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Unformatted text preview: CHAPTER 6Intro to Inference (6.1, 6.2, 6.3) Why do we even bother analyzing data?.....We want to draw conclusions from the data. Why cant we just accept our sample mean as the official mean for the population? Every time we estimate the population mean with a different sample, we get a different estimate, , due to sampling variability. Statistical inference: The purpose of statistical inference is to draw conclusions from data. It adds to the graphing and analyzing because we substantiate our conclusions by probability calculations. 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) (Also called Hypothesis testing) Point Estimate of Parameter: A point estimate of a parameter consists of a single number calculated from a random sample of units. For example, is a point estimate of. Point estimates, however, give us very little information. Example 1: You want to estimate the mean SAT Math score for high school seniors in California. At considerable effort and expense, you give the test to a simple random sample of 500 high school seniors. The mean score for your sample is = 461 points. The standard deviation of the SAT Math test is a known points. Questions of interest: 1. Can we include a measure of the precision associated with the point estimate? 2. Can we include a measure of our confidence in our results? Answer: Yes, we can construct a confidence interval for . A confidence interval is calculated from the sample data and it represents an interval estimate of the population parameter. A confidence interval includes: STAT 301 Spring 2012 Chapter 6 Page 1 1. an interval computed from the sample. (The interval is a measure of the variability of our point estimate). 2. a confidence level. (This confidence level measures the confidence that our inference is correct). In this lesson we want to find a confidence interval for our population mean, . The true mean or proportion for the population exists and is a fixed number, but we just dont 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 dont know exactly where the butterfly is, but from our sample, we have a pretty good estimate of the location. If we just take a single sample, our single confidence interval net may or may not include the population parameter. However if we take many samples of the same size and create a confidence interval from each sample statistic, over the long run 95% of our confidence intervals will contain the true population parameter (if we are using a 95% confidence level)....
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- Spring '08