is there an interaction be-
tween region and teaching method?- In analyzing the hotel data there ap-
peared to be a problem of unequal popu-
lation variances. Does it help to use the
logarithm of price in place of price?
a. Open the Hotel workbook from the
Chapter10 data folder and save it as
Hotel Log ANOVA.
b. Compute a new variable LogPrice, the
natural log of price.
c. Repeat the one-way ANOVA using
LogPrice in place of Price (remember,
you will have to unstack the data to
use the Analysis ToolPak). Does there
now appear to be a problem of un-
equal population variances?
d. Recalculate the matrix of paired dif-
ferences (use the Bonferroni correc-
tion in calculating the p values).
e. Save your workbook and write a report
summarizing your results. Do your
conclusions differ in any important
way from what was obtained for Price?- The Hotel Two-Way workbook is taken
from the same source as the Hotel work-
book, except that the data are balanced
for a two-way ANOVA. This means that
the random sample was forced to have the
same number of hotels in each of 20 cells
of city and stars (four levels of city and
fi ve levels of stars). For each of the 20 cells
specifi ed by a level of city and a level of
stars, a random sample of two hotels was
taken. Therefore, the sample has 40 hotels.
Included in the fi le is a variable, city stars,
which indicates the combination of city
and stars. Perform the following analysis:
a. Open the Hotel Two-Way workbook
from the Chapter10 folder and save it
as Hotel Two-Way? ANOVA.
b. Using Excel’s PivotTable feature, create
an interaction plot of the average hotel
price for the different combinations of
city and stars. Is there evidence of an
interaction apparent in the plot?
c. Do a two-way ANOVA for price versus
stars and city. (You will have to create
a two-way table that has stars as the
row variable and city as the column
variable.) Is there a signifi cant interac-
tion? Are the main effects signifi cant?
d. On the basis of the means for the fi ve
levels of stars, give an approximate
fi gure for the additional cost per star.
e. Compare the city effect in this model
to the one-way analysis, which did
not take into account the rating for
each hotel.
f. As the number of stars increases, the
mean price increases approximately
linearly. Graph price versus stars.
Break down the chart into categories