lec5.3

# Lec5.3 - 115 Lecture 12 CHAPTER 5 CONFIDENCE INTERVALS Large-Sample Confidence Intervals for a Population Mean Contd(Section 5.1 page 323 Recall

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115 Lecture 12: CHAPTER 5: CONFIDENCE INTERVALS Large-Sample Confidence Intervals for a Population Mean – Cont’d (Section 5.1, page 323) Recall: Last class, we took a look at the most common confidence intervals: Summary Other Confidence Levels Note: Other commonly used large sample confidence intervals for a population or process mean are given below: Let n X X ,..., 1 be a large ) 30 ( n random sample from a population with mean and standard deviation , so that x is approximately normal. Then a level )% 1 ( 100 two sided confidence interval for is x z x 2 where n x . When the value of is unknown, it can be replaced with the sample standard deviation s .

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116 There are two methods for finding the critical value (i.e., 2 z ):
117 Example: The sample mean and standard deviation for the fill weights of 100 boxes are 05 . 12 x and 1 . 0 s . Find an 85% confidence interval for the mean fill weight of the boxes. Example: In a sample of 50 microdrills drilling a low-carbon alloy steel, the average lifetime (expressed as the number of holes drilled before failure) was 12.68 with a standard deviation of 6.83. An engineer reported a confidence interval of (11.09, 14.27) but neglected to specify the level. What is the level of this confidence interval?

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118 Determining the Sample Size Needed for a Confidence Interval of Specified Width The half-width 1.96 n s of the 95% CI is sometimes called the bound on the error of estimation associated with a 95% confidence level;
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## This note was uploaded on 06/20/2011 for the course STAT 2800 taught by Professor Paula during the Winter '11 term at UOIT.

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Lec5.3 - 115 Lecture 12 CHAPTER 5 CONFIDENCE INTERVALS Large-Sample Confidence Intervals for a Population Mean Contd(Section 5.1 page 323 Recall

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