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7-2 Chapter Seven Confidence Intervals McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 這一章完全靠 背公式套之

7-3 Confidence Intervals 7.1Large Sample Confidence Intervals for a Population Mean 7.2Small Sample Confidence Intervals for a Population Mean 7.3Sample Size Determination 7.4Confidence Intervals for a Population Proportion *7.5A Comparison of Confidence Intervals and Tolerance Intervals

Large Sample Confidence Intervals for a Mean If  is unknown and the sample size is large (n  30), estimate by the sample standard deviation s and a  )100% confidence interval for  is If the sampled population is normal or the sample size is large (n  30), a  )100% confidence interval for  is (1-a)100%=confidence level 背公式套之

7-5 Example: Large Sample Confidence Interval for Mean Example 7.1: Gas Mileage Case 95% Confidence Interval 99% Confidence Interval 背公式套之

7-6 Three  Confidence Intervals for  Gas Mileage Example best coverage

7-7 The Effect of  on Confidence Interval Width

Small Sample Confidence Intervals for a Mean If the sampled population is normally distributed with mean , then a  )100% confidence interval for  is is the t point giving a right-hand tail area of  /2 under the t curve having n – 1 degrees of freedom. t 分配 : small sample is the key word

7-9 Example: Small Sample Confidence Interval for Mean Example 7.4: Debt-to-Equity Ratios 查表 t

7-10 Effect of Degrees of Freedom on the t-distribution As the number of degrees of freedom increases, the spread of the t distribution decreases and the t curve approaches the standard normal curve. df makes difference

Sample Size Determination A sample size will yield an estimate of, precise to within B units of , with 100(1-  ) confidence. 背公式套之, 從信 賴區間而來, 誤差 界線, 民調用之, 1068

Confidence Intervals for a Population Proportion If the sample size n is large, then a  )100% confidence interval for p is 背公式套之； Bernouli trial, condition is above, based on central limit theory n

7-13 Example: Confidence Interval for a Proportion Example 7.8: Phe-Mycin side effects

7-14 Determining Sample Size for Confidence Interval for p A sample size will yield an estimate, precise to within B units of p, with 100(1-  ) confidence. Note that the formula requires a preliminary estimate of p. The conservative value of p = 0.5 is generally used when there is no prior information on p. 背公式套之

7-15 *7.5 A Comparison of Confidence Intervals and Tolerance Intervals

7-16 Summary: Selecting an Appropriate Confidence Interval for a Population Mean

7-17 Confidence Intervals Summary: 7.1Large Sample Confidence Intervals for a Population Mean 7.2Small Sample Confidence Intervals for a Population Mean 7.3Sample Size Determination 7.4Confidence Intervals for a Population Proportion *7.5A Comparison of Confidence Intervals and Tolerance Intervals