You will be submitting a SINGLE PDF DOCUMENT that contains your entire project. Your project must be typed, though you may choose to hand-write such items as statistical notation (such as μ1or α )

You will be submitting a SINGLE PDF  DOCUMENT that contains your entire project.  

• Your project must be typed, though you may choose to hand-write such items as statistical notation (such as μ1or α ) and statistical graphs (your boxplots, normal curves, etc).   You MUST use correct statistical notation!  Below are a couple of links that will help you with how to do this, if you use Google Docs or Microsoft Word.  You will need to do your own search for inserting statistical notation is you are using a different word processing program.
  • For Google Docs:  https://support.google.com/docs/answer/160749?hl=en&co=GENIE.Platform%3DDesktopLinks to an external site.
  • In Microsoft Word: https://support.microsoft.com/en-us/office/write-an-equation-or-formula-1d01cabc-ceb1-458d-bc70-7f9737722702Links to an external site.
• You are expected to use correct statistical notation and terminology, and you should be using statistical concepts as they were covered in our class.
• Any large numbers that your calculator gives to you in scientific notation must be written out in standard form (for example, 3.2E5 needs to be written as 320,000). If numbers are more than 4 digits, you must use commas when writing the numbers (for example, 320,000 not 320000).
• When describing/explaining your data and results, be sure to include appropriate units (for example, dollars or degrees Fahrenheit per year or deaths per 10,000 people).  All graphs and tables should  also be appropriately labeled, including units.

Your project must include the following elements, and the elements should be included in the following order. Refer to the assignment rubric for more detail about points for each sub-element.

1. Title and Introduction (8 points):
2. Data  (5 points):  A separate page that shows a table with all the data you used for both samples, as well as information about where you got your data (how you gathered it, or what website you used for it). If you do not include your data correctly, you cannot get credit for the rest of your project!
3. Description of your two data groups (material comes from Part B) (20 points total).
   1. Create a histogram for each of your samples. (These can be CAREFULLY hand-drawn images or made with technology.) Be sure you are using the same class limits and vertical scale for BOTH histograms, and that both histograms appear together on the same page so they can be easily compared.  Include the frequency distribution table you used to create the histograms.
   2. Create a side-by-side box plot for each of your samples; make sure these use the same scale. (These can be CAREFULLY hand-drawn images or made with technology.) Each boxplot must have the 5-number summary values listed in the appropriate location on the boxplot.
   3. State the sample mean and standard deviation for each of your groups.
   4. Talk about any similarities and differences you detect between the samples.  Talk about what the mean and the standard deviation tell you about the data sets, as well as what conclusions you can draw from these descriptive statistics about the two populations you are studying.
4. Construct a 95% confidence interval for the data (15 points total)
   1. Use the PANIC process.
   2. If you have paired data, be sure your confidence interval is for the MEAN of the DIFFERENCES (μd ).
   3. If you have independent data, be sure your confidence interval is for the DIFFERENCE of the MEANS (μ1−μ2)
   4. Be clear about what order you are doing the subtraction in.
5. Conduct a two-sample t-test or paired t-test.  (24 points total)
   1. Use the PHANTOMS process.
   2. Use a 2.5% level of significance.
6. Conclusion (8 points)
   1. What are the results of your study? State in your own words an interpretation of both the confidence interval and hypothesis test.  BE AWARE:  If you have done your statistical analysis correctly, the hypothesis test and the confidence interval should come to the same conclusion.  If they do NOT, that is an invitation to go back and try to find any errors you may have made.
   2. What connections do you see, if any, between the DESCRIPTIVE statistics (your boxplots & histograms) and the INFERENTIAL statistics (your confidence interval & hypothesis test).
   3. Did you discover anything that surprised you when you analyzed the data?
   4. What additional questions do you have based on your results?  What additional research, if any, is warranted by the results?

AN IMPORTANT NOTE!  Many of you are working on data that you can see does NOT come from a normally distributed population (based on your histogram & boxplot from Part B).  This of course is somewhat problematic for the processes we are using.  Be sure to make note of this when checking your assumptions!  What is it that allows us to proceed anyway?  (In other words, what other assumption that we check gives us the OK to proceed?)

Keep in mind, it is ALL RIGHT if the data does not support your alternate hypothesis.  That’s why we do statistical research!  It’s much more interesting when surprising things happen with our data.