In this project you
will conduct a hypothesis test of the type we have been studying in class. You will formulate a problem, collect
data, perform calculations, and present your results in a short
paper.
Your first step will
be to select a parameter, such as a mean, a proportion, the difference of two means, or the
difference of two proportions, for which a doubtful (to you) claim has been
made. Try to choose a problem that
is meaningful and/or creative:
parameters such as the probability of obtaining a head when a coin is
tossed will be considered trivial and not acceptable. Set up hypotheses for your problem in
terms of the claimed value and what you believe to be true. Do not use “artificial” alternatives, i.
e., those made up for the sole purpose of completing the
project.
Having formulated the
problem, you are ready to select a sample from your population. The size of the sample will, of course,
depend on the test you are performing.
Though it may not be possible to select a true random sample, do the best
you can.
Type up your results in a 3 – 5 page
report. The first page should
contain only the formal steps of the hypothesis test. Include computation of the p-value, but
make your decision based on the a = 0.05 decision rule. On succeeding pages, explain your
problem, motivating your choice of hypotheses, and giving references. Explain your sampling and any problems
that might have arisen from it.
Make conclusions and indicate how your study could be improved. Comment on any assumptions necessary for
your test to be valid. List your
data at the end of the report.
Take care in your
paper to present your work clearly.
Just as important as the formal calculations and conclusion are an
intelligent motivation and statement of the problem, and the discussion of your
sampling and results. Make every
effort to write an interesting and understandable paper.
Summary of Project
Requirements
1. Collect your own
data.
2. Use a sample size of at least 30 (at
least 60 if your study involves two independent samples)
3. Give a specific reference (date, title
of publication, author, pages) as a basis for formulating
your
hypotheses.
4.
Type the paper . (An automatic 10% grade penalty
will apply to any paper not typed)
You only need to type the
discussion (pages 2 – 3) part of the paper.
5. Use the following
format:
Page 1. Statement of the
hypotheses, significance level = 0.05,
test statistic, rejection
region, calculation of the test statistic, conclusion,
p-value.
Page 2-3 Describe what your project is
about. Discuss the choice and
motivation for
the hypotheses, how the sample was taken, the population sampled, and
any
problems you encountered in collecting the data. Use your reference to
explain
the motivation for your choice of hypotheses.
Page 4 List the data
collected and show how you made the summary calculations; a
sample proportion if your project involved the parameter p, sample
means
and variances if your project involved one or more population means,
etc.
First Step of the
Project: To formulate the
hypotheses, you must first find a published article
(newspaper, magazine, etc.)
concerning an advertised claim, the results of a public opinion poll,
a
consumer preference study, etc. The
parameter involved in your hypotheses may be a population mean, a population
proportion, the difference of two proportions, or the difference
of
two
population means. (You may use any of the tests described in Chapters 7 and 8 of
the text)
Some
Examples:
1. Supermarket A claims to have lower
prices than supermarket B (Give a reference). The
purpose of my
study is to show ___________.
Parameter: m = mean price difference (B
– A)
of all items
sold at A and B. Population: all items of the same brand and size
available for
sale at
supermarkets A and B.
Data:
Item
Price at A
Price at B
Price Difference (B – A)
1
$ .48
$ .54
.06
2
1.52
1.23
- .29
n
4.93
5.62
.69
Analysis of
paired data reduces to the one sample inference procedures
studied
in Sections 6.4
and 7.5 of the text
2. A recent Newsweek poll (give a specific
reference) indicates that only 30 percent of the
American public
support paying a salary to college athletes. A much higher percentage
of
the population
of ODU students is likely to support paying athletes for their services for
the following
reasons _______. Therefore, the
purpose of my study is to show _____.
Parameter: the population proportion p of ODU
students that support paying a salary to
college
athletes. Null hypothesis: p £ 0.30. Alternative hypothesis: p > 0.30.
Data: a list of
students (excluding their names) and their support (yes or no) for paying
a salary to
college athletes.
3.
Two independently selected
samples (of at least 30 each) can be used to compare (1) men’s
and women’s
views about a particular social or campus issue, (2) the GPA of students
who
join fraternities or sororities with those of students who do not join
such organizations, and
(3) more generally, to compare two populations by
making inferences about their means
or proportions. Examples in Sections 8.2 and 8.3 of the
text illustrate how two independently
selected samples can be used to compare
two population means or proportions.