Chapter20

# 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 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 • 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 ˆ 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 α • Do not reject H o – When p-value 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...
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Chapter20 - Chapter 20 Testing Hypotheses About Proportions...

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