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Lecture 3

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University of Ottawa

Administration

ADM2304

Tony Quon

Fall

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> A 100(1) C.I. for , when SD is unknown: > where t 2,n1s the tvalue with n 1 degrees of freedom for which there is 2 probability in the right tail. We have replaced by s and the zvalue by a tvalue > If is unknown and n is large, then we can approximate the 100(1) condence interval for the population mean by Assumptions: a. Random sample not a convenience sample b. For small samples, the underlying population must be normally distributed. Why? c. For larger samples, the underlying distribution is not important. Sample Proportion: > Since the sample proportion has a known sampling distribution namely it is approximately normal with mean p and standard deviation squrt (p(1p)n) provided n is large enough! > Therefore, an approximate 100(1) C.I. for p has the form: e.g, Of 56 students polled, 10 found the midterm easier than expected and 46 found it harder than expected. Compute a 95 condence interval around the proportion of students who found the midterm easier than expected 10 p = 56=.18 > the value for z in this case is 1.96 (since 95) check assumptions:np =10.08 >10,n(1 p) = 45.92 >10 95C.I.for the truepopulationproportionof of allstudents whofound themidterm easier than expectedis (.18 .82 .181.96 56 = .08,.28 Go back to Margin of Error: > Suppose you want to insure that your estimate is within E of the true population proportion > but we dont know the sample proportion until we take the sample! So, either use a previous estimate of the proportion OR Chose the proportion that would makes the required n the largest Option 1: A Previous Estimate > If there exists a previous estimate for the proportion that can be used to determine the appropriate n

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