Two men A and B who usually commute to work together decide

Two men, A and B, who usually commute to work together, decide to conduct an experiment to see whether one route is faster than the other. The men believe that their driving habits are approximately the same, and therefore they decide on the following procedure. Each morning for 2 weeks, A will drive to work on one route and B will use the other route. On the first morning, A will toss a coin. If heads appear, he will use route I; if tails appear, he will use route II. On the second morning, B will toss the coin: heads, route I; tails, route II. The times, recorded to the nearest minute, are shown in the following table. Assuming commute times are normal, find the 95% confidence interval estimate for the mean of the differences _d, where d = route I route II. (Round your answers to two decimal places.)

Day
Route	M	Tu	W	Th	F	M	Tu	W	Th	F
I	30	30	26	28	31	26	29	24	30	25
II	29	23	27	27	23	23	27	27	26	23

Solution

Day Route M Tu W Th F M Tu W Th F I 30 30 26 28 31 26 29 24 30 25 27.9 2.469818 II 29 23 27 27 23 23 27 27 26 23 25.5 2.27303 d Mean diff 2.4 s std error 1.061477 Margin of error 2.080495 Lower limit 0.319505 Upper limit 4.480495