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.
• Incorrect. The general form of these
confidence intervals is xbar + or – m (margin
of error), so xbar is always in the center of the
10.2 page 625
c) 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.
10.2 page 625
d) 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.
e)The probability of the interval
(107.8, 116.2) captures µ is either 0 or
1, but we don’t know which!

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