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 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 DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 20 Testing Hypotheses About Proportions Comparing Confidence Intervals with Hypothesis Tests • Confidence Interval: A level of confidence is chosen. We determine a range of possible values for the parameter that are consistent with the data (at the chosen confidence level). Comparing Confidence Intervals with Hypothesis Tests • Hypothesis Test: Only one possible value for the parameter, called the hypothesized value, is tested . We determine the strength of the evidence provided by the data against the proposition that the hypothesized value is the true value. Hypothesis Tests • Test a claim about the population proportion, p • Start by taking a sample and calculating • Ask: Would the value of be likely to come from a population with a mean p ? – If it is likely, then I have no reason to question the value for p . – If it is unlikely, then we do have reason to question the value of p . p ˆ p ˆ Parts to a Hypothesis Test • Null Hypothesis (H ) – What the model is believed to be – H : p = p • Ex: Fair coin: H : p = 0.5 Parts to a Hypothesis Test • Alternative Hypothesis (H a ) – Claim you would like to prove – H a : p < p – H a : p > p – H a : p ≠ p • Ex: Fair Coin?: H a : p ≠ 0.5 Relationship Between H and H a • Law & Order – We assume people accused of a crime are innocent until proven guilty. • H : person is innocent – You, as the prosecutor, must gather enough evidence to prove that the person accused is guilty beyond a shadow of a doubt. • H a : person is not innocent. Parts to a Hypothesis Test • Check your assumptions! – np o and nq o are greater than or equal to 10 – n is less than 10% of the population – random sample – independent values Parts to a Hypothesis Test • Sampling Distribution of if Null Hypothesis is True  n p p p N o o o ) 1 ( , p ˆ Parts to a Hypothesis Test • Calculate a Test Statistic n p p p p z o o o ) 1 ( ˆ = Parts to a Hypothesis Test • Pvalue = The probability of getting the observed statistic (i.e. ) or one more extreme given that the null hypothesis is true. • H a : p < p o (onesided test) – pvalue = P(Z < z) • H a : p > p o (onesided test) – pvalue = P(Z > z) • H a : p ≠ p o (twosided test) – pvalue = 2*P(Z > z) p ˆ pvalue = P(Z < z) pvalue = P(Z > z) = P(Z < z) pvalue = 2*P(Z > z) = 2*P(Z < z) Parts to a Hypothesis Test • Decision (in terms of H o ) • Reject H o – When pvalue is smaller than α • Do not reject H o – When pvalue is larger than α Parts to a Hypothesis Test • Conclusion (in terms of H a ) • If we reject H o , the conclusion would be: – There is evidence in favor of H a • If we fail to reject H o , the conclusion would be – There is not evidence in favor of H a Parts to a Hypothesis Test...
View
Full Document
 Spring '08
 Graham
 Null hypothesis, Statistical hypothesis testing, New Mexico

Click to edit the document details