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). 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	26	32	25	31	27	33	29	31	30	31
Route II	31	30	30	27	32	30	33	32	27	35

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.

Step 4 of 4: Construct the 90% confidence interval.

Answer 1

Step 1 of 4 : Find the mean of the paired differences .

Answer:

Step 2 of 4 : Find the critical value that should be used in constructing the confidence interval.

Answer:  The critical value can be found at 0.1 significance level for . Using the t distribution table we have:

Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval.

Answer: The standard deviation of the paired differences to be used in constructing the confidence interval is:

rounded to 4 decimal places

Step 4 of 4: Construct the 90% confidence interval.

Answer: The 90% confidence interval is:

rounded to 2 decimal places

Therefore the 90% confidence interval is