Confidence Intervals - 12 CONFIDENCE INTERVALS FOR THE MEAN...

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12. CONFIDENCE INTERVALS FOR THE MEAN, UNKNOWN VARIANCE If the population standard deviation σ is unknown, as it usually will be in practice, we will have to estimate it by the sample standard deviation s . Since σ is unknown, we cannot use the confidence intervals described previously. The practical versions presented here use s in place of σ . Eg 1 : A random sample of 8 “Quarter Pounders” yields a mean weight of pounds, with a sample standard deviation of s = 0.07 pounds. Construct a 95% CI for the unknown population mean weight for all “Quarter Pounders”. (Solution on next slide). x = 0 2 . Remember that s is the square root of the sample variance, There are two cases to consider: “Large Sample” and “Small Sample”. • If n 30 (and σ is unknown), just replace σ by s and proceed as before. The CI is This works because is approximately standard normal, regardless of the population distribution, when n 30.
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