A biologist is interested in comparing the size of blue crabs in two river basins: Cooper River and Stone River. Based on the health of the rivers, she believes the crabs in Stone River will have a higher average weight. She samples 34 crabs from the Stone River and this sample has a mean weight of 800g with standard deviation of 225g. She also takes a sample of 35 crabs from the Cooper River and finds the crabs have a mean weight of 700g with standard deviation of 175g. What are the appropriate hypotheses used to determine if her claim is correct. OH. : µs = µc_ versus µs > µc O H. : µs = µc versus ps < µc O H. : µs = µc versus ps # µc %3D
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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