PSLS.PPT.Ch14

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

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
    Introduction to inference PSLS chapter 14 © 2009 W.H. Freeman and Company
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 2
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 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 ).
Background image of page 4
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 ̅
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 6
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 ̅
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 8
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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The weight of single eggs varies Normally with standard deviation 5g. Think of a carton of 12 eggs as an SRS of size 12.
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 34

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

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online