Chapter6 - Chapter 6: Confidence Intervals and Hypothesis...

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1 Chapter 6: Confidence Intervals and Hypothesis Testing Using Z for the CI and test of the population mean Learning goals for this chapter: Understand what inference is and why it is needed. Know that all inference techniques give us information about the population parameter. Explain what a confidence interval is and when it is needed. Calculate a confidence interval for the population mean when the population standard deviation is known. Know the assumptions that must be met for doing inference for the population mean. Calculate the needed sample size if you have a pre-determined margin of error. Know how to write hypotheses, calculate a test statistic and P-value, and write conclusions in terms of the story. Draw Normal curve pictures to match the hypothesis test. Understand the logic of hypothesis testing and when a hypothesis test is needed. Use the confidence interval to perform a two-sided hypothesis test. Explain sampling variability and the difference between the population mean and the sample mean. Explain the difference between the population standard deviation and the sample standard deviation. Know which technique is most appropriate for a story: confidence interval, hypothesis test, or simple summary statistics. When we collect data from our sample, we can calculate sample statistics. However, usually we are interested in what is true for the whole population, not just for the sample. (Remember that a census is very hard and expensive to do well.) Why can’t we just accept our sample mean or sample proportion as the official mean or proportion for the population? Every time we estimate the statistics ˆ , xp (sample mean and sample proportion), we get a different answer due to sampling variability. Two most common types of formal statistical inference: Confidence Intervals : when we want to estimate a population parameter Significance Tests : when we want to assess the evidence provided by the data in favor of some claim about the population (yes/no question about the population) Confidence Intervals allow us to estimate the population mean or population proportion.
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2 The true mean or proportion for the population exists and is a fixed number, but we just don’t know what it is. Using our sample statistic, we can create a “net” to give us an estimate of where to expect the population parameter to be. Confidence interval = net Population parameter = invisible, stationary butterfly We don’t know exactly where the butterfly is, but from our sample, we have a pretty good estimate of the location. We don’t need to take a lot of random samples to recreate the sampling distribution with the population mean μ at its center. All we need is one Simple Random Sample of size n. Because of what we know about the sample mean distribution, we can use that one sample mean’s confidence interval to infer what the population mean really is.
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This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Chapter6 - Chapter 6: Confidence Intervals and Hypothesis...

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