spring2008stat201-hw10KEY

spring2008stat201-hw10KEY - 36-201 Spring 2008 Homework 10...

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This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html 36-201 Spring 2008 Homework 10 – KEY
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Stat 201 Spring 2008 Page 1 of 9 Homework 10 – KEY This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html Due: Wednesday, April 9 , 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 8.1 to 8.3 in the course textbook. Point Distribution: Exercise 1 Exercise 2 Exercise 3 Exercise 4 effort & neatness TOTAL 15 24 27 14 20 100 NOTE: To save paper, you are encouraged to print double-sided (‘duplex’ mode).
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Stat 201 Spring 2008 Page 2 of 9 Homework 10 – KEY This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html IMPORTANT NOTE: The third hourly exam will be held Monday, April 21, in lecture. The exam will cover the material through this homework (hw 10), which you will get back in the prior lab. 1. hypothesis test for mean with sigma assumed to be known (hypothetical scenario) Statistical analysis of writing style is used in many disciplines, including criminal investigation (where it is known as ‘forensic linguistics’) as well as the humanities (where it is known as ‘stylometry’). One simple method of analyzing writing style is to measure word length (i.e., count the number of letters per word). Here is an example. Suppose the total known writings of Shakespeare have a mean word length of 9 8 . letters, with standard deviation 6 3 . = σ letters. Now suppose a new poem has been discovered. We are interested in deciding if the newly discovered poem might be by Shakespeare. If we let μ denote the population mean of all words by the poem’s true author, then the competing possibilities that the poem’s author is, or is not, Shakespeare, are represented by the following hypotheses: 9 . 8 : 9 . 8 : 0 = A H H Considering the words of the poem to be a random sample of all the words written by its author, the average word length of the poem is then a sample mean, which can be used to test the hypotheses. Suppose the poem contains 36 words, whose mean word length is
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spring2008stat201-hw10KEY - 36-201 Spring 2008 Homework 10...

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