PSLS.PPT.Ch14

# PSLS.PPT.Ch14 - Introductiontoinference PSLS chapter 14...

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Introduction to inference PSLS chapter 14 © 2009 W.H. Freeman and Company

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Objectives (PSLS chapter 14) Introduction to inference Uncertainty and confidence Confidence intervals Confidence interval for a Normal population mean (σ known) Null and alternative hypotheses The P -value Test for a Normal population mean (σ known)
Uncertainty and confidence If you picked different samples from a population, you would probably get different sample means ( x ̅ ) and virtually none of them would actually equal the true population mean, μ .

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But the sample distribution is narrower than the population distribution, by a factor of √ n . Thus, the estimates gained from our samples are always relatively close to the population parameter µ . n Sample means, n subjects μ n σ Population, x individual subjects x x If the population is normally distributed N ( µ , σ ), so will the sampling distribution N ( µ , σ /√ n ).
Blue dot: mean value of individual sample σ n 95% of all sample means will be within roughly 2 standard deviations (2* /√ n ) of the population parameter μ. The population parameter μ should be within roughly 2 standard deviations from the sample average x ̅ , in 95% of all samples. x ̅

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Implication: To estimate the population mean μ, we don’t need to “measure” all individuals in the population, and we don’t need to take many random samples of n individuals; all we need is one random sample of size n , and relying on the known properties of the sampling distribution . n n Sample Population μ
Reworded With 95% confidence, we can say that µ should be within a margin of error m from our sample mean . In 95% of all possible samples of this size n , µ will indeed fall in our confidence interval. In only 5% of samples would be farther from µ. σ n x http://www.whfreeman.com/psls/ Blue dot: mean value of individual sample n x ̅

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Confidence interval A confidence interval is a range of values with an associated probability or confidence level C . This probability quantifies the chance that the interval contains the unknown population parameter. μ falls within the interval with probability (confidence level) C.
A confidence interval can be expressed as: a center ± a margin of error m : μ within x ̅ ± m ( Example: 120 ± 6) an interval: within ( x ̅ m ) to ( x ̅ + m ) ( Example: 114 to 126) [Note that not all CI are symmetric about the parameter. Some complex methods produce asymmetric intervals.] The confidence level C (in %) represents an area of corresponding size C under the sampling distribution. m m

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The weight of single eggs varies Normally with standard deviation 5g. Think of a carton of 12 eggs as an SRS of size 12.
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## This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.

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PSLS.PPT.Ch14 - Introductiontoinference PSLS chapter 14...

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