MATH 318 Homework 15 Solutions
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Apr 3, 2024
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MATH 318
Homework 15 Solutions
Due: Mon, 03-25-2024
1. (2.5 pts) In each of the following situations, identify the sample as either an SRS
(simple random sample), a stratified random sample, a multistage random sample, a
systematic random sample, or a voluntary response sample.
(a) Five hundred registered voters are considered for jury duty. A table of random
numbers is used to select 20 potential jurists.
simple random sample
(b) Facebook wants more user feedback and thus posts an optional survey on users’
timelines.
voluntary response sample
(c) A bipartisan committee of US Representatives is needed. First, a random sample
of 25 Republicans and 25 Democrats is chosen. Then, random samples of 4 rep-
resentatives from each party are chosen.
multistage random sample
(d) A marketing firm is gathering data on whether customers prefer an ad with a
male featured or a female featured.
They survey every 10th customer to get a
sample of 30 customers.
systematic response sample
(e) Separate random samples of male and female first-year college students in an
introductory psychology course are selected to receive a one-week alternative in-
structional method.
stratified random sample
2. (3 pts) Explain what is wrong with each of the following sampling procedures, and
then explain how the sampling procedure could be improved.
(a) To determine the reading level of an introductory statistics textbook, you evalu-
ate all the written material in the third chapter.
Entire third chapter may not be representative of the entire textbook. Instead,
sample a few pages from each chapter.
(b) You want to sample student opinions about a proposed change in procedures for
changing majors. You hand out questionnaires to 100 students as they arrive for
class at 8:00 AM.
Students who attend an early morning class may not be representative of all
students. Instead, randomly sample a few students throughout the day.
(c) Twenty students are to be used to evaluate a new treatment. Ten men are as-
signed to receive the treatment and ten women are assigned to be the controls.
Gender would be a confounding variable.
Instead, randomly assign both men
and women to the treatment and to the control group.
3. Suppose you want to investigate whether or not the expression “an apple a day keeps
the doctor away” has any validity. In other words, you want to investigate whether or
not eating apples has any health benefit. For each of the following three approaches,
identify if the approach is an experiment, an observational study, or an anecdote.
(a) (1 pt) You recall that your Uncle Joe loved apples and was never sick a day in his
life, while your Uncle Tom despised apples and was often ill.
anecdote
(b) (1 pt) You take a random sample of individuals, identify who does and does not
eat apples regularly, and then follow them for 6 months to see who requires a visit
to a doctor and who does not.
observational study
(c) (1 pt) You take a random sample of individuals, randomly assigning half to eat
an apple every day and the other half not to. You then follow them for 6 months
to see who requires a visit to the doctor and who does not.
experiment
(d) (3 pts) Which of these methods is the best for investigating the effect of eating
apples on health? For the other methods, why are they not ideal?
Experiment is best.
The anectode is the worst; we cannot use what happens
to one or two people to generalize to the larger population.
The observational
study may be biased because people who
choose
to eat apples regularly may also
choose
other healthy lifestyles that contribute to less visits to the doctor.
The
experiment uses random allocation in order to remove the human choice from
confounding the results.
4. (4.5 pts) A local high school wants to see how many of its students from the class of
2011 went on to graduate college in May of 2015. The high school was able to find
addresses for 422 members of the 611 member class. The school sent surveys to these
422 members and 319 were returned. Based upon the survey results, the school was
proud to announce in all of the local newspapers that 90% of the Class of 2011 had
graduated college in just four years. Suppose an online database pulls data from high
school and college student information to report the number of students from each
graduating high school class that go to college. For this high school, it states that only
75% of the Class of 2011 graduated college in just four years.
(a) Explain how the survey results reported were affected by undercoverage bias.
Only 422 of the 611 members of the class had addresses available. Those whose
addresses are not available may be more likely to have not graduated from college.
(b) Explain how the survey results reported were affected by nonresponse bias.
Only 319 of the 422 surveys that were mailed were returned.
Those who did
not return the survey may be more likely to have not graduated from college.
(c) Explain how the survey results reported were affected by response bias.
Some class members who returned the survey may have lied about completing
college to make themselves look better.
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5. (4 pts) The figure below shows histograms of four sampling distributions of statistics
intended to estimate the same parameter. Label each distribution relative to the others
as high or low bias and as high or low variability.
(a) high bias, high variability
(b) low bias, low variability
(c) low bias, high variability
(d) high bias, low variability