Project 3 - Hypothesis Testing
For due date, see syllabus
Objective:
The purpose of this project is to provide you with experience in defining and testing a
hypothesis, given data that you have selected..
Report Guidelines:
You should submit a report describing your activities. Your report should contain the
exact sections described below. The point values that will be assigned to the sections are
listed to the right of the section title.
- Problem Statement (10): In the problem statement, you should
introduce the data you will be describin and the random variable that you are
investigating . You should then state very precisely the null and alternate
hypothesis that you will be testing. Finally, you should provide some explanation
for why this hypothesis is important and/or interesting.
- Data Description (10): This section should contain the information
about your data necessary to understand the rest of the report. This section should
contain (at minimum), the precise statement of the random variable, a description of the
source of your data and the data collection procedures, the descriptive statistics, and
some assertion about the model that is consistent with the data.
- Hypothesis Testing Procedure (20): In this section, you should present
the details concerning how you will test your hypothesis. You should describe the
logic behind your null and alternate hypotheses -- where did they come from, why are they
interesting. You should describe the test statistic will you use (i.e., z, t, f) and
why? For example, if you are testing a hypothesis about a mean, you have what
appears to be normal data, and you have a small n, then you would use a T-test. When
explaining your choice of test statistic, you need to discuss whether you have satisfied
the assumptions necessary for using the specific statistic (e.g., does the statistic
require your population to be normal and is it?). You should also determine the
alpha level you will use (i.e., 0.01, 0.05).
- Hypothesis Testing Results (20): This section should start with
the results of your test. Clearly you should state the value of the test statistics
and the result of the accept/reject decision. You should probably identify the p
value of the test. If appropriate, you should state what the point estimate is for
the parameter and construct a confidence interval around the parameter.
- Discussion of Test Sensitivity (20): If you conducted a test on a
parameter (e.g., m, p, s), then you might comment on the following: the practical
significance of the finding in the event that your null hypothesis is rejected and the
power of the test (1-ß) for the given alpha level and sample size, and the effect of
changing the sample size. If you conducted a goodness of fit test, you should comment on
the effect of different bin sizes, different numbers of bins, and different estimates of
the parameters of the hypothesized model.
- Summary and Conclusions (10): In this section, you should summarize the
process of the project and then provide the concluding statement concerning the
hypothesis, the results, and the sensitivity of the testing.
- "What I learned" Statements (10): This section should contain
brief reflections (1-2 paragraphs) on what was learned from the hypothesis testing
project. For example, you might comment on the effort and difficulty associated with
identifying a hypothesis, the amount of time involved, and/or the complexity of the
overall processl. You might particularly focus on things that you did not expect to learn
- what surprised you, frustrated you, made you curious, etc. For example, did you try to
use Excel's hypothesis testing functions and not understand how to interpret them?
As before, this component of the report is to be done individually. If you are
completing the project with another student, this section should contain individual
statements from each student.
Hints:
1. Choosing a dataset: An acceptable approach to getting data
for this project would be to use the data you analyzed for project 2. Your results
from project 2 become the basis for the second section of this project report. Of
course, you may also switch to a new dataset.
2. Checking Assumptions: Many of the tests covered in chapters 8
and 9 require that the data be normally distributed. In discussing your choice of
test statistic, you need to attend to whether you data satisfies the assumptions of the
test you are using. For example, if your dataset did not appear to be normal and you
do not have a large enough sample for the central limit theorem to aply, then you cannot
use the hypothesis testing procedures we have been discussing. If you were to try to
test a hypothesis with your data, you would violate the assumptions underlying the tests
that we have learned to use.
3. Identifying the Hypotheses: You can generate several different
types of hypotheses, based on the material that is covered in the book. You may
choose to test hypotheses about
 | the mean of the population (e.g., the mean height of a student is the same as the
50% percentile height given in the handbook of human factors). |
| the difference between the means of two populations (e.g., the mean height of
women is less than men) |
| a population proportion (e.g., the proportion of all-star games attended by more
then 45000 is greater than 50%). |
| the difference between two population proportions (e.g., the percent of
pennies in circulation that are 1968 is equal to the percent of pennies in
circulation that are 1971) |
| the variance of a population (e.g., the standard deviation in engr 315 student
age is 1 year). |
| the ratio of variances of two populations (e.g, the standard deviation of engr
315 male shoe size is greater than than the standard deviation of engr 315 female shoe
size). |
| the underlying distribution of a population (e.g., whether the height data for the class
is normally or non-normally distributed) |
4. Using Excel: This project does not require the use of Excel.
Just like the homwork, the project can be done without the use of tools other than
a calculator. However, there are functions in Excel that can help you. As
before, I encourage you to explore.
Extra Credit:
If you are willing to have us publish your report on the web and would like a little
extra credit, send us your report electronically (as well as submitting the paper copy).
Other students may be interested in seeing your analysis.
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