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Stat 430/830 Solutions 1
Solutions for #1, 2 and 3 are in soln4301.doc, as well as computer output and plots for #4 and 5.
4.
a) From the dot plot of the data we see that the duration is very slightly skewed to the right for
the queens. There are not enough workers to say much about their distribution other than the
durations are spread out more so that the data for the queens. The workers do have more higher
durations than the queens, although whether this is significant or not will need to be tested. More
worker data really should have been collected.
0Q
W
b) H : the population average duration is the same for the queens and the workers OR
:
=
:
a
H : the population average duration is different for the queens and the workers
QW
OR
:
±
:
where
:
represents the population average duration for the queens and
:
represents that for
the workers.
c) Note: the following comment about Levene’s test is NOT required. Levene’s test for equal
variances indicates that the population variances are not equal (Pvalue < 0.0001). (Note, for
testing for differences in variances, Levene’s test is preferred to Bartlett’s since the latter is not
robust to nonnormality.
As I have mentioned in class, plots of the data/residuals, however, are
better ways of checking for nonconstant variance.) The two ttests, one assuming equal
variances and the other assuming unequal variances, give different results if an of
"
of 0.01 is
used. That assuming equal variances strongly (Pvalue < 0.0001)
indicates that the workers
spend more time at the sources of pollination while the ttest assuming unequal variances gives
only borderline evidence (Pvalue = 0.014). Given the evidence that the population variabilities
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 Winter '09
 OHaraHines

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