A man who moves to a new city sees that there are two routes he could take to wo

Question

A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to go, driving each route 20 days. He finds that Route A takes an average of 45 minutes, with standard deviation 5 minutes, and Route B takes an average of 49 minutes, with standard deviation 1 minute. Histograms of travel imes for the routes are roughly symmetric and show no outliers Complete parts a and b. Use a-0.05 a) Find a 95% confidence interval for the difference between the Route B and Route A com u ting times, Yu-YA) The confidence interval is (Round to two decimal places as needed.)

Explanation / Answer

1 - 2 = (M1 - M2) = 4, 95% CI [3.47, 4.53].

Calculation

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 26 / 38 = 0.68

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((0.68/20) + (0.68/20)) = 0.26

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 4 ± (2.02 * 0.26) = 4 ± 0.53

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