STAT 269 - Introductory Statistics
Confidence Intervals
1. Parameter: In each of the intervals that we will look at the interest is in finding a reliable estimate of
some parameter. The first step in our process will be to clearly define what the parameter represents
in the particular situation we are considering.
2. Assumptions: As with hypothesis testing, each method we discuss will make certain assumptions
about the way we collected our data and the nature of the population, or populations, from which
they came. These assumptions are just as important here as they are in hypothesis testing.
3. Point Estimate: Our intervals will each start with the most reasonable estimate we have, which will
generally be a statistic calculated from our data, that summarizes for the data the same characteristic
as the parameter measures for the population.
4. Margin of Error: From our assumptions, we will use our data to determine how far out on each side
of the point estimate we need to go to account for the variability, or error, that is a result of having
only a sample of data, and not the whole population. In most cases the bound is the same value in
both directions, but this is not always the case.
5. Confidence Interval: The interval is found by subtracting the lower bound from the point estimate
and adding the upper bound to the point estimate. We then have a certain confidence that the true
value of the parameter is within these values.
6. Conclusion: Once again, we will be careful to state the conclusion in terms of the problem. In the
conclusion we will give the bounds, with the units of measurement, and state our level of confidence.
Confidence Interval Details: For µ, large sample
1. Parameter: µis the mean for all
2. Assumptions: We have independent, random observations from some population, and the sample
size is large enough that we can use the Central Limit Theorem.
3. Point Estimate: ¯
X
4. Margin of Error:
Z·
σ
√n
5. Confidence Interval: 3.-4., and 3.+4.
6. Conclusion: We are % confident that the mean for all is
between (lower bound) and (upper bound).
Confidence Interval Details: For µ, small sample
1. Parameter: µis the mean for all
