Scientists at LUMS looked at the steel strength (MPa) for a sample of 12 columns used in a developmental project in Lake City, Lahore. The purpose of this study was to understand whether the steel strength differs when columns are exposed to sunny conditions vs. rainy conditions. Each of these columns was then exposed to sunny conditions (denoted by M) and rainy conditions (denoted by LD). The results are shown below: 1 2 3 4 5 6 M: 82.6 87.1 89.5 88.8 94.3 80.0 LD: 86.9 87.3 92.0 89.3 91.4 85.9 7 8 9 10 11 12 M: 86.7 92.5 97.8 90.4 94.6 91.6 LD: 89.4 91.8 94.3 92.0 93.1 91.3 a. Formulate the relevant hypotheses for this study (2) b. Estimate the difference in the true average strength between the sunny conditions and rainy conditions. Test the hypotheses in a reliable and precise way, and interpret the estimate as well. Use an alpha of 0.06 (6) c. What are some of the assumptions you made for this analysis? (2)