# Home work - Home work Statistics 401 Experimental Methods I...

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Home work Statistics 401 Experimental Methods I Spring 2000 Homework #1 Do problems 1.13, 1.25, 1.33, 1.51, 1.65, 2.6, and 2.22 from the 5th edition of Devore. Homework #2 Do problems 2.29, 2.47, 2.62, 2.76, 2.102, 3.9, 3.12, and 3.22 from the 5th edition of Devore. Homework #3 Assigned: Friday, January 28 Due: Friday, February 4 Do problems 3.31, 3.34, 3.46, 3.48, 3.66, 3.69, 3.74, 4.6, and 4.12 from the 5th edition of Devore. For this assignment, you may find Tables A.1 and A.2 helpful, though they are not necessary. Homework #4 Assigned: Friday, February 4 Due: Friday, February 11 Do problems 4.17, 4.18, 4.30, 4.35, 4.48, 4.59, and 4.81 from the 5th edition of Devore. For the last problem, you may this helpful if you would like to use Minitab: How to produce a probability plot in Minitab There are a couple ways to do this. One is more automatic but less informative; the other gives you more of a chance to figure out how the plot is produced. In either case, you'll need to start Minitab and then enter your univariate quantitative sample into one column. The columns are labeled in Minitab as C1, C2, C3, etc. I'll use Exercise 4.80, p. 195, as an example. This example asks for a normal probability plot for the following dataset:

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152.7 172.0 172.5 173.3 193.0 204.7 216.5 234.9 262.6 422.6 After you enter these data into Minitab correctly, the worksheet should look something like this (note that I used column C1): Notice that I added the title "Lifetime" to column C1. This is optional but makes it easier to keep track of what each column means. If you want to produce a normal probability plot in a single step, you can select Probability Plot from the Graph menu. You'll should then fill in the dialog box you get as follows:
When you click OK, you'll see the normal probability plot. There is some curvature in the plot which makes me doubt that these data should be considered to have come from a normal distribution. If you want to produce a normal probability plot using several steps (but still making Minitab do all the work for you), you first need to make sure the column is sorted in order from smallest to largest. To do this, select Sort from the Manip menu and then fill in the dialog box like this: Click OK and you should get sorted data. In my example, the data were already sorted. Next, set up a column of the values (i-0.5)/n as i goes from 1 to n (as explained on the bottom of page 189). There's a systematic way of doing this in Minitab: From the Calc menu, select Make Patterned Data and then Simple Set of Numbers. You'll get this dialog box:

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In filling out the above dialog box, make sure you put 0.5/n in the "From first value" blank, (n- 0.5)/n in the "To last value" blank, and 1/n in the "In steps of" blank. In my example, n=10 so you can see why I chose 0.05, 0.95, and 0.1, respectively. This box will create a new column of numbers in column C2. Check to see that the new column is exactly the same length as C1. The next step is to fill in the z-values corresponding to each value in C2. Minitab will do it for you automatically: In the Calc menu, select Probability Distributions and then Normal. You want the inverse cumulative probability for every value in column C2 (and then to put these in C3), so
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• Spring '00
• Akritas

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