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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 μ...
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This note was uploaded on 09/26/2011 for the course 06E 071 taught by Professor Stuff during the Spring '11 term at University of Iowa.
 Spring '11
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