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.
The final report will include a description of the problem, and why you think it is important, or what you hope to gain from testing the hypothesis. It should also include the context of the data, all data collected, and the values generated by Minitab or the calculator. A decision and conclusion should be stated. An analysis should follow with what the conclusion means in terms of the original problem.
The final report should be in narrative format like you were writing for a newspaper or magazine, must be typed, printed, and should be double spaced. An excellent final report will have the following components.
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
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 single mean that requires a number as the claimed value. 2. A test about two independent means doesn’t need 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).
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.
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