What Is a Confidence Interval Anyway?

Definitions Confidence: firm belief, trust, reliance Interval: the set containing all numbers between two given numbers and including one, or both, endpoints

What Do We Trust The interval? The method used to produce the interval?

Central Limit Theorem Basis of our firm belief and trust Shape of Sampling Distribution of Sample Means

Properties of Distribution Mean Standard Deviation

Before Sampling Probability that sampling method will produce a sample mean within z standard deviations of the MEAN. Amount of error that is acceptable?

Calculation of Error Error = Margin of error in a confidence interval covers only random sampling errors

Reminder: no sample yet Will our sample produce a sample mean that is in this interval? What proportion of all samples will produce a sample mean in this interval? What is the probability that our sample will produce a sample mean in this interval? Reminder: no sample yet

After Sampling Sample mean is on the horizontal axis of sampling distribution Where is it?

Is Our Sample Mean In

Sample Mean In the interval. So what? Not in the interval.

Interval of Plausible Parameters for which statistic is likely to occur

in

Confidence? Question of probability? What exactly are we confident of?

What Is a Confidence Interval Anyway? An interval that may or may not contain When will the interval contain ? An interval that gives us a range of plausible values of An interval that has probability of 0 or 1of actually containing

Statement With ____% confidence, I believe to lie within the interval calculated. Therefore I am ___% confident that this interval contains