Hypotheses Testing-ECO6416

Hypotheses Testing-ECO6416 - becomes our random variable...

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Hypotheses Testing Let us consider a simple problem of inference about population mean. We have a large population with known mean. We take a sample and wish to know whether the sample mean is significantly different from the population mean. Our null hypothesis is that it is not. The theory of probability is only capable of dealing with random variables which generate a frequency distribution "in the long run". We have one fixed population and one fixed sample. There is nothing random about this problem and the experiment is conducted once, so there is no "long run". We pretend that the experiment was not conducted once, but an infinite number of times, that is, we consider all possible samples of the same size. We assume that each sample mean includes an "error", which is independently and normally distributed about zero. The sample mean now
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Unformatted text preview: becomes our random variable, which we call our "statistic". We can now apply the t-test or z-test interpretation of probability. We are now able to determine the probability of a randomly chosen sample mean having a value at least as extreme as our original sample mean. Note that we are implicitly assuming that the null hypothesis is true. This probability is our p-value which we apply to the original problem. Remember that, in the t-tests for differences in means, there is a condition of equal population variances that must be examined. One way to test for possible differences in variances is to do an F test. However, the F test is very sensitive to violations of the normality condition ; i.e., if populations appear not to be normal, then the F test will tend to reject too often the null of no differences in population variances....
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