Your task is to perform some real-world inferential statistics. You will take a claim that someone has made,
form a hypothesis from that, collect the data necessary to test the hypothesis, perform a hypothesis test, and
interpret the results. If you use pre-existing data, rather than collecting it yourself, then you will need to do more
analysis to get the full points. You should try to come up with something of interest to you instead of some
contrived situation.
• An introduction to the problem including the claim(s) being tested
• How and when the data was collected including possible problems
• The context (who, what, where, when, why, how) of the data (remember this is in narrative format)
• Descriptive statistics and/or tables depending on your type of data
• Appropriate graphs (every project should have at least one graph or chart of the data in it)
• Inferential statistics including …
• the null and alternative hypotheses written symbolically
• statistical output including a test statistic or p-value
• a graph showing the critical and non-critical regions, test statistic, or p-value
• the decision and a conclusion written in terms of the original claim
• Conclusion
• Suggestions for the next time this project is done
What can we test?
Some things are easier to test than other things. The purpose of this project is not to do a full-scale PhD level
research project, it is to expose you to the process of hypothesis testing in a real-world application. You may
test means, proportions, or linear correlation. It is also possible (in your textbook, but not covered in class) to
test a standard deviation. You may have one or more samples. You may categorize your variables in one or
two ways. If you are dealing with one sample, then you will need some numerical value to test against. The
claim “more people prefer Pepsi than Coke” becomes a claim that the proportion of Pepsi drinkers is greater
than 0.5. There are not two independent samples (Pepsi drinkers / Coke drinkers), just one sample categorized
in two ways. A problem with the Pepsi / Coke thing is that it omits other soft drinks because that is more difficult
to do. A chi-square goodness of fit test would be more appropriate in this case. You should try to come up with
a claim that you have heard or that interests you. Categorical Data If your data consists solely of categories
and not measured quantities, then you should be looking at proportions or counts. Things to look for that let
you know you’re dealing with categorical data or proportions include proportions, percent’s, counts,
frequencies, fractions, or ratios.
If your data consists of names or labels, you’re dealing with categorical data. This list is a guideline, but counts
can also be used as quantitative data as well. You really need to think about the response that was recorded
for each case (a row in Minitab terms). Did you record a yes/no response for each case, or did you record a
number that means something? If it was a yes/no or other categorical data, then this is the place to be.
Example Claims about Categorical Data
• 93.1% of Americans feel there should not be nudity on television during children’s viewing time.
http://www.parentstv.org/PTC/publications/lbbcolumns/2003/0528.asp This is a claim about a single proportion.
We know this because the value includes a percentage and the data is categorical (yes or no), not numerical.
The original claim here could be written as p=0.931.
• Blacks are more likely to die from a stroke than whites. http://www.medicalnewstoday.com/medicalnews.php?
newsid=64812 Depending on how this is analyzed, it could either be a comparison of two independent
proportions or one dependent sample. If you compare the percent of blacks that die from stroke to the percent
of whites that die from stroke, then you have a test of two independent proportions and your original claim
could be written as pb>pw. However, if the wording was “stroke victims are more likely to be black than white,”
then your population would just be stroke victims and you would have one sample. Each person can be
classified as either black or white (success or failure). In that case, you’re testing that the proportion of blacks
is greater than 50% and your original claim could be written as p>0.50.
Quantitative (Numerical) Data If your data consists of measured quantities, then you will probably be testing a
mean or perhaps correlation between two variables. It is possible to test a claim about a standard deviation,
but that is rare, and not covered in this course. There are four main ways to analyze means. 1. A test about a
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a number because you compare them to each other. This compares the same thing in two different groups. 3.
A test for two dependent means, often called paired samples, compares two values for each case in the same
group. 4. The Analysis of Variance is an extension of the two independent samples case where there are more
than two groups. You can also perform correlation and regression with two quantitative variables. Simple
regression, with just one predictor variable, is covered in the book. Multiple regression, with several predictor
variables, is not covered in the textbook but is available online.
Example Claims about Quantitative Data:
Women live five years longer than men. http://www.medicalnewstoday.com/medicalnews.php?newsid=18866
This is a claim about two averages, the average lifespan of women and that of men. We don’t know the
average of either gender (they’re given in the article), we just know that women are supposed to live five years
longer than men. When you’re working with one sample, it’s important to have a value to compare against, but
with two samples, you don’t need a value for each, just the difference between the two (in this case 5 years).
The original claim here could be written as μw-μm=5 (the difference in the mean ages of women and men is 5
years).
• Gasoline costs more on the West Coast than other regions.
http://tonto.eia.doe.gov/oog/info/gdu/gasdiesel.asp This information comes from the US Department of Energy
and includes a sampling frame of 115,000 gas stations from across the country. The US is broken down into
regions of the East Coast, Midwest, Gulf Coast, Rocky Mountain, and West Coast. Since we are looking at the
average of more than two independent samples, we’ll use the Analysis of Variance. Notice that there is only
one measurement variable (gasoline prices) but there is also a categorical variable (region). The categorical
variable is used only for grouping purposes. The ANOVA tests that all the means are equal, written as μE = μM
= μG = μR = μW.
• Seat belts save lives. http://dot.state.il.us/trafficsafety/seatbelt june 2006.pdf and http://wwwfars.nhtsa.dot.gov/FinalReport.cfm?stateid=17&title=states&title2=fatalities_and_fatality_rates&year=2005
Okay, this claim is all over the place, but I wanted to give some links on how it would be tested. You could take
the data regarding the percent of people wearing their seat belts and compare it to the fatality rate. These are
two numerical values that are paired together for each case (probably based on an annual report). Remember
that you can not perform correlation and regression with categorical variables. The original claim that seat belts
save lives would be interpreted as a negative correlation (as seat belt use goes up, fatalities go down) and
would be written as ρ<0.
Some previous projects:
These are some of the many projects that students have worked on before. You should not limit yourself to
these topics, but they may give you guidance for picking your topic. Topics that are related to people’s work
usually turn out to be the best projects. You can also get ideas from reading newspapers or online news sites. I
typed in keywords like “average”, “more likely”, or “correlation” to get some of the claims used as examples.
• Are the rates paid by the insurance company for dental cleaning in line with the rates charged by the
dentists? A student called 30 dentists to find out the rates.
• Do the blood type ratios in McClean county agree with the national percentages as published by the
American Red Cross? Students went through Red Cross records using stratified sampling until there were over
two hundred people in the sample.
• Do people prefer Pepsi over Coke? People’s preference was asked and then given a taste test. • Are the men
and women’s shoe prices at Foot Locker, MC Sports, and Finish Line the same?
• Does Firestone/Bridgestone produce splices with the mean size claimed?
• Is the GPA of smokers lower than the GPA of non-smokers?
• Do higher priced bullets have a smaller shot pattern?
• Do Chex potato chips have 60% less fat than their competitors?
Sample Solution
