fall2009stat201-hw08KEY

fall2009stat201-hw08KEY - 36-201 Fall 2009 Homework 8 KEY...

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36-201 Fall 2009 Homework 8 – KEY
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Stat 201 Fall 2009 Page 1 of 13 Homework 8 – KEY ± Due: Wednesday, October 21 , 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 7 in the text. Point Distribution: Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 effort & neatness TOTAL 5 14 19 23 19 20 100 NOTE: To save paper, you are encouraged to print double-side (‘duplex’ mode).
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Stat 201 Fall 2009 Page 2 of 13 Homework 8 – KEY IMPORTANT NOTE: The second hourly exam will be held Monday November 9, in lecture. The exam will cover through the material on this homework, which you will get back in the prior lab. 1. [spread of the sampling distribution of mean] Suppose that, in a chemistry class, you want to measure the mass of a certain substance, using a certain laboratory apparatus. The apparatus is not perfect. Readings with the apparatus will fluctuate independently. Suppose it is known that individual readings with this apparatus will fluctuate with standard deviation of 10 = σ grams. The lab book says to make 4 measurements and then report the mean, x , of the four measurements. 1 (a) Repeated averages will also fluctuate. Use the ‘one-over-square-root law’ as shown in lecture [also shown on page 323 of the text] to compute the standard deviation x of the averages of 4 measurements each. [Show work.] Solution: = = = = 2 10 4 10 n σ x σ 5 . 1 (b) Substitute the appropriate numbers to complete the following sentence: With this apparatus, an individual measurement is expected to be ‘off’ (from truth) by about 10 grams, while the average of four measurements is expected to be ‘off’ (from truth) by about 5 grams. 1 (c) Suppose a classmate (who is in a hurry to leave the lab) complains that, since repeated averages will fluctuate, there is no advantage to taking four measurements instead of just one. In light of your answers in part (b), is there any advantage to averaging four measurements, instead of taking just one? [Say yes or no .] If yes, briefly say what that advantage is. Answers: Yes, there is an advantage to averaging four measurements, rather than taking just one. The advantage is that the average of four measurements has less variability , or equivalently, the average of four measurements will generally be closer to the true value .
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Stat 201 Fall 2009 Page 3 of 13 Homework 8 – KEY 2. [the Normal Sampling Distribution of mean] Students’ scores on the ACT college entrance examination in a certain year had mean 25 = µ points and standard deviation 4 = σ points. The distribution of scores was reasonably Normal.
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fall2009stat201-hw08KEY - 36-201 Fall 2009 Homework 8 KEY...

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