Chapter 15

# Chapter 15 - STAT 2053 Elementary Statistics Chapters 15...

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STAT 2053 – Elementary Statistics Chapters 15 – Thinking about Inference 1

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Thinking about Inference In Chapter 15 we go a little further into the specifics of confidence intervals and significance tests. We will also start to stray away from the assumptions that made life easier on us. 2
Inference in Practice The tests of significance and the confidence intervals we used in Chapter 14 are called z procedures , because we calculate a z-score in both of them and use the standard Normal distribution. 3

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Chapter 15 4 If we know the standard deviation σ of the population, a confidence interval for the mean μ is: To test a hypothesis H 0 : = 0 we use the one-sample z statistic: These are called z procedures because they both involve a one-sample z statistic and use the standard Normal distribution. z Procedures n σ μ x z 0 - = n σ z x ±
Inference in Practice Assumption #1: Where your data comes from matters! In order to do inference, our data must come from a process in which the laws of probability apply (i.e. randomly). If the data doesn’t come from a random sample or experiment, your results may be challenged. The data must be an SRS from the population (ask: “where did the data come from?”). Different methods are needed for different designs. The z procedures are not correct for samples other than SRS. 5

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Inference in Practice Example : Suppose you randomly select women who are at a shopping mall and ask them about how much they would be willing to pay for a comfortable pair of shoes. This data will NOT give useful information about women in general. Why not? What groups of women will this data provide useful information for? 6
Assumption #2: The shape of the population distribution We have assumed that the data comes from a Normal distribution. We rarely know if this is the actual case. However, our tests and our confidence intervals are based on our sample mean. Thankfully, the CLT applies even when our data is not normal. The shape of the population distribution matters. Skewness and outliers make the z procedures untrustworthy unless the sample is large. In practice, the z procedures are reasonably accurate for any sample of at least moderate size from a fairly symmetric distribution. 7

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Chapter 15 - STAT 2053 Elementary Statistics Chapters 15...

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