Graded Assignment 4252grass4-041 3/29/07 (Open this document in 'Page Layout' view!)Name, Student Number:Class days and time:Please include this on what you hand in!Graded Assignment 4The data set is part of a problem due to Pelosi and Sandifer.20 Employees (A-T) are timed in a computer entry task initially (0hr), after 2 hours of work (2hr), after 4 hours (4hr) and after 6 hours (6hr). The times, in seconds are reported below. a) At a 5% significance level do the four mean times differ? b) determine which of the times actually differ. c) On the basis of these data, how would you react to a proposal that employees only be allowed to work for four hours a day at this task? Only neat and legible papers with written answers in complete sentences will be read! 0 H o u r s 2 H o u r s 4 H o u r s 6 H o u r s 67 84 52 5764 78 53 5369 74 56 7188 91 66 6172 70 59 7380 73 77 5085 86 64 53116 71 62 8077 76 54 6378 76 65 4168 61 71 6351 62 92 4154 94 71 5375 63 50 6371 70 71 6164 63 58 4686 66 77 6898 71 53 64103 53 81 4991 81 70 70Do this problem in Excel as follows.Use columns A, B, C, D, E and F on the Excel spreadsheet for data In the first row of Columns B, C, D and E put in 0hr, 2hr, 4hr and 6hr. Head column A with the word ‘employee.’ Starting in Cell A2 Put in the letters A through T to identify the employees – unless, of course,you want to suggest some names.Now put in the data in columns B, C, D and E, skipping column AIf you bring this document into Word, the data can be moved into the Excel worksheet by highlighting the cells you want and copying and pasting.To fill column F in cell F2 write =B2 after your 'enter' this cell should read '67'Use the 'edit' pull-down menu and 'copy' cell F2Use the 'edit' pull-down menu and 'paste' in cells F3 through F21. Now column F will be identical to B except for the heading. This can also be done as a simple copy and paste. Save your data as time1.xlsVersion A – One-way ANOVAUse 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$21. Select 'New worksheet ply' and 'columns' , check 'labels in first row' hit 'OK' and save your results as treslt1.xls.Version B – Two way ANOVAIn orderto check for the effect of the fact that the data is blocked by employees, repeat the analysis using ‘ANOVA: Two-Factor without replication. Set input range to $A$1:$E$21, check ‘labels,’ and save your results as treslt2.xlsAnswer the following: Is there a significant difference between the task completion times according to the number of hours worked? How is this conclusion affected by blocking by employees? Cite p-values and /orF-testsVersion C – One way ANOVATake the last digit of your student number (if it's zero, use 10). Go back to your original data or use the 'file' pull-down menu to open time1.xls. To fill column B this time in cell B2 write =F2+x, replacing x with the last digit of your social security number.Use the 'edit' pull down menu and 'copy' cell B2Use the 'edit' pull down menu and 'paste' in cells B3 through B21. Now column B will be more than the original B by the amount of your value of x. Save your data as time3.xls.Run the one-way ANOVA again and save your results as treslt3.xlsSubmit 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 do a Scheffe confidence interval and a Tukey-Kramer interval or procedure for each of the 642C possible differences between means and report which are different at the 5% level according to each of the 2 methods. Now on the basis of these data, how would you react to a proposal that employees only be allowed to work for four hours a day at this task? Why?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.The easiest way to do this is to copy the first five columns from the original Excel spreadsheet. Enter Minitab and use ‘editor’ to enable commands. Highlight the column labels and cells 1-20 of the first five columns. Remember that your column labels should be written in above the columns (Put row labels in column 1). Just to make sure that you are in the right place. Thr the following Minitab commands.print c1-c5AOVO c2-c5You should get results equivalent to your first ANOVA.To set up for a 2-way ANOVA stack your data in columns 6 and 7. Stack c2 c3 c4 c5 c6;Subscripts c7 ;UseNames.To move the row labels, copy the A through T from column 1. Highlight all 80 cells of column 8 and pasteyour A-T into the column. Every number should now have a correct row label. Use the material from computer assignment 2 to check your data. I combined the ANOVA and the table of means command by using the following.Twoway c6 c8 c7;Means c8 c7. 2) Take the data from your last ANOVA. Use the instructions in 1) above to copy it into the Minitab spreadsheet and perform Levene and Bartlett tests 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. There are two ways to do this. If you want to do it on the unstacked data use the following.Vartest c2-c5;Unstacked.To do the tests on the stacked data use the following.Vartest c6 c7.2Extra Extra Credit: Do Bartlett and Levene tests 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
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