spring2008stat201-hw11KEY

spring2008stat201-hw11KEY - 36-201 Spring 2008 Homework 11...

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Unformatted text preview: 36-201 Spring 2008 Homework 11 – KEYStat 201 Spring 2008 Page 1of 11Homework 11 – KEY&Due:Wednesday, April 16, at the beginning of lecture. Homework considered late beyond the first 10 minutes of lecture. &Late Homework Policy:Late homework may be turned-in for a maximum of half credit, up to 4:00 PM on the same Wednesday the homework is due. Late homework should be placed in the manila envelope which will be posted by room 328-C, Facilities Management Building (FMS). Late homework should be labeled with the course as well as your name. Please do not turn in any homework to any mailboxes. &Please include the top-page ‘coversheet’, filled-out and stapled to your homework. &Show all work. This homework covers sections 7.3, 9.2, 13.1, and 13.2 in the course textbook. Point Distribution: Exercise 1 Exercise 2 Exercise 3 effort & neatness TOTAL 31252420100NOTE: To save paper, you are encouraged to print double-sided (‘duplex’ mode). Stat 201 Spring 2008 Page 2of 11Homework 11 – KEY1. [Gosset, and the t-distribution] The agricultural revolution in the 19thand 20thcenturies is one of the socially significant problems that spurred the development of statistics. One important example is the discovery of the t-distribution. William S. Gosset was an Oxford-educated mathematician, employed by the Guinness brewing company of Dublin. Since breweries use lots of grain, they are naturally involved in agricultural research, so part of Gosset’s work involved experimenting with crop yields. He realized that new mathematical techniques for handling the resulting data were needed, and he worked on the problem with Karl Pearson of University College, London. The outcome of Gosset’s study was perhaps the most famous paper in statistical literature, “The Probable Error of a Mean” (1908), which introduced the t-distribution. William S. Gosset (1867 – 1937)Since Gosset was contractually bound by Guinness, he published under the pseudonym “Student”, hence the t-distribution is often referred to as student’st-distribution. Here is one of the actual datasets that led to his analysis. There is reason to believe that drying seeds before planting them will increase the yield of the crop. As part of his analysis, Gosset reported on the results of 11 trials in which crop yields were obtained from ‘regular’ seeds as well as ‘dried’ seeds, and the change in yield (after drying the seeds) was recorded. The resulting data* is as follows: Trial Change in Crop Yield due to Drying the Seeds 1 106 2 -20 3 101 4 -33 5 72 6 -36 7 62 8 38 9 -70 10 127 11 24 * available from the online CMU Data and Story Library, http://lib.stat.cmu.edu/DASL/Datafiles/differencetestdat.htmlBecause few prior studies had been done, nothing was known about the standard deviation of...
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This note was uploaded on 02/01/2009 for the course STAT 36-201 taught by Professor Gordon during the Fall '08 term at Carnegie Mellon.

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spring2008stat201-hw11KEY - 36-201 Spring 2008 Homework 11...

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