Slide 1Practice ProblemsAdditional Reading and ExamplesTest 5Slide 5Statistical InferenceConfidence IntervalsPoint EstimateConfidence IntervalConfidence Interval – Z*Slide 11Confidence Interval for πConfidence IntervalsConfidence Interval for πTI-83/84 CalculatorExample 71/89Example 71/89Example 71/89Example 71/89Example 71/89Example 71/89Example 71/89Example 71/89Example 72/90Example 72/90Example 72/90Example 72/90Example 72/90Example 72/90Slide 30Example 72/90Example 72/90Example 72/90Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Example 73/91Slide 46PropertiesSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationSample Size DeterminationExample 74/92Example 74/92Example 74/92Example 74/92Example 74/92Example 74/92Example 74/92Tests of Significance for pPoint EstimateSampling Distribution of pTests of Significance for pTests of Significance 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 76/94See you tomorrow!STAT 210Lecture 28Confidence Intervals for Population Proportions ANDSignificance Tests on Population ProportionsNovember 2, 2016Practice ProblemsSailboat: Pages 252 through 257Relevant problems: IX.8, IX.12 (a) and (b), IX.13, IX.15 (a) and (b), IX.16, IX.17 and IX.18Recommended problems: IX.13 and IX.18Hummingbird: Pages 210 through 215Relevant problems: VIII.8, VIII.12 (a) and (b), VIII.13, VIII.15 (a) and (b), VIII.16, VIII.17 and VIII.18Recommended problems: VIII.13 and VIII.18Additional Reading and ExamplesSailboat: Read pages 248 through 251Pay particular attention to pages 249 and 250Hummingbird: Read pages 206 through 209Pay particular attention to pages 207 and 208Test 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 data collected in a sample to make statements about unknown population parameters.This chapter we want to make inferences about the population proportion p.Confidence IntervalsA confidence interval is an inference procedure that allows us to estimate the value of an unknown population parameter.Point EstimateThe point estimate of the population proportion p is the sample proportion p.p = number of successes in the sample sample size nConfidence IntervalAssumptions:1. Simple random sample from the population2. Large sample quantified as both the number of successes in the sample np and the number of failures in the sample n(1-p) are both greater than or equal to 10.Then a C% confidence interval for p is:p + z* p(1 - p)/nConfidence Interval – Z*The value of Z* depends on the amount of confidence stated and is determined from the t-table on page 340.One looks up the confidence level across the bottom row, and then reads the Z* value from the row directly above it.Z*Confidence levelConfidence Interval for πThe interpretation of the confidence interval is the statistical inference and should be stated as follows.“We have C% confidence that the population proportion π falls between the lower limit and the upper limit.”Confidence IntervalsThe term confidence refers to the amount of confidence that we have that our interval will contain the true value of π. Since π is unknown, we will never know for sure whether our interval contains π or not, but we typically choose a confidence level that is relatively high, such as 90%, 95%, 98%, or 99%, so that our confidence of success is high.Note that the only way to have 100% confidence is to actually know the value of π.Confidence Interval for πIn writing an interpretation, we do not use the term “probability” (use “confidence” instead), we do not talk about the sample proportion (rather the population proportion) and we do not talk about individual values.TI-83/84 CalculatorSee the end of the chapter for instructions on using a calculator to determine confidence intervalsfor proportions.1. Hit STAT2. Scroll over to TESTS3. Choose A:1-PropZInt4. X is the number of successes (a whole number), n is the sample size5. Enter required components and hit CalculateExample 71/89Population of interest: ???Parameter of interest: ???Example 71/89Population of interest: all current college presidentsParameter of interest: p = proportion of all current college presidents who favor the planExample 71/89Simple random sample of n = 100 college presidentsp = number of successes = Clicker nExample 71/89Simple random sample of n = 100 college presidentsp = number of successes = 6 = .06 n 100Example 71/89Assumptions:1. Do we have a simple random sample?Example 71/89Assumptions:1. Do we have a simple random sample? YESExample 71/89Assumptions:1. Do we have a simple random sample? YES2. Do we have a large enough sample for the CLT to apply?Example 71/89Assumptions:1. Do we have a simple random sample? YES2. Do we have a large enough sample for the CLT to apply?NO – the number of successes in the sample is only 6, which is less than 10. np = 100(.06) = 6 < 10Hence the assumptions are not satisfied and the confidence interval should not be calculated.Example 72/90Population of interest: ???Parameter of interest: ???Example 72/90Population of interest: all current athletic directorsParameter of interest: p = proportion of all athletic directors who favor the planExample 72/90Simple random sample of n = 100 athletic directorsp = number of successes = ??? nExample 72/90Simple
View Full Document
Unlocking...