Chapter20 - Chapter 20 Testing Hypotheses About Proportions...

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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 p 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 Parts to a Hypothesis Test Calculate a Test Statistic n p p p p z o o o ) 1 ( -- = Parts to a Hypothesis Test P-value = 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 (one-sided test) p-value = P(Z < z) H a : p > p o (one-sided test) p-value = P(Z > z) H a : p p o (two-sided test) p-value = 2*P(Z > |z|) p p-value = P(Z < z) p-value = P(Z > z) = P(Z < -z) p-value = 2*P(Z > |z|) = 2*P(Z < -|z|) Parts to a Hypothesis Test Decision (in terms of H o ) Reject H o When p-value is smaller than Do not reject H o When p-value is larger than 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...
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Chapter20 - Chapter 20 Testing Hypotheses About Proportions...

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