Graded Assignment 4252grass4-061 11/14/06 Open this document in 'Page Layout' view!) Name: Class days and time:Please include this on what you hand in!Graded Assignment 4The data set is based on problem 11.52 in the 10th edition or 11.66 of 9th edition of the text. It gives theamount of dirt removed according to the cycle time blocked by the detergent used. You must answerquestions a-c for versions A, B and C of the problem. To enable statistical functions, enter Excel and usethe Tools pull-down menu. Select Add-Ins and check the two Analysis Tool Pack items. If you do not haveat least the first of these available on your home computer, you may have to use the school computers.This year’s data is below.Row 18m 20m 22m 24m 1 0.12 0.13 0.17 0.17 2 0.10 0.13 0.19 0.18 3 0.13 0.14 0.17 0.19 4 0.11 0.15 0.18 0.17 5 0.09 0.16 0.18 0.20 6 0.10 0.13 0.17 0.16 7 0.12 0.12 0.16 0.15 8 0.14 0.13 0.17 0.17Note that Rows 1 and 2 are data for Detergent A, Rows 3 and 4 are data for Detergent B etc. Only neat and legible papers with written answers in complete sentences will be read!a) At a 5% level is there evidence of a difference in the average amount of dirt removed by cycles of different length? Why? b) What assumptions are necessary in (a)? c) What cycle lengths should be recommended?Do this problem in Excel as follows.Use columns A, B, C, E and F on the Excel spreadsheet for data In the first row of Columns B, C, D and F put in 18m, 20m, 22m and 24m. Label Column E with 24ma and Column A with ‘brand.’ Starting in Cell A2 Put in the letters A through D to identify the detergents – unless, of course, you want to suggest some names. Now put in the data in columns B, C, D and F, skipping column E.Version A – One-way ANOVATo fill column E in cell E2 write =F2. After your 'enter' this cell should read '0.17.’'Highlight cell E2 and use the fill handle on cell E2 to make column E identical to column F except for theheading. Do not go on unless this is true. Save your data as wdataA.xlsUse the 'tools' pull-down menu and pick 'data analysis' (If you cannot find this, use Tools and Add-Ins to put in the analysis packs.)Pick 'ANOVA: Single Factor. Set input range to $B$1:$E$9. Select 'New worksheet ply' and ‘columns’, check 'labels in first row' hit 'OK' and save your results as wrslA.xls. Version B – Two-way ANOVAIn order to check for the effect of the fact that the data is blocked by detergent, repeat the analysis using ‘ANOVA: Two-Factor with replication. Set input range to $A$1:$E$9, check ‘labels’ (if it’s there)and saveyour results as gresltB.xls. Put 2 in ‘rows per sample.’ Citing the F’s or p-values answer questions a-c and question d), is there a significant difference between the amount of dirt removed by the detergents and does the use of the detergents as a factor change your conclusion about wash cycles? Cite p-values and/or F values.Version CTake the last digit of your student number (if it's zero, use 10) and divide it by 100. Call this y and make sure that I know its value. For example Seymour Butz’s student number is 101321, so he uses01.y. Go back to your original data or use the 'file' pull-down menu to open wdataA.xls. To fill column E this time in cell E2 write =F2 y, where y is the number you just figured out. Now highlight cell E2 and use the fill handle to make column E equal to column F minus y. Do not go onunless this is true. Relabel Column E as 24mc. Save your data as wdataC.xls. Run the one-way ANOVA again and save your results as wrsltC.xls.Submit the data and results with your Student number. The most effective way to do this is to paste the results into a Word document and then add neat hand or typed notes. Indicate what hypotheses were tested, what the p-value was and whether, using the p-value, you would reject the null if (i) the significance level was 5% and (ii) the significance level was 10%, explaining why. You will have two answers for each of your two problems.For your version C ANOVA do a Scheffe confidence interval and a Tukey-Kramer interval or procedure for the mean of the best cycle length versus the other 3 means and report which are different at the 5% level according to each of the 2 methods. Extra Credit: 1) Show that you learned something from computer problem 2 by doing part B on Minitab. There should be very little difference in your result.2) Take the data from your last ANOVA and perform a Levene test on it using the third example in 252mvarex. as a pattern for your calculations using Minitab. Make sure that you explain what is being tested and what you conclude. To do this copy your data into columns 1-5. If you did 1) and have your numbers in c1 and your column names in c2, you can unstack the data by using: MTB > Unstack (c1);SUBC> Subscripts c2;SUBC> After;SUBC> VarNames. (But you will have to move it around afterwards. You can do a lot by using the ‘data’ pull-down menu and clicking on ‘copy’ and letting it prompt you on what move you want.)Remember that your column labels should be written in above the columns (Put row labels in column1). Just to make sure that you are in the right place, print out your data and run a one-way ANOVA using:print c1-c5AOVO c2-c5The test is simply vartest c2-c5;unstacked.Don’t give me results without explaining them.Extra Extra Credit: Do Bartlett and Levene tests by hand using the examples in 252mvar as your pattern. It turns out that your ANOVA has just enough columns to do this test.This is an awful lot of work unless you cheat and use the computer. If you cover your tracks, I’ll never know. To do the Bartlett test you need logarithms of variances. Label Columns 10-12 ‘stdev,’ ‘var’ and ‘log.’ Use the data that you already have in four columns in Minitab c2-c5 (labels in c1) and get the variances as follows:name k2 ‘stdv1’ name k3 ‘stdv2’name k4 ‘stdv3’name k5 ‘stdv4’stdev c2 k2 stdev c3 k3 stdev c4 k4 stdev c5 k5print k2-k5 #These are the standard deviations of the columns.stack k2-k5 c10let c11 = c10 * c10 #Now you have variances.2let c12 = logten(c11)let k11 = mean(c11) #This is the pooled variance when you have equal sized samples.let k12 = logten(k11)print k11 – k12print c10 – c12.Now you are on your own. The rest of this should be pretty easy because all your jn s are equal.The Levene test is longer, but should be much more familiar
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