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pp.150-156 mgsc 291 spring 09

pp.150-156 mgsc 291 spring 09 - 150 Re-cap for Confidence...

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Re-cap for Confidence Interval for the Mean (σ Known) A confidence interval is a range of values that has a pre-specified probability of including the true value of the parameter. Therefore, a confidence interval for the mean is a range of values that has a pre-specified probability of including the mean, µ. The formula for a confidence interval for the mean when σ is known is: x ± z α /2 σ / n . The value of α/2 z (sometimes written as just “z”) depends on the level of confidence. The higher the level of confidence, the larger the z-score. For example, an 80% confidence interval for the mean is: x 1.28 n σ ± , whereas a 95% confidence interval for µ is: x 1.96 n σ ± . You should know how to determine the value of α/2 z for the desired confidence level. 150

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Example : Genron Corp. would like to determine the mean length of life for the high-performance model of tires that it supplies to an American automobile manufacturer. Forty tires are randomly selected from the manufacturing process and subjected to accelerated life-testing. The mean from the sample is 33,127 miles. Assume that the standard deviation for the population of tires (that is, σ) is 7,500 miles.
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pp.150-156 mgsc 291 spring 09 - 150 Re-cap for Confidence...

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