Chapter 8: Estimating With Confidence What is a confidence interval?

Statistical Inference: Using sample data to draw conclusions about a population Note: Each sample may vary, but the population parameter doesn’t! Point Estimator – a statistic that provides an estimate of a population parameter Example: Estimate the percent (proportion) of time a Hershey’s kiss will land on its base when dropped

Confidence Interval: Uses the sample distribution to predict population parameter It is an interval of numbers above and below the sample statistic Example: “I am 95% confident that the interval 45% to 55% captures the true percentage of Harrison students that did all of their homework last night.

Confidence Level: The probability the interval will capture the true parameter value in repeated samples – 90% or higher Critical Value: The value that has the probability p lying to its right under the standard Normal curve. ( Z* )

Margin of Error: How accurate our estimate is based on the variability of the sample distribution. We add and subtract this from our estimate. estimate  margin of error Caution: Margin of error is only from random sampling errors. This does not include errors in collecting the data!

Most Common Critical Values Confidence Level (C) Upper tail prob. Z* Value 90%  1.645 0.05 0.90 0.05 0.05 Z=? Z=?

Most Common Critical Values Confidence Level (C) Upper tail prob. Z* Value 95%  1.96 0.025 0.95 0.0255 0.025 Z=? Z=?

Most Common Critical Values Confidence Level (C) Upper tail prob. Z* Value 99%  2.576 0.005 0.005 0.99 0.005 0.005 Z=? Z=?

Interpreting a Confidence Interval: What you will say: I am C% confident that interval _______ to ________ captures the true parameter. What it means: If we took many, many SRS from a population and calculated a confidence interval for each sample, C% of the confidence intervals will contain the true parameter.

CAUTION! Never Say: The interval will capture the true mean C% of the time. It either does or does not!

Steps to Construct ANY Confidence Interval: PANIC P: Parameter of Interest (what are you looking for?) A: Assumptions (what are the conditions?) N: Name the type of interval (what type of data do we have?) I: Interval (Finally! You can calculate!) C: Conclusion in context (I am ___% confident the interval ______ to _______ captures the true parameter (in context).