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Confidence Intervals

Confidence Intervals. 10.2 page 625 a) There is a 95% probability (chance) that the interval from 107.8 to 116.2 contains µ. Incorrect. The probability is 1 or 0. We don’t know which!. 10.2 page 625 b) There is a 95% chance that the interval (107.8 ,116.2) contains x bar.

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Confidence Intervals

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  1. Confidence Intervals 10.2 page 625 a) There is a 95% probability (chance) that the interval from 107.8 to 116.2 contains µ Incorrect. The probability is 1 or 0. We don’t know which!

  2. 10.2 page 625b) There is a 95% chance that the interval (107.8 ,116.2) contains x bar. • Incorrect. The general form of these confidence intervals is xbar + or – m (margin of error), so xbar is always in the center of the interval!

  3. 10.2 page 625c) This interval was constructed using a method that results in intervals which capture the true mean in 95% of all possible samples. • Incorrect. The different samples will yield different sample means, and the distribution of those sample means is used to provide an interval that captures the population mean.

  4. 10.2 page 625d) 95% of all possible samples will contain the interval (107.8, 116.2) • Incorrect. There is nothing magical about the interval from this one sample! Our method of computing confidence intervals is based on capturing the mean of the population, not a particular interval from one sample.

  5. e)The probability of the interval (107.8, 116.2) captures µ is either 0 or 1, but we don’t know which! • YEAH! CORRECT INTERPRETATION!

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