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Unformatted text preview: I. Alpha: the critical region of a probability distribution We know that with a normal probability distribution, values far from the mean are less likely than values close to the mean. We need to establish a critical region in the ends of the distribution, which we define as unlikely. Usually, we decide that the outer 5% of the distribution is unlikely, and we call this value alpha here alpha =.05 (5% expressed as a proportion). II. Confidence intervals The goal of inferential statistics is to learn about the population, based on a sample statistic (also known as a point estimate). This involves uncertainty, so we can calculate a confidence interval around out point estimate, which limits our uncertainty. A confidence interval : is therefore an interval within which we are confident the actual population value lies. For example, when we hear about statistics such as polling percentages, they often come with a margin of error this is a confidence interval. Normally, we use a 95% Confidence Interval. This means we are 95% confident that our range includes the true population parameter, or that 95 times out of a hundred, this interval around our point estimate will include the population parameter. A 95% CI means we use an alpha of .05, with 5% risk of Type I error (erring by not including the population parameter)....
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- Spring '09