Chapter 8 Student Notes - CHAPTER 8 NOTES Day 1 8.1...

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CHAPTER 8 NOTES Day 1 : 8.1 Confidence Intervals: The Basics, part 1 How is this chapter different than chapter 7? In chapter 7, we pretended to know the truth (e.g. ) and asked questions about the possible values of x In this chapter, we start getting real—we begin with what we actually know (e.g. x ) and ask questions about the possible values of . Activity: The Mystery Mean Read 469-470 Including example on page 470 What is a point estimate? Why is it called a point estimate? Best guess for the value of a population parameter. A single value on the number line. However, almost certainly not correct. Explain the logic of confidence intervals. Summarize: 1. Distance from x to is the same as the distance from to x . 2. In 95% of samples, x will be within 2 SD of . 3. Therefore, in 95% of samples, will be within 2 SD of x . Read 470-473 What is a confidence interval? An interval of plausible values for a parameter; point estimate M.E. What is the confidence level? The expected success rate for intervals calculated in this manner. For example, we would expect about 95% of all 95% confidence intervals to capture the parameter they are trying to estimate. What is the margin of error? The margin of error is added and subtracted from the point estimate to create a confidence interval with the desired level of confidence. With 95% confidence intervals, the distance 83
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between the statistic and the parameter will be less than the margin of error in 95% of the intervals. 84
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Why do we include the margin of error? To account for sampling variability (different samples will give different estimates), NOT bias! Also, to greatly increase our chances of being correct—see Garfield comic Read 473-476 How do you interpret a confidence level ? In other words, what does it mean to be 90% confident? *To say that we are 95 % confident is shorthand for “95% of all possible samples of size n from this population will result in an interval that captures the unknown parameter.” In real life we only get one interval. Point to an interval and ask for the probability it captures the true value. Give some wrong statements about 90% probability. Do get it right: describe the picture! Also, mention that this can be done before the interval is calculated—it is about the method, not a particular interval How do you interpret a confidence interval ? *To interpret a C% confidence interval for an unknown parameter, say, “We are C% confident that the interval from ____ to ____ captures the actual value of the [population parameter in context].” This can be done only after the interval is calculated Alternate Example: According to , on August 13, 2010, the 95% confidence interval for the true proportion of Americans who approved of the job Barack Obama was doing as president was 0.44 0.03. Interpret the confidence interval and the confidence level.
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