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Chapter14

# The Basic Practice of Statistics (Paper) & Student CD

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Confidence intervals: The basics BPS chapter 14 © 2006 W.H. Freeman and Company

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Objectives (BPS chapter 14) Confidence intervals: the basics Estimating with confidence Confidence intervals for the mean μ How confidence intervals behave Choosing the sample size
Estimating with confidence Although the sample mean, , is a unique number for any particular sample, if you pick a different sample, you will probably get a different sample mean. In fact, you could get many different values for the sample mean, and virtually none of them would actually equal the true population mean, μ . x

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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 ! " Population, x individual subjects x x If the population is normally distributed N ( µ , σ ), so will the sampling distribution N ( µ , σ / n ).
Red dot: mean value of individual sample 95% of all sample means will be within roughly 2 standard deviations (2* σ / n ) of the population parameter μ . Because distances are symmetrical, this implies that the population parameter must be within roughly 2 standard deviations from the sample average , in 95% of all samples. " n This reasoning is the essence of statistical inference. x

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The weight of single eggs of the brown variety is normally distributed N (65g,5g). Think of a carton of 12 brown eggs as an SRS of size 12. You buy a carton of 12 white eggs instead. The box weighs 770g. The average egg weight from that SRS is thus = 64.2g. Knowing that the standard deviation of egg weight is 5g, what can you infer about the mean µ of the white egg population? There is a 95% chance that the population mean
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Chapter14 - Confidence intervals The basics BPS chapter 14...

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