Question

1. THIS PROBLEM GIVES YOU MORE INFORMATION THAN YOU NEED SO PLEASE READ THE QUESTIONS CAREFULLY; I try to clarify by referring to the sample sizes. TBNF is a new computer program that is supposed to solve transportation planning problems. We would like to compare the results of TBNF to a currently used solver called TRoute. TRoute is known to give the best routes in the fastest time so the same problems will be submitted to both systems and the results compared.

One comparison ran the same problem 25 times on TBNF and 23 times on TRoute and the time it took to solve the problem was recorded as was the total trip distance.

	Sample Size	Average Time to Solve Problem	Standard Deviation of time to solve problem	Average Trip Distance	Standard Deviation in Trip Distance
TBNF	25	72.5 minutes	12.8 minutes	232 miles	87 miles
TRoute	23	66.4 minutes	14.9 minutes	263 miles	45 miles

Another comparison wanted to look at the consistency of the solutions so the same trip was run 200 times using both TBNF and TRoute. 167 out of the 200 runs for TBNF the route was the same and 146 out of 200 runs the TRoute was the same.

1. Test the claim that TBNF gives consistent routing less than 85% of the time (Use the info from the 200 trials) with 1% significance.

2. Find a 90% confidence interval to estimate the difference in the average time to solve the problem between TBNF and TRoute (use the table information for time).

Answer 1

Ho2o-s 0-83 16 200 ㄧ -o.ois 0-83S - 0-S 0 Sx 0-15 200 O-595 2+ 11-S 46 1 9 2.5 0-62, 1282) ait