STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

• The pairing is not always as obvious as the ‘before’ and ‘after’ example above; see for
example, question 2, where we have observations on pairs of dogs, each pair taken from
the same litter (dogs from the same litter have the same parents, and hence should be
more alike genetically than dogs from different litters). Here, the random sample is of
litters of dogs arriving at the pound.
• See also question 2 in the 1998 mid-year examination, where you have a random sample
of women and information on their incomes and the incomes of their partners: the
question relates to the difference between a woman’s and her partner’s income.
• ***** ASSUMPTIONS: We need make absolutely no assumptions about the original
observations. If they are not normally distributed, it does not matter, as long as the
differences are. Plot the differences to check that the assumption is not seriously violated.
QUESTION 2. (from Stat171 tutorial exercises)
In order to investigate whether the time of neutering of male
dogs had any effect on their rate of growth, Crenshaw and
Carter (1995) neutered dogs at 2 months and 7 months of age
and measured their weight at 18 months of age. As litters of
any breed became available at a pound, two male dogs were
randomly selected from each litter. One was neuterd at 2
months, the other was neutered at 7 months. All the dogs were
kept under identical conditions during the 18 months of the
trial. The weights (in kg) of the dogs at 18 months were:
Litter 1 2 3 4 5 6 7 8 9 10
2 months 19.0 23.2 16.1 30.3 27.1 22.3 18.1 27.8 34.2 17.3
7 months 18.9 23.5 16.7 30.3 27.8 22.4 18.2 28.1 34.1 17.7
c) Is there any evidence that early neutering affects the rate of growth of the dogs?
d) Comment on why you think the experimenter chose this particular design in setting up
the experiment. Do you think the right choice of design was made?
QUESTION 3. A researcher wants to know the average sucrose content in a certain
concentration of sugar-beet juice. There are two methods of measurement and the researcher
wants to find out whether they both give the same mean dry weight. Ten sample containers
of beet juice were randomly selected from ten different batches. Half the liquid in each
container is measured using method A and the remaining half using method B. The
measuring process yields the following data:
METH
OD
20
BATCH
1 2 3 4 5 6 7 8 9 10
A 11.0 5.0 9.8 5.7 6.5 8.2 5.9 6.0 7.5 5.4
B 11.1 5.6 9.7 5.3 6.7 8.5 5.6 5.8 7.1 5.5
Do these data support the hypothesis that both methods of
measuring yield the same mean concentration?
Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.