Problem 2. (14 points) A study reported the results of an analysis of the weight of calcium in standard cement and cement doped with lead. Reduced levels of calcium would indicate that the hydration mechanism in the cement is blocked and would allow water to attack various locations in the cement structure. 10 samples of standard cement had an average weight percent calcium of E1 = 90.0 with sample standard deviation of 31 = 5.0 and 15 samples of leaddoped cement had an average weight percentage calcium of E2 = 87.0 with a sample standard deviation of 32 = 4.0. Assume the weight percent calcium is normally distributed and that both distribution has same standard deviation. Suppose we are interested in whether the data provide convincing evidence in the difference of the weight percent calcium between the standard cement and the lead doped cement is not zero. (a) (2 points) Provide the Null and Alternative hypotheses by dening all the parameters you use. (b) (3 points) Compute the test statistic for the GLRT test we discussed for above hypotheses in (a) and specify the distribution. (0) (3 points) Use the test specied in (b) to compute the pvalue and make a conclusion at signicance level oz 2 0.05. 1 (d) (6 points) Assume that the real distribution of the weight percent calcium in standard cement and in the leadadopted cement independently follow N (1,42) and N (0.5,42) respectively. Compute the typeII error probability of the problem. Compute the typeII error probability for o. = 0.05