Here’s a problem that occurs in automatic program analysis. for a set of variables x1, . . , xn, you are given some equality constraints, of the form xi = xj and some disequality constraints, of the form xi 6= xj . is it possible to satisfy all of them? example: x1 = x2, x2 = x3, x3 = x4, x1 6= x4 cannot be satisfied. give an efficient algorithm that takes as input m constraints across n variables and determines if they can or cannot be satisfied. for full credit, your running time must be o(m log n) ; there is a solution that is faster than θ(m log n), but you do not need to come up with it for full credit.

A. find the power of the test, when the null hypothesis assumes a population mean of mu = 450, with a population standard deviation of 156, the sample size is 5 and the true mean is 638.47 with confidence intervals of 95 b. find the power of the test, when the null hypothesis assumes a population mean of mu = 644, with a population standard deviation of 174, the sample size is 3 and the true mean is 744.04 with confidence intervals of 95% c. find the power of the test, when the null hypothesis assumes a population mean of mu = 510, with a population standard deviation of 126, the sample size is 10 and the true mean is 529.44 with confidence intervals of 95