# Chapter05 - Chapter 5 Confidence Intervals 5.1 Large-Sample...

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Chapter 5. Confidence Intervals

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5.1 Large-Sample Confidence Intervals Let X 1 ,…, X n be a large ( n > 30) random sample from a population with mean μ and standard deviation σ , so that is approximately normal. Then a level 100(1 – α )% confidence interval for μ is Where . When the value of σ is unknown, it can be replaced with the sample standard deviation s . X X α σ z X 2 / ± n σ σ X / =
Example 5.1 The sample mean and standard deviation for the fill weights of 100 boxes are 12.05 and 0.1. Find an 85% confidence interval for the mean fill weight of the boxes.

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Example 5.2 A sample of 50 microdrills drilling a low-carbon alloy steel, the average lifetime was 12.68 with a standard deviation of 6.83. Find a 95% confidence interval for the mean lifetime of microdrills under these conditions.
5.2 Small-Sample Confidence Intervals Let X 1 ,…, X n be a small ( n < 30) sample from a normal population with mean μ. Then the quantity has a Student’s t distribution with n – 1 degrees of freedom, denoted t n-1 .

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