Math 143 C/E, Spring 2001
IPS Reading Discussion Questions
Chapter 3, Section 4
- How do the concepts of statistic and parameter
relate to those of population and sample?
- In class on Wed., 2/7, we carried out an activity in which
we randomly selected 10 Senators, determining the percentage
in our sample that were women, Democrats and from states
beginning in the letter `M'. For each of these three
random variables, we made a dot plot that included
the percentage in your sample as well as that of each of
your classmates. Was this dotplot an example of a
sampling distribution?
- A statistic is a number that describes a sample.
Examples include things like the mean height of a sample
of students, the proportion of clam shells in a day's
catch that contain pearls, etc. When a statistic is
computed and plotted for each of many samples of size
n, we begin to get this statistic's sampling
distribution (actually, we would have to get all
samples of the given size, computing the statistic each
time, before we could have the full sampling distribution).
As we will see, it is not unusual for a sampling
distribution to be approximately normal, with a
large spread (standard deviation) for when the statistic
demonstrates a good deal of variability and a small
spread when the statistic has little variability (from
sample to sample). How does increasing sample size affect
variability?
- Read the last two paragraphs on p. 273. Does the
information from these two paragraphs contradict your
answer above? Why or why not?
- Statistics for samples that are SRSs tend to be
unbiased estimators of population parameters. Give
an example of a sample selection process and a
statistic one might calculate from the resulting
sample that would not be an unbiased estimator
of a population parameter.