Download Confidence Intervals - Lecture Notes | STAT 269 and more Study notes Statistics in PDF only on Docsity! 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: µ is 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: X̄ 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: µ is the mean for all
