Would shifting to a four-day work week reduce commuting mileage, fuel consumption and exhaust emissions? We will use the data comparing mileage driven for four and five day work weeks that is the main example at the start of Chapter 25 of De Veaux, Velleman and Bock, Stats.: Data and Models 2nd ed., 2008, Addison Wesley, Boston.. If you have this book (or another by the same authors) run the ActivStats CD that comes with it but instead of starting ActivStats click on the Datasets button at the lower left of the start-up window. Choose the version of the text you have and go to the Text folder and findCh25_mileage.txt. Copy it to the R folder on your computer. If you do not have the CD, the dataset is small enough that you can just type it in from the printout below..
We had already copied all these files to the R folder on our computer so we looked at the files in the R directory to find out what the name of the file was, then read it into a frame named mileage. We just read it to see what the variable names were. Then we created a variable diff for the differences, typed diff to see them (and compare them to the textbook), and then used t.test.
> mileage <- read.delim(file="Ch25_mileage.txt",header=TRUE) > attach(mileage) > read.delim(file="Ch25_mileage.txt",header=TRUE) Name X5.Day_mileage X4.Day_mileage 1 Jeff 2798 2914 2 Betty 7724 6112 3 Roger 7505 6177 4 Tom 838 1102 5 Aimee 4592 3281 6 Greg 8107 4997 7 Larry G 1228 1695 8 Tad 8718 6606 9 Larry M 1097 1063 10 Leslie 8089 6392 11 Lee 3807 3362 > diff = X5.Day_mileage - X4.Day_mileage > diff  -116 1612 1328 -264 1311 3110 -467 2112 34 1697 445 > t.test(diff) One Sample t-test data: diff t = 2.858, df = 10, p-value = 0.01701 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 216.4276 1747.5724 sample estimates: mean of x 982
Note the free confidence interval. We should also
> stem(diff) The decimal point is 3 digit(s) to the right of the | -0 | 531 0 | 04 1 | 3367 2 | 1 3 | 1
This is not too bad for such a small dataset. Note that we check assumptions on the differences, not the original data.
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