The breaking strengths of cables produced by a certain manufacturer have a mean, µ, of 1825 pounds, and a standard deviation of 55 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 60 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1828 pounds. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H1. H : H :0 (b) Determine the type of test statistic to use. (Choose one) D=0 Oso O20 (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) (e) Can we support the claim that the mean breaking strength has increased? OYes ONo
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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