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Research Paper
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Develop your own research hypothesis to use in a one-sided two-sample z-test for population proportions.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Part A.  One-sided, Two-Sample z-Test of Population Proportions (See LN8.) 

In Part A, get your data from the U.S. Census using the methods discussed in LN8.  I recommend using FamilySearch.org.40 points

A1. Develop your own research hypothesis to use in a one-sided two-sample z-test for population proportions.  One way to start is to imagine the potential social impacts of a major historical event, such as the Civil War, Industrialization, or the Great Migration.  Then, think how such an impact might be reflected in a quantitative form in the Census. 

Full Census data is available at 10-year intervals from 1790 to 1940.  The full records of the 1950 Census have just recently been released and are not yet in a form usable to us. What can be measured depends on what questions were asked in Census used at that time.  You can easily search for "index of census questions" to find a breakdown of which questions were asked and when.  I fear that sometimes two versions of a census were used in the same year, as appears to be the case with 1820.  

Finding a good topic requires working back-and-forth between history and data availability.  For example, consider the Pike's Peak Gold Rush, occurring 1858-1861 in parts of what became Kansas and Nebraska.  In principle, comparing data from the 1850 and 1860 Census could be used to study the impact of that event.  However, Kansas and Nebraska would not appear in either of the 1850 or 1860 Census because they had not yet achieved statehood.  Be flexible!

A2.  State your null and alternate hypothesis in symbols.  Then explain in words what those hypotheses say, being specific to your setting.  Explain to a novice how your particular population proportions would in principle be computed.  

 

A3.  Gather your data from U.S. Census using original handwritten records.  Those are readily accessed using FamilySearch.  For each of the two samples, I recommend working from all persons shown on a single sheet of the census, which is usually between 30 and 40 people per sheet.  If you are restricting yourself to a smaller group, say, school-age children, then your working sample sizes will of course be smaller.  

Describe what you are doing as you present and process the data to get your two sample proportions.  Show the reader where and how you went from the census sheets to the proportions.  Those images will not be self-explanatory; they must be accompanied with text.  Write as if you are interested in the subject and the people, and are addressing someone else who is interested, too.  

 

A4.  Walk the reader through the steps of the hypothesis test in the context of your data.  As you go, explain how the test progressively answers the question, “How far is far?”

 

A5.  Graph the test, labeling all relevant portions.  

 

A6.  As we have stressed, taking a single page from the U.S. Census does not give a truly random sample.  What specific problems could arise your sample as a result?  How would using a random sample, of the same sample size, have helped overcome those problems?   

Part B. One-sided, Two-Sample t-Test of Population Averages 

(see LN7 and Section 4 of LN8)

40 pts

 

In Part B, get your data from ship manifests.  I recommend using either FamilySearch.org or the "Ellis Island."  I use that second site in Section 4 of LN8.  If you plan to use a different site, please come to me office hours, and clear it with me, first. No surprises, please! 

 

B1. Develop a research hypothesis to use in a one-sided two-sample test of population averages concerning age, height, or family size.  To do so, consider how an event such as a World War, famine, or the shifts in immigration policy could produce a change in who immigrates and when.  As always, write as if you are interested and even curious as to the nature of things that you encounter, and are addressing someone else who is interested, too.    

 

B2.  Gather your two samples from immigration data.  Use sample sizes between 5 and 70.  Show details of the sourcing and context.  Show and use images of the manifests of the ships.  Explain what you are doing as you go.  Annotate the images so the reader can follow your explanation, 

 

B3.  State the null hypotheses in words that apply to the particular topic you are addressing.  Define the populations you are referencing, their approximate sizes, and how the population averages would (in principle) be computed.  

 

B4.  Perform a one-sided, two-sample t-test.  Explain what the software is doing on each line of the table of output.  In particular, name the sample statistics that are computed and explain how those are connected with population parameters. 

B5. State the conclusion of the test and the grounds.  Explain the reasoning behind the conclusion.  

B6.  All serious studies are preceded by a small trial run to look for problems, including lack of clarity in definitions, problems in acquiring data, or a mismatch between the available measurements and what was desired to be measured.  Think of your study as a trial run for a larger study, in which many ships will be selected at random.  In terms of preparing for that larger study, what problems did you encounter and what changes would you make?

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