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H-SC MATH 121 - Lecture 36 - Confidence Intervals Mean

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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 IntervalsTo 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 IntervalsWhat is the point estimate for ?What is the standard deviation for this estimator?How do we determine the appropriate number of standard deviations?Confidence IntervalsThe confidence interval will beorornzxnszxnstxWhen to Use ZIfThe population is normal (or nearly normal) and  is known, orThe population is not normal, but the sample size is at least 30,Then use Z.When to Use tIfThe population is normal (or nearly normal), and is not known, Then use t.ExampleExample 10.4, p. 641.Construct a 95% confidence interval for the true mean weight of such boxes.ExampleUse Z. (Why?)n = 25.x = 9.82.Assume that  = 0.29. (Why?)Level of confidence = 95%, so z = 1.96.ExampleThe confidence interval is).934.9,706.9(114.082.92529.096.182.9TI-83 – Confidence IntervalsWhen the standard normal distribution applies, do the following.Press STAT.Select TESTS.Select ZInterval.A window appears requesting information.TI-83 – Confidence IntervalsSelect Data or Stats.Assume we selected Stats.Enter .Enterx.Enter n.Enter the level of confidence.Select Calculate and press ENTER.TI-83 – Confidence IntervalsA window appears containingThe title “ZInterval”.The confidence interval in interval notation.The sample mean.The sample size.ExampleExample 10.5, p. 643.Construct a 99% confidence interval for the mean number of unoccupied seats.ExampleShould we use Z or t? Why?n = 61. x = 12.6.s = 4.4.Level of confidence = 99%. Find t.ExampleThe confidence interval is).099.14,101.11(499.16.12614.4660.26.12TI-83 – Confidence IntervalsTo use t, do the following.Press STAT.Select TESTS.Select TInterval.A window appears requesting information.TI-83 – Confidence IntervalsSelect Data or Stats.Assume we selected Stats.Enterx.Enter s.Enter n.Enter the level of confidence.Select Calculate and press ENTER.TI-83 – Confidence IntervalsA window appears containingThe title “TInterval”.The confidence interval in interval notation.The sample mean.The sample standard deviation.The sample


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H-SC MATH 121 - Lecture 36 - Confidence Intervals Mean

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