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Lecture3-2-2

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Topics of Statistical Inference Estimation Point Estimate (Chapter 7) Confidence Interval (Chapter 8) Hypothesis Testing (Chapters 9, 10 and 12) Simple/Multiple Linear Regression (Chapters 13 and 14) 2
Statistical Inference Uses probability theory to help us draw conclusions about a population on the basis of a random sample. Conclusions are not exact and are not always correct; this problem is inevitable, unless we examine the entire population. We can, however, control probability of making an error. If we focus completely on what happened to us in our given sample, without putting it into some context, we can’t infer anything. All we can do then is hope that our guess isn’t too far off the mark. This isn’t very scientific, and can get us into trouble. Success of statistical inference depends critically on our ability to understand sampling variability . 3

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Four Words Used in Statistical Inference Typical situation: Want to answer a question about a population of individuals. To answer the question we use a sample of individuals from the population. Parameter : a number (unknown in practice) that describes the population Statistic : a number describing the sample ( changes from sample to sample ) a point estimate of the population parameter of interest 4
Examples 5 A politician selects a random sample of 200 working U.S. women who are 16 to 24 years old. Of the women in the sample, 14 are being paid minimum wage or less. Population ? Sample ? Parameter ? (true proportion) Statistic ? (sample proportion) In a survey of college-bound high school seniors, 33% said “academic reputation” was the most important characteristic in choosing a college. ( Source: USA Today, March 2001 )

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Population Distribution Population distribution of a variable is the distribution of its values for all members of the population. It is also the probability distribution of a variable when we choose one individual from the population at random. E.g., the distribution of heights of women between 18 and 24 yrs old is approximately normal with μ=64.5 and σ=2.5. Select a woman at random and measure her height. The result is a random variable X . The probability distribution of X is the same normal with μ=64.5 and σ=2.5. 6
Sampling Distribution Statistical inference draws conclusions about a population or process on the basis of data.

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