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Unformatted text preview: 133 Chapter 6: GREAT STUFF; QUALITY CONTROL CHARTS TAKE THE CLASS IN THE SPRING WE ARE SKIPPING ALL OF CHAPTER 6. Section 7.2 LargeSample Confidence Intervals for a Population Mean We will be asking questions about population parameters , such as , Information from the sample statistics (such as x , s ) can be used to estimate population parameters ( , ) A sample mean x may be quite different from a population mean A single number estimate by itself, like x , provides no information about the precision and reliability of the estimate with respect to the larger population Researchers sometimes use a sample statistic to provide an interval of plausible estimates for the population parameter; this interval is called a confidence interval Definition : A confidence interval is an entire interval of plausible values for a population parameter, such as , based on observations obtained from a random sample of the population. Definition : The confidence level is a measure of the degree of reliability of the confidence interval PERFORM A MINITAB SIMULATION: Randomly select n = 100 values from a Normal( = 0, = 1) and place them in column C1 Do this for 100 different columns: C1C100 Determine 95% confidence intervals for each column: Stat > Basic Stat > 1 Sample z OUTCOME: On average, approximately 95 of the 100 intervals will contain the true value of (which we set as 0). How many of your 95% confidence intervals contained 0? This is what is meant by a 95% confidence interval theres a 95% chance, before constructing the interval , that the interval will actually contain the parameter of interest The true isn't changing. It is fixed. We hope to catch it in our confidence interval. Before we cast our net for , we have a 95% chance of catching . But, once we decide on x , the net has been tossed and either we have caught or not caught . We expect 95% of the intervals we construct to contain , but we also expect a little variation. That is, in any group of 100 samples, it is possible to find only, say, 92 that contain . In another group of 100 samples, we might find 97 that contain , and so forth. So, the 95% refers to the long run percentage of intervals that will contain the mean. WHAT THE ABOVE IS SAYING: A confidence interval may or may not actually contain the true value of the population parameter. Each confidence interval computed for the exact same parameter may be different depending on the sample taken....
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 Spring '08
 DeVasher
 Statistics

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