Slide 1Test 5Practice ProblemsAdditional Reading and ExamplesStatistical InferenceSlide 6General Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureSlide 12Point EstimateSampling Distribution of pConfidence IntervalTests of Significance for pExample 3Example 3Example 3Example 3Tests of Significance for pTests of Significance for pTests of Significance for pTests of Significance for pSignificance Test for pTI-83/84 CalculatorExample 93/75Example 93/75Example 93/75Example 93/75Example 93/75Example 93/75Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 94/76Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77Example 95/77STAT 210Lecture 28Inferences on Population Proportions November 1, 2017Test 5Monday, November 6Covers the chapter on proportions and relevant concepts from chapter VII.Combination of multiple choice/fill in the blank questions and problems/written questions.Formulas and tables provided, please bring calculator and writing instrument.Practice 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 and IX.11Hummingbird: 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 and VIII.11Additional Reading and ExamplesSailboat: Read pages 248 through 251Pay particular attention to pages 250 and 251Hummingbird: Read pages 206 through 209Pay particular attention to pages 208 and 209Statistical InferenceStatistical inference involves using statistics computed from data collected in a sample to make statements about unknown population parameters.This chapter we want to make inferences about the population proportion p.Top HatGeneral 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. 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).5. Make a conclusion statement in the words of the original problem. This is the statistical inference.Top HatPoint 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 IntervalA 100 C% confidence interval for p is:p + z* p(1 - p)/nThe z* values are found in the table on page 340.Tests of Significance 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 0Example 3It is conjectured that at any given Major League Baseball game approximately 5% of fans in attendance are attending their first Major League Baseball game. Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0.05. What is the population of interest?What is the parameter of interest?Example 3It is conjectured that at any given Major League Baseball game approximately 5% of fans in attendance are attending their first Major League Baseball game. Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0.05. In this situation the population consists of all fans attending Major League Baseball games, and the parameter of interest is p = the proportion of all fans attending Major League Baseball games who are attending their first Major League Baseball game.Example 3It is conjectured that at any given Major League Baseball game approximately 5% of fans in attendance are attending their first Major League Baseball game. Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0.05. In this situation the population consists of all fans attending Major League Baseball games, and the parameter of interest is p = the proportion of all fans attending Major League Baseball games who are attending their first Major League Baseball game.Hypotheses: H0: ??? Ha: ???Example 3It is conjectured that at any given Major League Baseball game approximately
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