Chapter 8 - Ch 8 Inferences on Mean and Variance of a...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Ch 8 Inferences on Mean and Variance of a Distribution
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 8.1 Confidence Interval for Variance of a Normal Population Let X 1 , …, X n be a random sample from a normal distribution with mean μ and variance σ 2 . The random variable has a χ 2 distribution with n-1 degrees of freedom. 2 2 2 ) 1 ( σ χ s n - =
Background image of page 2
Deriving a 100(1-a)% Confidence Interval α χ σ - = - - - = - - = - - - - 1 ] ) 1 ( ) 1 ( [ 1 ] 1 ) 1 ( 1 [ 1 ] ) 1 ( [ 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 s n s n P s n P s n P
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 Confidence Interval Formula for Variance: 2 1 ], 2 [ 1 2 2 2 1 , 2 2 ) 1 ( ) 1 ( - - - - - n n s n s n α χ σ Confidence Interval for Standard Deviation: Find CI for variance and then take the positive square root of each limit.
Background image of page 4
5 Example: Find the 95% CI for a variance, using 15 degrees of freedom and s 2 = 10. = = - 2 15 , 025 . 2 1 , 2 / χ α n = = - - 2 15 , 975 . 2 1 , 2 / 1 n
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 8.3 The Language of Hypothesis Testing A hypothesis is a statement or claim regarding a parameter of one or more populations. Hypothesis testing is a procedure, based on sample evidence and probability, used to test claims regarding a characteristic of one or more populations. The null hypothesis , denoted H 0 , is a statement to be tested. It will be a statement regarding the value of a population parameter. For this class, it will always be in the form of H 0 : parameter = some value. The alternative hypothesis, denoted H 1 or H A , is what we are trying to prove.
Background image of page 6
7 Parametric vs Nonparametric Hypothesis Testing Parametric – These methods require that the data meet a specific set of assumptions: generally that the data is from a normal distribution or that the Central Limit Theorem applies. Nonparametric – Also known as “distribution-free” methods. These do not have a requirement of normality and are appropriate for smaller sample sizes as well.
Background image of page 7

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

View Full DocumentRight Arrow Icon
8 There are three ways to set up the alternative hypothesis. 1. “Not equal” ( two-tailed test ) H o: parameter = some value H 1: parameter does not equal some value 2. “Less than” ( one-tailed test ) H o: parameter = some value H 1: parameter < some value 3. “Greater than” ( one-tailed test ) H o: parameter = some value H 1: parameter > some value
Background image of page 8
9 Two possible decisions and conclusions: 1) Reject the Null Hypothesis: There is enough evidence to show that the alternative hypothesis is true. Interpretation: The sample evidence refutes the
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/17/2011 for the course STAT 4714 at Virginia Tech.

Page1 / 35

Chapter 8 - Ch 8 Inferences on Mean and Variance of a...

This preview shows document pages 1 - 10. Sign up to view the full document.

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