3) A rural county presently uses Asphalt A to pave its highways, but is considering using the more expensive Asphalt B (which is reported to be more durable). The two types of asphalt are tested using 200m test strips on five different two-lane highways. On each test strip, a randomly selected lane was paved with Asphalt A and the lane in the opposing direction was paved with Asphalt B. It has been determined that it is more economical to use Asphalt B if the length of time before resurfacing is required (i.e. longevity) is at least 2.5 years longer on average than that of Asphalt A. The data are summarized in Table 1. Assume that the longevity of each type of asphalt is normally distributed. Table 1: Longevity (in years) of 200m asphalt test-strips on 5 rural two-lane highways Location 2 3 4 5 Mean Std. Dev Asphalt A 11.2 9.0 10.7 11.4 8.5 10.16 1.32 Asphalt B 18.8 11.7 19.9 19.0 13.4 16.56 3.73 D = XB - XA 7.6 2.7 9.2 7.6 4.9 6.40 2.58 Using a 2% significance level and assuming that the data for the two types of asphalt at each test strip can be paired, determine if Asphalt B lasts at least 2.5 years longer than Asphalt A on average. (7 marks)