Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have reached a weight with an average of 971? and standard deviation of 15.2 ?. Propose a model for the weight of the hammers including a probability distribution for the weight. What are the assumptions for this model to hold? What parameters does this model have? A new production system is configured, and one wants to evaluate if the new system makes more constant weights. For this a random sample of newly produced hammers is evaluated yielding the following weights: 987, 966, 955, 977, 981, 967, 975, 980, 953, 972 What hypothesis can you formulate and what test and decision rule can you make to estimate if the new system produces a more constant weight? Express these assertions as logical statements involving critical values. What error probabilities can you suggest and why? Calculate the ?-value. Perform the test and express conclusions.
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!
Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have reached a weight with an average of 971? and standard deviation of 15.2 ?. Propose a model for the weight of the hammers including a probability distribution for the weight. What are the assumptions for this model to hold? What parameters does this model have?
A new production system is configured, and one wants to evaluate if the new system makes more constant weights. For this a random sample of newly produced hammers is evaluated yielding the following weights:
987, 966, 955, 977, 981, 967, 975, 980, 953, 972
What hypothesis can you formulate and what test and decision rule can you make to estimate if the new system produces a more constant weight?
Express these assertions as logical statements involving critical values. What error probabilities can you suggest and why?
Calculate the ?-value. Perform the test and express conclusions.
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