Ten years ago, the average acreage of farms in a certain geographic region was 65 acres. The standard deviation of the population was 7 acres. A recent study consisting of 26 farms showed that the average was 62.6 acres per farm. Test the claim, at α=0.01, that the average has not changed by finding the P-value for the test. Assume σ has not changed and the variable is normally distributed. Use a graphing calculator. Find the P-value. Round the answer to at least four decimal places.
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!
Farm Sizes Ten years ago, the average acreage of farms in a certain geographic region was 65 acres. The standard deviation of the population was 7 acres. A recent study consisting of 26 farms showed that the average was 62.6 acres per farm. Test the claim, at α=0.01, that the average has not changed by finding the P-value for the test. Assume σ has not changed and the variable is
Find the P-value. Round the answer to at least four decimal places.
P-value=
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