Homework ReviewIntroductionThe Hypothesis Testing ProcedureExampleThe HypothesesThe Significance LevelThe Test StatisticThe Value of the Test StatisticThe p-ValueThe DecisionThe ConclusionAssignmentHypothesis Testing for ProportionsLecture 29Sections 9.1 - 9.2Robb T. KoetherHampden-Sydney CollegeFri, Mar 5, 2010Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 1 / 46Outline1Homework Review2Introduction3The Hypothesis Testing Procedure4ExampleThe HypothesesThe Significance LevelThe Test StatisticThe Value of the Test StatisticThe p-ValueThe DecisionThe Conclusion5AssignmentRobb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 2 / 46Outline1Homework Review2Introduction3The Hypothesis Testing Procedure4ExampleThe HypothesesThe Significance LevelThe Test StatisticThe Value of the Test StatisticThe p-ValueThe DecisionThe Conclusion5AssignmentRobb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 3 / 46Homework ReviewExercise 8.24, page 552.Suppose that for a population, the response variable X has a N(−1, 2)distribution.(a) Draw the distribution of X. Clearly indicate in your drawing themean and the standard deviation.-6-4-2240.050.100.150.20Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 4 / 46Homework ReviewExercise 8.24, page 552.Suppose that for a population, the response variable X has a N(−1, 2)distribution.(a) Draw the distribution of X. Clearly indicate in your drawing themean and the standard deviation.-6-4-2240.050.100.150.20Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 4 / 46Homework ReviewExercise 8.24, page 552.(b) Suppose that a simple random sample of size n = 100 is selectedfrom this population. Let X represent the sample mean response.(i) What is the distribution of X for a simple random sample of sizen = 100? Give all relevant features of the distribution.The CLT says thatµx= µ = −1andσx=σ√n=2√100= 0.2.So the distribution of x is N(−1, 0.2).Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 5 / 46Homework ReviewExercise 8.24, page 552.(b) Suppose that a simple random sample of size n = 100 is selectedfrom this population. Let X represent the sample mean response.(i) What is the distribution of X for a simple random sample of sizen = 100? Give all relevant features of the distribution.The CLT says thatµx= µ = −1andσx=σ√n=2√100= 0.2.So the distribution of x is N(−1, 0.2).Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 5 / 46Homework ReviewExercise 8.24, page 552.(b) Suppose that a simple random sample of size n = 100 is selectedfrom this population. Let X represent the sample mean response.(i) What is the distribution of X for a simple random sample of sizen = 100? Give all relevant features of the distribution.The CLT says thatµx= µ = −1andσx=σ√n=2√100= 0.2.So the distribution of x is N(−1, 0.2).Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 5 / 46Homework ReviewExercise 8.24, page 552.(ii) Draw the distribution of X. Clearly indicate in your drawing themodel, the mean, and the standard deviation.-1.4-1.2-1.0-0.8-0.6-0.40.51.01.52.0Calculate P(X > −0.9). Show all steps used to get your answer.normalcdf(-0.9,E99,-1,0.2) = 0.3085.Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 6 / 46Homework ReviewExercise 8.24, page 552.(iii) (ii) Draw the distribution of X. Clearly indicate in your drawing themodel, the mean, and the standard deviation.-1.4-1.2-1.0-0.8-0.6-0.40.51.01.52.0Calculate P(X > −0.9). Show all steps used to get your answer.normalcdf(-0.9,E99,-1,0.2) = 0.3085.Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 6 / 46Homework ReviewExercise 8.24, page 552.(iii) (ii) Draw the distribution of X. Clearly indicate in your drawing themodel, the mean, and the standard deviation.-1.4-1.2-1.0-0.8-0.6-0.40.51.01.52.0Calculate P(X > −0.9). Show all steps used to get your answer.normalcdf(-0.9,E99,-1,0.2) = 0.3085.Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 6 / 46Homework ReviewExercise 8.24, page 552.(iii) (ii) Draw the distribution of X. Clearly indicate in your drawing themodel, the mean, and the standard deviation.-1.4-1.2-1.0-0.8-0.6-0.40.51.01.52.0Calculate P(X > −0.9). Show all steps used to get your answer.normalcdf(-0.9,E99,-1,0.2) = 0.3085.Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 6 / 46Homework ReviewExercise 8.24, page 552.(iii)-6-4-20240.51.01.52.0The distributions of X and XRobb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 7 / 46Outline1Homework Review2Introduction3The Hypothesis Testing Procedure4ExampleThe HypothesesThe Significance LevelThe Test StatisticThe Value of the Test StatisticThe p-ValueThe DecisionThe Conclusion5AssignmentRobb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 8 / 46IntroductionAny question about a population must first be stated in terms of apopulation parameter.We will work with only two parameters:IThe population mean µ.IThe population proportion p.Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 9 / 46IntroductionThere are only two basic questions that we ask:What is the value of the parameter? (Estimation)Does the evidence support or refute a claim about the value of theparameter? (Hypothesis testing)Robb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 10 / 46Outline1Homework Review2Introduction3The Hypothesis Testing Procedure4ExampleThe HypothesesThe Significance LevelThe Test StatisticThe Value of the Test StatisticThe p-ValueThe DecisionThe Conclusion5AssignmentRobb T. Koether (Hampden-Sydney College) Hypothesis Testing for Proportions Fri, Mar 5, 2010 11 / 46The Steps of Testing a Hypothesisp -Value ApproachThe seven steps of hypothesis testing.1State the null and alternative hypotheses.2State the significance level.3State the formula for the test statistic.4Compute the value of the test statistic.5Compute the p-value.6Make a decision.7State the conclusion.Robb T. Koether (Hampden-Sydney
View Full Document
Unlocking...