AG-Ch-9-Notes-WI10

# AG-Ch-9-Notes-WI10 - Chapter 9 Statistical Inference...

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1 AG-Ch 9 Notes 3/16/2010 Chapter 9 Statistical Inference: Significance Tests about Hypotheses Inferential Statistics Inferential statistics are used when you need to estimate or make a decision about an unknown population parameter. You make a hypothesis based on a model. The theoretical model is just a way to identify the pattern of information you are working with. The model may be useful or not depending on if the model’s underlying assumptions are met. For example, if you think the pattern of information fits the Normal distribution then you must verify that the pattern fits the Normal Distribution’s underlying as sumptions such as symmetric about the average, etc. Once you have verified that the information pattern follows the theoretical distribution you can then use your observed sample statistic to answer your original question. Plus, the model gives you a way of quantifying the sampling error. If we did not have a way to do this, random variability would disguise the pattern from the “noise” or random variation and we would miss the key information we need to make our decision. Inferential statistics uses models to get at information so that you can make an informed decision. Confidence Intervals An estimate of a population parameter using an interval of values calculated from a sample of the population you are interested in. Based on a Statistic that you have arrived at by random sampling. o Random sample representing the population you are interested in. o Large enough sample relative to the size of the population Used to estimate the population parameter, not a statistic Determine a critical value by deciding on the level of confidence needed by the situation. o Ex. Money or resources needed to sample or the consequences if you are wrong. Level of Confidence: measure of how confident one is that the interval does contain the true population parameter. o An increase in the confidence level, increases the width of the interval o A larger sample size produces a narrower confidence interval, as long as other factors remain the same. Interpretation: o One is 95% (or whatever level you want) confident that the interval contains the population parameter. You are not guaranteed the parameter is in the interval. o Repeated random samples from the population, over time, used to construct confidence intervals will capture the parameter 95% ( or whatever level you want) of the time o Margin of error is the half width of the interval.

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2 AG-Ch 9 Notes 3/16/2010 Hypothesis Testing Looks at how well the sample data supports a particular statement about the value of the population parameter you are interested in. Think about what the person or group is claiming. Think about how it relates to your experience and if it “sounds right” based on your past experience. State the claim mathematically using the correct notation.
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