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Unformatted text preview: The CLT Hypothesis tests Confidence intervals Inference Review : Outline The central limit theorem Onesample hypothesis tests for population parameters For a mean (variance known or unknown) For a proportion Confidence intervals for population parameters T. Parker () 1 / 20 The CLT Hypothesis tests Confidence intervals Inference? This class will cover two broad topics: estimation and inference . For example, last time we looked at how the least squares estimator is constructed. Infer ence comes from the word infer . What do we like to infer? Whether or not hypotheses seem to be true hypothesis tests. Approximately where we think a statistic is confidence intervals. We also want to say how confident we are of our inferences. T. Parker () 2 / 20 The CLT Hypothesis tests Confidence intervals A note on sample statistics Last time we defined everything as a descriptive statistic. These would be appropriate if we had all the data. We almost never do. Instead we assume those descriptive statistics exist and try to estimate them with analogous statistics from samples . When applied to the population, we call these descriptive statistics parameters . The estimates we make from samples are called statistics . There are all sorts of statistics (like we saw last time) and estimators for them, so how can we look at all of them in one class? T. Parker () 3 / 20 The CLT Hypothesis tests Confidence intervals The central limit theorem Why is the normal distribution used so much? The Central Limit Theorem is the answer. The CLT does not imply that everything is distributed normally. It is a good approximation for certain estimates. Samples have to be pretty big ( n 50? it depends). What does the CLT say? T. Parker () 4 / 20 The CLT Hypothesis tests Confidence intervals The CLT: an illustration Suppose we have some data x 1 , x 2 ,... x n and we want to know the mean of the data. That is, we assume a population mean...
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 Spring '11
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