A special diet is intended to reduce the cholesterol of patients at risk of heart disease. If the diet is effective, the target is to have the average cholesterol of this group be below 200. After six months of the diet, SRS of 15 patients at risk for heart disease had an average cholesterol level of 192 with a standard deviation of 21. At 5% significance level, determine if there is sufficient evidence to claim that the diet is effective in meeting the target.
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!
A special diet is intended to reduce the cholesterol of patients at risk of heart disease. If the diet is effective, the target is to have the average cholesterol of this group be below 200. After six months of the diet, SRS of 15 patients at risk for heart disease had an average cholesterol level of 192 with a standard deviation of 21.
At 5% significance level, determine if there is sufficient evidence to claim that the diet is effective in meeting the target.
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