Homework 7 Solutions - Homework set 8 Solutions Math 3200 Renato Feres Problems 1 Problem 8.6 textbook page 292 Production lines in a manufacturing

Homework 7 Solutions - Homework set 8 Solutions Math 3200...

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Homework set 8 - Solutions Math 3200 – Renato Feres Problems 1. Problem 8.6, textbook, page 292. Production lines in a manufacturing plant are set to make steel ball bearings with a diameter of 1 micron. Ten ball bearings were randomly selected from two production lines. The diameters of the ball bearings measured in microns were as follows: Line1 Line2 1.18 1.72 1.42 1.62 0.69 1.69 0.88 0.79 1.62 1.79 1.09 0.77 1.53 1.44 1.02 1.29 1.19 1.96 1.32 0.99 (a) Explain why these samples are independent. (b) Make a Q-Q plot of the data. Superimpose to it a 45 line through the origin. Does one set of ball bearing diameters tend to be larger than the other? If so, which set? Solution: (a) The ball bearings in each line are independently chosen, and not matched by any other factor or characteristic. (b) After importing the data under the table name D , I use the qqplot function: x=D[,1] y=D[,2] qqplot(x,y,xlab=’First line’,ylab=’Second line’) lines(x,x) This produces the following graph:

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0.8 1.0 1.2 1.4 1.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 First line Second line The ball bearings of the first production line have, by and large, smaller diameter. 2. Problem 8.7, textbook, page 292. To determine whether glaucoma affects the corneal thickness, measurements were made in 8 people affected by glaucoma in one eye but not in the other. The corneal thickness (in microns) were as follows: Glauc NoGlauc 488 484 478 478 480 492 426 444 440 436 410 398 458 464 460 476 (a) Explain why these samples are matched pairs. (b) Make a scatter plot of the corneal thickness. Do the pairs tend to lie above or below the 45% line through the origin? Do eyes affected by glaucoma tend to have either thicker or thinner corneas than unaffected eyes?

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