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### Research Paper Examples

How many letters on average does the average SJC student have in his or her last name? How about the first name? My claim is that the average for both is 7 letters. Your goal is to test this claim and decide whether or not it is plausible. You are to do a statistical analysis and report your finding both numerically and in the form of a short paper.

Among the issues you will need to confront are:

How can you get a random sample of students? Each student must have an equal chance of being selected. I suggest using random numbers generated by Excel with the student directory. I explained an acceptable way of getting the sample in class. You must explain exactly how you drew your sample in your paper. If the sample is not taken correctly, then the results will mean nothing.

You should also explain why not all students are listed in the directly, and try to justify why the omission of some students is unlikely to alter the results.

After you get a sample of 25 (which is a very small sample, but we are more interested in showing the procedure than finding an accurate estimate), you need to compute a test statistic, which will be not a z-score but a t-score. You can follow the example in the textbook on page 337 to do this. Then you need to explain clearly what your results show you in words that would make sense to someone who has never taken a statistics class.

You will quickly discover that the hard part of this assignment is taking the sample. The rest should be fairly easy, even the writing up of results.

If you have any questions, ask.

(For many years I required students to do a paper in which they took a random sample of books from the library to determine the average age of the library books. Sometimes this was an assignment of estimation; here it is presented as an assignment in hypothesis testing. Early on they could do a systematic random sample using the card catalog that contained paper cards. Then the library discarded the paper and went digital, and they could use the record numbers. Then the library changed their database system and I could never again figure out a simple way to have the students take a random sample, so the assignment died. It is given here as an example of something that can (or could) be done in an introductory course.)

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Jack and Joan had an argument last week about the age of the books in the college library. Jack, knowing only enough about statistics to be dangerous, decided to settle the argument by sampling. He went to the library's economics section, where all the really good books hang out, and took a sample of nine books that happened to be sitting on the shelf. From this he assumed that the average age of books in the library was 26 years old.

Joan was dubious about this claim, and thought that the way Jack took the sample might lead to questionable results. She asked a professor to settle this dispute. Upon hearing this story, the professor exclaimed, "What a wonderful assignment for my class. I will have them test the hypothesis that the average age of books in the library is 26 years."

The above story is mostly fictitious. The part that is not fictitious is the part about the assignment. You are to test the claim discussed above by taking a random sample of 50 books from the SJC library. You need to find a way to take a random sample, and the following may be of some use.

All the books in the library have a record number that you can find in the following way. Start with the main screen (the one which has the crude picture of the building) on the on-line catalog and hit return. This takes you to a search screen. Now press the Find key. This gives you an expanded search list that most people do not know exists. (In fact this is Library Top Secret (LTS) and unspeakable things can happen to those who pass this secret on to those who are not authorized for LTSs.) Use the arrow key to get to the RN Record Number item. Then enter a record number. All record numbers at SJC are between 1-1 and 1-138290. However, included in these numbers are some items that are not books (records, for example) and some items that no longer have a book assigned because the book has been discarded. When you enter the record number of a book, you will get information about the book, including the year in which the book was published.

Your assignment is to take random sample of 50 books using random numbers generated by SPSS. (Look at Chapter 1 in the text and the second lab worksheet.) Then, using SPSS test the hypothesis that the true mean age of library books is 26 years. After you are finished, you are to write up your results in a three or four page paper that clearly explains exactly what you did (including especially how you got your sample) and what the results mean. Include as an appendix printed results from SPSS.

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