fall2009stat201-hw09KEY

fall2009stat201-hw09KEY - 36-201 Fall 2009 Homework 9 KEY...

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36-201 Fall 2009 Homework 9 – KEY
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Stat 201 Fall 2009 Page 1 of 7 Homework 9 – KEY ± Due: Wednesday, November 4 , 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 just outside the instructor’s office, room 132-B Baker Hall. 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 chapter 8 in the text. Point Distribution: Exercise 1 Exercise 2 Exercise 3 Exercise 4 effort & neatness TOTAL 35 10 13 22 80 100 NOTE: To save paper, you are encouraged to print double-side (‘duplex’ mode).
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Stat 201 Fall 2009 Page 2 of 7 Homework 9 – KEY 1. [confidence interval for mean] Suppose a company wants to estimate µ , the mean number of daily hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean daily computer usage time of 2 . 25 hours. Suppose that, from prior studies, the population standard deviation is assumed to be σ = 0 . 45 hours. 1 (a) (i) What is the population in this scenario? All U.S. adults. (ii) What is the sample in this scenario? The 81 adults. (or similar wording) (iii) What is the symbol that represents the unknown parameter of interest, and what does that symbol refer to in this scenario? Symbol: (“mu”) μ Meaning: The (true) population mean number of hours that all U.S. adults use computers at home. 1 (b) What is the ‘point estimate’ for in the scenario? [Give both its value and the symbol.] Symbol: x (“ex-bar”) Value: 2.25 1 (c) Briefly say why the conditions for constructing a confidence interval will be satisfied in this case. Answer: (1) Sampling random (as stated in the exercise) (2) The size of the population (all adults in U.S.) is many times larger than n=81 (like, more than 20 times as large), so the sampling can be considered to be “approximately” with replacement (this guarantees that the population can be considered ‘fixed’ [the more sophisticated term is ‘identically distributed’], and also plays a role in guaranteeing statistical independence ) (3) The Central Limit Theorem condition for ‘means’ is satisfied, because the sample size of 81 is [exercise 1 continues on next page]
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Stat 201 Fa mework ll 2009 Page 3 of 7 Ho 9 – KEY 1 (d) Construct a 95% confidence interval for µ . Show your calculations, and report the interval. Solution: A confidence interval for mean is given by: n σ z x ± Using z=2 (for 95%) gives: = 81 .45 2 2.25 ± = 9 .45 2 2.25 ± = 2(.05) 2.25 ± = .1 2.25 ± = ( 2.15 , 2.35) 1 (e) State the margin of error.
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This note was uploaded on 04/07/2010 for the course STAT 36-201 taught by Professor Gordon during the Spring '08 term at Carnegie Mellon.

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fall2009stat201-hw09KEY - 36-201 Fall 2009 Homework 9 KEY...

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