ch09 - 9-1 Hypothesis Testing9-1.1 Statistical

Info iconThis preview shows pages 1–21. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: 9-1 Hypothesis Testing9-1.1 Statistical HypothesesDefinitionStatistical hypothesis testing and confidence interval estimation of parameters are the fundamental methods used at the data analysis stage of a comparative experiment, in which the engineer is interested, for example, in comparing the mean of a population to a specified value.9-1 Hypothesis Testing9-1.1 Statistical HypothesesFor example, suppose that we are interested in the burning rate of a solid propellant used to power aircrew escape systems. • Now burning rate is a random variable that can be described by a probability distribution. • Suppose that our interest focuses on the meanburning rate (a parameter of this distribution). • Specifically, we are interested in deciding whether or not the mean burning rate is 50 centimeters per second. 9-1 Hypothesis Testing9-1.1 Statistical Hypothesesnull hypothesisalternative hypothesisOne-sided Alternative HypothesesTwo-sided Alternative Hypothesis9-1 Hypothesis Testing9-1.1 Statistical HypothesesTest of a Hypothesis• A procedure leading to a decision about a particular hypothesis• Hypothesis-testing procedures rely on using the information in a random sample from the population of interest. • If this information is consistentwith the hypothesis, then we will conclude that the hypothesis is true; if this information is inconsistentwith the hypothesis, we will conclude that the hypothesis is false.9-1 Hypothesis Testing9-1.2 Tests of Statistical HypothesesFigure 9-1Decision criteria for testing H:μ= 50 centimeters per second versus H1:μ ≠50 centimeters per second.9-1 Hypothesis Testing9-1.2 Tests of Statistical HypothesesDefinitions9-1 Hypothesis Testing9-1.2 Tests of Statistical HypothesesSometimes the type I error probability is called the significance level, or the α-error, or the sizeof the test.9-1 Hypothesis Testing9-1.2 Tests of Statistical Hypotheses9-1 Hypothesis Testing9-1 Hypothesis TestingFigure 9-3The probability of type II error when μ= 52 and n= 10.9-1 Hypothesis Testing9-1 Hypothesis TestingFigure 9-4The probability of type II error when μ= 50.5 and n= 10.9-1 Hypothesis Testing9-1 Hypothesis TestingFigure 9-5The probability of type II error when μ= 2 and n= 16.9-1 Hypothesis Testing9-1 Hypothesis Testing9-1 Hypothesis TestingDefinition• The power is computed as 1 -β, and power can be interpreted as the probability of correctly rejecting a false null hypothesis. We often compare statistical tests by comparing their power properties....
View Full Document

This note was uploaded on 09/21/2010 for the course EIN 3235 taught by Professor Zhai during the Spring '10 term at FIU.

Page1 / 88

ch09 - 9-1 Hypothesis Testing9-1.1 Statistical

This preview shows document pages 1 - 21. Sign up to view the full document.

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