lecture_6_1 - Introduction to inference Estimating with...

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    Introduction to inference Estimating with confidence IPS chapter 6.1 © 2006 W.H. Freeman and Company
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Objectives (IPS chapter 6.1) Estimating with confidence Uncertainty and confidence Confidence interval Varying confidence levels Impact of sample size
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Introduction In chapter 6, and the other chapters that we are going to cover in the rest of this semester, we will learn about statistical inference. In statistics, we make inference about a population, from a sample from that population. We are particularly interested about the population mean. We make inference about an unknown population mean, from a sample mean and from the sampling distribution of sample mean.
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Throughout chapter 6, we will assume that we do not know the population mean, but we do know the population standard deviation. In chapter 7, we are going to discuss the cases where do not know the population mean and we also do not know the population standard deviation.
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Uncertainty and confidence Although the sample mean, , is a unique number for any particular sample, if you pick a different sample you will probably get a different sample mean. In fact, you could get many different values for the sample mean, and virtually none of them would actually equal the true population mean, μ . x
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But we know, from chapter 5, that if the population distribution is normal, then the sampling distribution of sample mean follows a normal distribution.
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