Exam 1 (take-home only)
Data were collected on the average runs scored per game for
each of the 30 teams in major league baseball in this
file. The teams are divided into six divisions, each with five teams.
Write one or more sentences summarizing your conclusions
for each of the following problems. Your summary should allow a person to
understand your results even if they do not know the software that you used
(SAS, R, etc.).
1.
Conduct an analysis of
variance (fill out the ANOVA table, including sums of squares, mean squares, F
statistic, and P value. Be sure to include a line for total SS and df) to test the null hypothesis of equality of runs scored
by division. Include a boxplot to visualize potential differences by division.
2.
Examine a residual by
predicted plot and a normal plot of the residuals to assess model assumptions.
3.
Use the log(standard
deviation) and log(mean) regression to examine whether a power transformation is
needed. Is the test for a transformation significant? What power transformation
is recommended? [You do not need to reanalyze the data]
4.
If we were going to test for
a difference in runs scored by division, and the true mean values were: 4, 4.5,
4.5, 4.5, 4.5, and 5., with a variance as estimated from these data, what is the
power of the ANOVA test to detect these group differences with 5 teams per
division? Use alpha=.05.