Let X and Y equal the forces required to pull different objects out of a window. Assume that the distribution of X and Y are N(ux,o²)and N(Hy,o), respectively. (a) If m = n = 10 observations are selected randomly, define a test statistic and a 2 critical region_for testing Ho : Hx = µy against H1: µx # µy, at the level of significance o = 0.05. Assume that o is unknown and use Sx = 14.08)6y = 12.26. (b) Given n = 10 observations of X, namely, 111 120 139 136 138 149 143 145 111 123 and m = 10 observations of Y, namely 152 155 133 134 119 155 142 146 157 149 calculate the value of the test statistic and-state your conclusion clearly. (c) Find the bounds of the p-value of this test?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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