Homework ReviewOther Confidence LevelsConfidence Intervals in the TI-83Which Confidence Interval is Best?AssignmentConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentConfidence Intervals for ProportionsLecture 32Sections 9.4Robb T. KoetherHampden-Sydney CollegeTue, Oct 27, 2009ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentOutline1Homework Review2Other Confidence Levels3Confidence Intervals in the TI-834Which Confidence Interval is Best?5AssignmentConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentOutline1Homework Review2Other Confidence Levels3Confidence Intervals in the TI-834Which Confidence Interval is Best?5AssignmentConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentHomework ReviewExercise 9.20, page 595A simple random sample of 400 voters is taken afterthey have just voted “yes” or “no” on a certain proposalin a small city. Of the 400 polled, 36% voted “yes” and64% voted “no.” The total number of voters in theelection is 40, 000.(a) Give a 95% confidence interval for the proportion of allvoters in the election who voted “yes.”(b) Interpret your interval and explain what the 95%confidence level means.(c) How would your interval change if the total number ofvoters in the election were 400, 000 instead of 40, 000?(d) How would your interval change if 4000 voters werepolled (instead of 400) and 36% voted “yes?”ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentHomework ReviewSolution(a) We are told that n = 400 and ˆp = 0.36.For a 95% confidence interval, we should use thecoefficient 1.96.The confidence interval isˆp ± 1.96rˆp(1 − ˆp)n= 0.36 ± 1.96r(0.36)(0.64)400= 0.36 ± (1.96)(0.024)= 0.36 ± 0.047.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentHomework ReviewSolution(b) For the standard interpretation, see page 587:If we repeated this procedure over and over, yieldingmany 95% confidence intervals for p, we wouldexpect that approximately 95% of these intervalswould contain p and approximately 5% would not.More briefly, “95% of all such intervals contain p and 5%do not.”ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentHomework ReviewSolution(c) If the population size were N = 400, 000 instead ofN = 40, 000, it would not change the confidence intervalat all. The parameter N does not appear anywhere inthe formula.(d) If the sample size were n = 4000 instead of n = 400(and ˆp were still 0.36), the confidence interval would benarrower. That is because n appears in thedenominator. A larger n gives a smaller margin of error.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentOutline1Homework Review2Other Confidence Levels3Confidence Intervals in the TI-834Which Confidence Interval is Best?5AssignmentConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentStandard Confidence LevelsThe most common confidence levels are 90%, 95%,99%, and 99.9%.Confidence Level z90% 1.64595% 1.96099% 2.57699.9% 3.291ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentThe Confidence IntervalThe confidence interval is given by the formulaˆp ± zrˆp(1 − ˆp)n,where z is obtained using the invNorm function on theTI-83 and depends on the confidence level.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentProbability of ErrorWe use the symbol α to represent the probability thatthe confidence interval is in error.That is, α is the probability that p is not in theconfidence interval.In a 95% confidence interval, α = 0.05.The area in each tail is α/2.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentProbability of ErrorLet zAdenote the value of z that cuts off a lower tail ofarea A.For example, z0.05is the 5thpercentile of Z.(The book uses z∗, but it is often better to specify thevalue.)The confidence interval requires zα/2.To find zα/2, we should compute invNorm(α/2).The confidence interval isˆp ± zα/2rˆp(1 − ˆp)n.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentConfidence LevelCompute new confidence intervals for Exercise 9.20using these confidence levels.90% confidence interval.99% confidence interval.99.9% confidence interval.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentOutline1Homework Review2Other Confidence Levels3Confidence Intervals in the TI-834Which Confidence Interval is Best?5AssignmentConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentTI-83 - Confidence IntervalsTI-83 Confidence intervals for ˆpPress STAT.Select TESTS.Select 1-PropZInt. A display appears requestinginformation.Enter x, the numerator of the sample proportion.Enter n, the sample size.Enter the confidence level, as a decimal.Select Calculate and press ENTER.ConfidenceIntervals forProportionsRobb T.KoetherHomeworkReviewOtherConfidenceLevelsConfidenceIntervals inthe TI-83WhichConfidenceInterval isBest?AssignmentTI-83 - Confidence IntervalsTI-83 Confidence intervals for ˆpA display appears with several items.The title 1-PropZInt.The confidence interval, in interval notation.The sample proportion ˆp.The sample size.How would we find
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