1. Metro Atlanta Rapid Transit Authority determines bus routes through the city according to an equal amount of time for completion of all routes. Periodically they check these route times by conducting independent surveys. The Lennox Square Route was sampled 40 times and showed an average completion time of 80 minutes with a standard deviation of 5 minutes. The Turner Field Route was sampled 50 times and showed an average completion time of 76.5 minutes with a standard deviation of 6 minutes. At the ninety five percent confidence level, does this data support the belief that both routes in the city take an equal time to complete?
2E. Citizens in the Twin Cities are measured concerning use of a certain brand of toothpaste. In Minneapolis, 15% of the population has tried the product while in St. Paul, only 8% of the population has used the toothpaste. If a sample of 120 people is taken in Minneapolis, and an independent sample of 130 people is taken from St. Paul, construct the ninety-five percent confidence interval for the difference in the portion of the populations using the toothpaste.