This gives us an advantage over the conventional wisdom that some would say is unfair in some contexts. (Note that our options are much more vague than the conventional wisdom.
2) mu is greater than mu0 3) mu is less than mu0. (For example, conventional wisdom claims that the mean is 0.) We believe instead that something else is true. The conventional wisdom says that the mu is a particular value, let's call it mu0. We are interested in the value of the mean of the population, mu. We've collected data on a single variable which we assume has a normal distribution with mean mu and SD sigma. So we need to understand how our sample will vary. Because the sample is random (and because the population has a variety of values), we can't count on getting the exact same values if we repeat our experiment. And we test our hypothesis on this random sample. To test our hypotheses about the value of these parameters, we take a random sample of independent observations. For example, if I'm running for president, I want to know that my support is NOT less than 50%. In hypothesis testing, we are actually more interested in what value the parameters aren't. The probability distribution of this population can be summarized with one (or maybe two or three) parameters, and we wish to know what these parameters are. General Framework: There exists a population of wildly exciting observations, but, alas, the population is too large to observe them all.
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