This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Testing hypotheses about proportions Tests of significance Â§ The reasoning of significance tests Â§ Stating hypotheses Â§ The Pvalue Â§ Statistical significance Â§ Tests for a population proportion Â§ Confidence intervals to test hypotheses Reasoning of Significance Tests Example: A coin is toss 500 times. It lands heads 275 times, which is a bit more than we expect. Is the coin fair or not? â€˘ Is the somewhat higher number of heads due to chance variation? â€˘ Is it evidence that the coin is not fair? x Stating Hypotheses Situation: We observe some effect and we have two explanations for it: 1) the effect is due to chance variation 2) the effect is due to something significant How to decide? Statement 1) = null hypothesis H 0 (the coin is fair) x The null hypothesis is a very specific statement about a parameter of the population(s). It is labeled H 0 and states â€śstatus quoâ€ť, previous knowledge, â€śno effectâ€ť, â€śthe observed difference is due to chanceâ€ť. It is the one which we want to reject. The alternative hypothesis is a more general statement about a parameter of the population(s) that is the opposite of the null hypothesis. It is labeled Ha and is the one we try to prove. Coin tossing example: H 0 : p = 1/2 ( p is the probability that the coin lands heads) Ha : p â‰ 1/2 ( p is either larger or smaller) Analogy with a criminal trial â€˘ H 0 : the defendant is innocent If sufficient evidence is presented, the jury will reject this hypothesis and conclude that â€˘ H a : the defendant is guilty Onesided and twosided tests â€˘ A twotail or twosided test of the population proportion has these null and alternative hypotheses: H 0 : p = p 0 [a specific proportion] Ha : p p 0 â€˘ A onetail or onesided test of a population proportion has these null and alternative hypotheses: H 0 : p = p 0 [a specific proportion] Ha : p < p 0 OR The Pvalue Examplecontâ€™d: A coin is tossed 500 times. It lands heads 275 times. H 0 : p = 1/2 vs. Ha : p â‰ 1/2 What is the chance of observing something like what we observed if H 0 is true?...
View
Full
Document
This note was uploaded on 11/05/2011 for the course BMGT 220 taught by Professor Bulmash during the Spring '08 term at Maryland.
 Spring '08
 Bulmash

Click to edit the document details