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.Back to Lisa's Journal or Go to Journal 6 PROBABILITY DISTRIBUTIONS Because it is not practical to measure a parameter of a large population, we need to use sampling. To be able to infer the parameter for the population. Probability theory provides the ability to devise how we will sample the population to get results that are representative of the population parameter and also to specify exactly was the probable margin of error in the estimates will be. Sampling distribution shows us that as more and more random samples are taken from the sampling frame the probability of these samples falling close to the mean is great. So you will see a cluster forming (more sample means around the actual population mean) around the true mean. Probability theory also explains how much of a sampling error can be expected for the sampling method that you use. The parameter, the sample size, and the standard error all contribute to the sampling error.

What I understand is that the more samples that you take, the closer your samples will come to reflecting the actual mean of the population. This is only true if the samples are random and of normal distribution. And, because you are measuring mean, the variables need to be continuous. So, the more and more samples that you take, the more fine-grained becomes the answer AND the more accurate your measurement. Probability theory allows us to say how confident we are in our sample measurements being reflective of the sample frame/population. The calculation gives us a percent, for example within 5% of accuracy, and here is where it gets gray for me. We are working within the standard deviation from the norm, so if it is within one standard deviation that is, of course more accurate, or it can be within 2 or 3 standard deviations. How this translates into the % confidence is where I get lost.