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 1 of 4:

Find the mean of the paired differences, d‾. Round your answer to one decimal place.

Step 2 of 4:

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

Step 3 of 4:

Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place.

Step 4 of 4:

Construct the 98% confidence interval. Round your answers to one decimal place.

Answer 1

Number	Before	After	Difference
	32	33	-1	3.24
	35	30	5	17.64
	32	33	-1	3.24
	34	29	5	17.64
	30	26	4	10.24
	27	25	2	1.44
	34	29	5	17.64
	31	34	-3	14.44
	28	33	-5	33.64
	30	33	-3	14.44
Total	313	305	8	133.6

Confidence Interval :-



Lower Limit =
Lower Limit = -2.6377
Upper Limit =
Upper Limit = 4.2377
98% Confidence interval is ( -2.6 , 4.2 )

Since   lies in the interval  ( -2.6 , 4.2 ), hence we can conclude that there is no difference in the average travel time for route 1 and route 2 at 2% level of significance.