A truck farmer decides to test a new non-polluting insecticide which also, according to the inventor, definitely reduces the loss attributable to a common pest. The farmer treats 31 acres with the new spray and 41 with the standard spray. For the new insecticide, the mean yield is 980 pounds with a standard deviation of 60. For the standard spray there is a mean yield of 1040 pounds with a standard deviation of 50 pounds. At level of significance 0.05 do the results show that the new spray is worse than the old? State hypotheses, P- value, and conclusion.
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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