Slide 1Practice ProblemsAdditional Reading and ExamplesTest 5Slide 5Statistical InferenceSlide 7Point EstimateSampling Distribution of pConfidence Interval for pAssumptionsConfidence IntervalSignificance Test for pTests of Significance for pTests of Significance for pSignificance Test for pSignificance Test for pGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureTI-83/84 CalculatorExample 75/93Example 75/93Example 75/93Example 75/93Example 75/93Example 75/93Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 76/94Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Example 77/95Motivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating Example SolutionMotivating Example SolutionSlide 68STAT 210Lecture 29Significance Tests on Population ProportionsNovember 3, 2016Practice ProblemsSailboat: Pages 252 through 257Relevant problems: IX.9, IX.10, IX.11, IX.12 (c), IX.14 and IX.15 (c) Recommended problems: IX.9, IX.10, IX.11, and IX.15Hummingbird: Pages 210 through 215Relevant problems: VIII.9, VIII.10, VIII.11, VIII.12 (c), VIII.14 and VIII.15 (c) Recommended problems: VIII.9, VIII.10, VIII.11 and VIII.15Additional Reading and ExamplesSailboat: Read pages 248 through 251Hummingbird: Read pages 206 through 209Test 5Monday, November 7Questions for the first 10 minutes, then test – papers due promptly at the end of class!Covers chapters 7 & 8 (in Hummingbird book) or chapters 7 & 9 (in Sailboat book)Combination of multiple choice questions and written/short answer questions and problems.Formulas provided; Bring a calculator!Practice Tests and Formula Sheet on Blackboard.ClickerStatistical InferenceStatistical inference involves using statistics computed from sample data to make statements about some parameter of the population.This chapter we have made inferences about the population proportion p.ClickerPoint EstimateThe point estimate of the population proportion p is the sample proportion p.p = number of successes in the sample sample size nSampling Distribution of pAssumptions:1. Simple random sample from the population2. A large enough sample so that the central limit theorem applies. The sample is large if both np and n(1 - p) are greater than or equal to 10.Then the sample proportion p is distributed approximately normalwith mean m p = p and standard deviation sp = p(1 - p) . np ~ N( p, p(1-p)/n )Confidence Interval for pGoal: Estimate the unknown population proportion pPoint Estimate: Sample proportion pSituation: While p should be close to p, it is very unlikely that p will equal p exactly.Therefore, to the point estimate we subtract and add a margin of error to create a C% confidence interval estimate for p.Assumptions1. Simple random sample2. Both the number of successes in the sample np and the number of failures in the sample n(1-p) are greater than or equal to 10.Confidence IntervalThen a C% confidence interval for p is:p + z* p(1 - p)/nThe z* values are found in the table on page 340.Significance Test for pWe hypothesize that the population proportion p equals some specified value p0 and we want to use the data in a sample to test whether this null hypothesis is appropriate or whether we should reject the null hypothesis in favor of some alternative hypothesis.Null hypothesis H0: p = p 0Ha: p > p 0Alternative hypothesis Ha: p < p 0Ha: p = p 0Tests of Significance for pThe point estimate of p is the sample proportion p, and if we have asimple random sample and if both np and n(1 - p) are greater than 10,then the sampling distribution of p is:p ~ N( p, p(1 - p)/n )Then by the Z-score transformation we obtain the standard normalstatisticZ = p - p p(1 - p)/nThis statistic is a candidate for the test statistic.Tests of Significance for pHowever, since the population proportion p is unknown this statistic cannot be calculated. We need to replace p with some estimate. The logical estimate is to use the sample proportion p. However, if we use the sample proportion p, then the Z statistic will always equal 0.Since we carry out the test assuming the null hypothesis is true (H0: p = p0) then we estimate p with the hypothesized value p0.Significance Test for pHowever, since the population proportion p is unknown, it mustbe estimated. If we use the sample proportion p, then the Z statistic will always equal 0.Since we carry out the test assuming the null hypothesis is true(H0: p = p0) then we estimate p with the hypothesized value p0.Hence if we have a simple random sample and if both np0 > 10 and n(1 - p0 ) > 10, then the test statistic isZ = p - p0 p0(1 - p0)/nSignificance Test for pAssumptions:1. Simple random sample2. Both the hypothesized number of successes np0 and the hypothesized number of failures n(1 - p0 ) are greater than or equal to 10.Z = p - p0 p0(1 - p0)/nGeneral Significance Testing Procedure1. State the null and alternative hypotheses, and the significance level a that is going to be used.H0: ???Ha: ???a = ???General Significance Testing Procedure1. State the null and alternative hypotheses, and the significance level.2. Carry out the experiment, collect the data, verify the assumptions, and if appropriate compute the value of the test statistic.General Significance Testing Procedure1. State the null and alternative hypotheses, and the significance level.2. Carry out the experiment, collect the data, verify the assumptions, and if appropriate compute the value of the test statistic.3. Calculate the p-value (or rejection region).General Significance Testing Procedure1. State the null and alternative hypotheses, and state the significance level.2. Carry out the experiment, collect the data, verify the assumptions, and compute the value of the test statistic.3. Calculate the p-value.4. Make a decision on the significance of the test (reject or fail to reject H0).General Significance Testing Procedure1. State the null and alternative hypotheses, and state the significance level.2.
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