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(4) Show your work (a) The federal government awarded grants to the agricultural departinents of 6 universities to test the yield capacities of two new varieties of wheat. Each variety was planted on a plot of equal area and similar soil conditions at each university, and the yeilds, in kilograms per plot, were recorded as follows: University #1 #2 #3 #4 #6 Variety 1 23 35 Variety 2 31 38 45 05 44 50 41 38 25 29 33 Find a 90% confidence interval for the mean difference between the yields of the two varieties, assuming the differences of yields to be approximately normally distributed (b) SAT mathematics scores of a random sample of 400 high school seniors in the state of New York are collected, and the sample mean and standard deviation are found to be 530 and 108, respectively. For the next randomly selected high school senor in New York, find a 90% prediction interval on their SAT mathematics score.