Question

A freight transport company wants to choose the best route to take the merchandise from one deposit to another. The biggest concern is travel time. In the study, 5 drivers from a group of 10 were randomly selected and assigned to route A; the remaining five were assigned to route B. The data obtained were:

Route			Travel time in hours
A	18	24	30	21	32
B	22	29	34	25	35

a) Are there significant differences between the routes? Raise and test the corresponding statistical hypotheses.

b) In case of rejecting the hypothesis test. A) Draw the diagrams of simultaneous boxes to determine which route is better.
c) Suggest another way to obtain the data (alternative design) so that you can achieve a more effective comparison between the routes.

Note: The exercise must be done in two ways using excel. The first without using data analysis and the second using data analysis. Remember that the procedure must be clearly explained step by step.

Answer 1

a) Please see the excel screenshots below

we enter the data in excel and then goto data > data analysis tab and select t test

considering an alpha of 0.05 , we see that the p value is not less than 0.05 hence we fail to reject the null hypothesis

H0 : there are no significant differences between the routes
H1 : there are significant differences between the routes

c) The better design could be in terms of chosing the same drivers for the 2 routes and then performing a paired t test instead of independent samples t test. What if , the drivers ability directly effects the time taken to cover the route