Two men, A and B, who usually commute to work together decide to conduct an expe

Question

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 feel that their driving habits are approximately the same, so each morning for two weeks one driver is assigned to route I and the other to route II. The times, recorded to the nearest minute, are shown in the following table. Using this data, find the 98% confidence interval for the true mean difference between the average travel time for route I and the average travel time for route II.

Let d=(route I travel time)?(route II travel time) . Assume that the populations of travel times are normally distributed for both routes. Day M Tu W Th F M Tu W Th F Route I 32 35 32 34 30 27 34 31 28 30 Route II 33 30 33 29 26 25 29 34 33 33

Step 2 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Explanation / Answer

Ans:

n=10

df=10-1=9

critical t value=tinv(0.02,9)=2.821

98% confidence interval for the true mean difference

=0.80+/-2.821*(3.8528/sqrt(10))

=0.80+/-3.438

=(-2.638, 4.238)

Population 1 Population 2 difference(d) 1 32 33 -1 2 35 30 5 3 32 33 -1 4 34 29 5 5 30 26 4 6 27 25 2 7 34 29 5 8 31 34 -3 9 28 33 -5 10 30 33 -3 mean= 0.80 std dev= 3.8528

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