QUICK: Review of confidence intervals

Inference: provides methods for drawing conclusions about a population from sample data.

Confidence Intervals estimate a population parameter (mean or proportion) with some level of confidence.

Because of what we know of Sampling Distributions (μxbar = μ AND μphat = p), we express our confidence in being able to capture the true μ or p in our own ONE sample.

Here is the idea of a Sampling Distribution

Inference Toolbox for Confidence Intervals

1. State Population and parameter of interest.

2. Check Conditions.

3. Calculate actual confidence interval.

4. Interpret results: I am ___% confident that the true mean μ ____(context)_______ is between ______ and _______.

Conditions for Inference Procedures

SRS: The data are a SRS from the population of interest.

Normality:

Confidence Intervals with Means: 1. Use CLT when n>30.

2. Otherwise boxplot, stemplot, dotplot for symmetry, no extreme skewness or large outliers. Check Normal Probability Plot for linearity.

Confidence Intervals with Proportions: 1. Check normality with n*phat > 10 and n*qhat >10

Independence: When sampling without replacement, check that n*10 < population size

One Sample z interval (σ known)

One Sample t interval(σ unknown)

MEANS:

PROPORTIONS:

One Sample z interval Proportion (1-phat) = qhat

Formulas for Confidence Intervals

Vocabulary for Confidence Intervals

Confidence Level

Confidence Interval

Margin of Error

Standard Error