Confidence Interval Estimation for a Population MeanConfidence IntervalsSlide 3Slide 4When to Use ZWhen to Use tExampleSlide 8Slide 9TI-83 – Confidence IntervalsSlide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Confidence Interval Estimation for a Population MeanLecture 36Section 10.4Mon, Nov 5, 2007Confidence IntervalsTo estimate , we will use confidence intervals, as we did when estimating p.The basic form, as well as the theory, is the same as before:(pt. est.) (appropriate no. of st. devs.)Confidence IntervalsWhat is the point estimate for ?What is the standard deviation for this estimator?How do we determine the appropriate number of standard deviations?Confidence IntervalsThe confidence interval will beorornzxnszxnstxWhen to Use ZIfThe population is normal (or nearly normal) and is known, orThe population is not normal, but the sample size is at least 30,Then use Z.When to Use tIfThe population is normal (or nearly normal), and is not known, Then use t.ExampleExample 10.4, p. 641.Construct a 95% confidence interval for the true mean weight of such boxes.ExampleUse Z. (Why?)n = 25.x = 9.82.Assume that = 0.29. (Why?)Level of confidence = 95%, so z = 1.96.ExampleThe confidence interval is).934.9,706.9(114.082.92529.096.182.9TI-83 – Confidence IntervalsWhen the standard normal distribution applies, do the following.Press STAT.Select TESTS.Select ZInterval.A window appears requesting information.TI-83 – Confidence IntervalsSelect Data or Stats.Assume we selected Stats.Enter .Enterx.Enter n.Enter the level of confidence.Select Calculate and press ENTER.TI-83 – Confidence IntervalsA window appears containingThe title “ZInterval”.The confidence interval in interval notation.The sample mean.The sample size.ExampleExample 10.5, p. 643.Construct a 99% confidence interval for the mean number of unoccupied seats.ExampleShould we use Z or t? Why?n = 61. x = 12.6.s = 4.4.Level of confidence = 99%. Find t.ExampleThe confidence interval is).099.14,101.11(499.16.12614.4660.26.12TI-83 – Confidence IntervalsTo use t, do the following.Press STAT.Select TESTS.Select TInterval.A window appears requesting information.TI-83 – Confidence IntervalsSelect Data or Stats.Assume we selected Stats.Enterx.Enter s.Enter n.Enter the level of confidence.Select Calculate and press ENTER.TI-83 – Confidence IntervalsA window appears containingThe title “TInterval”.The confidence interval in interval notation.The sample mean.The sample standard deviation.The sample
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