Slide 1Practice ProblemsAdditional Reading and ExamplesTest 6Slide 5Statistical InferenceGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureTests of SignificanceTests of SignificanceTests of Significance for m: s KnownTests of Significance for m: s KnownTest of Significance for m: s KnownTests of Significance for m: s KnownTests of Significance for m: s KnownSignificance Test for mSignificance Test for mSignificance Test for mSignificance Test for mTI-83-84 CalculatorExample 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 90/77Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 91/78Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Example 92/79Motivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating Example SolutionSlide 77STAT 210Lecture 34Tests of Significance for m: s KnownNovember 16, 2016Practice ProblemsSailboat: Pages 220 through 230Relevant problems: VIII.11 through VIII.17Recommended problems: VIII.12 and VIII.17Hummingbird: Pages 250 through 260Relevant problems: IX.11 through IX.17Recommended problems: IX.12 and IX.17Additional Reading and ExamplesSailboat: Read pages 213 – 218 Pay particular attention to pages 216 – 218Hummingbird: Read pages 243 – 248 Pay particular attention to pages 246 – 248Test 6Monday, November 21Questions for the first 10 minutes, then test – papers due promptly at the end of class!Covers Chapter 9 in Hummingbird (pages 219 – 260) or Chapter 8 in Sailboat (pages 189 – 230)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 InferenceWe use statistics computed from data collected in a sample to make statements (inferences) about some parameter of a population.In this chapter we continue to make inferences about the population mean m. The last two lectures we have discussed confidence interval estimates of m. Today and next lecture we will discuss tests of significance for m.General Significance Testing Procedure1. State the null and alternative hypotheses, and the significance level a that is going to be used.H0: ???Ha: ???a = ???ClickerGeneral 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).ClickerGeneral 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.Tests of SignificanceToday we will discuss tests of significance for a population mean m when the population standard deviation s is known, and in the next lecture we will consider the situation in which the population standard deviation s is unknown (meaning we only know the sample standard deviation s).Tests of SignificanceAs was the case for confidence intervals, when the population standard deviation s is known, we will use the Z-distribution. When the population standard deviation s is unknown (meaning we only know the sample standard deviation s), we will use the t-distribution.In either case we must remember to check our assumptions!Tests of Significance for m: s KnownGoal:We hypothesize that the population mean equals some value m0, and state the alternative hypothesis that we wish to prove is true.H0: m = m0Ha: m > m0 or Ha: m < m0 or Ha: m = m0Tests of Significance for m: s KnownGoal:We hypothesize that the population mean equals some value m0, and state the alternative hypothesis that we wish to prove is true.H0: m = m0Ha: m > m0 or Ha: m < m0 or Ha: m = m0We collect data, calculate the test statistic, calculate the p-value, and make a decision and conclusion.Test of Significance for m: s KnownGoal:We hypothesize that the population mean equals some value m0, and state the alternative hypothesis that we wish to prove is true.H0: m = m0Ha: m > m0 or Ha: m < m0 or Ha: m = m0The point estimate of m is the sample mean X.Tests of Significance for m: s KnownAssumptions:1. Simple random sample2. The population is normal or the sample size is large enough for the Central Limit Theorem to apply.3. Population standard deviation s is known.Tests of Significance for m: s KnownThe sampling distribution of X is X ~ N(m, s/ n )Z-score transformation: Z = X - m s/ nand this statistic is a candidate for our test statistic.Significance Test for mThen a candidate for the test statistic isZ = X - m s/ nn is the sample size and X is the sample mean, both of which we determine from the sample.s is the population standard deviation, which we assume is known.Significance Test for mCandidate for Test StatisticZ = X - m s/ nThe problem is that the population mean m is unknown.Also, if we substitute the logical estimate for m, the
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