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 90% 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)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	29	29	30	25	27	24	32	27	25	25
Route II	34	26	31	24	26	26	27	29	24	26

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

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

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

4. Construct the 90% confidence interval. Round your answers to one decimal place.

Answer 1

The statistical software output for this problem is:

Hence,

1. Mean = 0

2. Critical value = 1.833

3. Standard deviation = 2.8

4. 90% confidence interval:

Lower limit = -1.6

Upper limit = 1.6