# Statistics Inference Confidence Intervals

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Common Core Standards
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The Card Deck Emulator for Teaching Statistical Inference and Confidence Intervals

FOR LINUX / MAC / PC

NOTE: Click on the Preview button to download a DEMO version of the card emulator. You will need to install LibreOffice to use the DEMO. See installation instructions below.

NOTE: This presentation application will open in Microsoft PowerPoint, but its macros run properly only in LibreOffice. To use this app, you must install LibreOffice (it's free; see below) and open the presentation file in LibreOffice.

The Card Deck Emulator lets students explore statistical inference concepts in a fun and convenient way.

You start by building a very large deck of value cards (the population) whose values have a specific and known mean and standard deviation. Students then attempt to infer the population mean and standard deviation by taking hands from the deck!

You can independently toggle two summary cards that show the statistics of the deck and the statistics of the hand. You can also toggle a dot plot that shows the values in the hand as well as the hand's mean. This plot will also show three intervals: one based on the hand standard deviation, another based on the standard error of the mean, and a third based on a confidence interval whose confidence level you choose (80%, 90%, 95%, or 99%).

Suggested Activities:

★ Draw a hand with the dot plot toggled to the visible state. Discuss the hand's mean as a measure of the center of the collection of hand values and discuss the hand's standard deviation as a measure of the distance between a typical hand value and the mean value.

★ Demonstrate with repeated hands of the same size that a hand's mean and standard deviation provide reasonable estimates of the deck's mean and standard deviation.

★ Demonstrate with repeated hands of the same size that the hand's mean and standard deviation vary from hand to hand. Conclude that, when we use hand statistics to infer deck statistics, we should expect some error.

★ Collect hand means for 10 hands and compute the standard deviation of these hand means. Compare the inferred standard error of the mean with the true one (visible on the Deck Properties reveal card).

★ For 20 repeated hands of the same size, the student uses tally marks to count the number of intervals that fail to capture the deck's true mean. Do the experiment twice: once using confidence intervals set at the 80% confidence level and again using intervals set at the 95% confidence level. Discuss the significance of the confidence level in the context of succeeding or failing to capture the true mean.

★ Team Contest: Each team draws a single hand of a fixed size. Which team gets the best estimates of the population properties?

★ Team Contest: Each team draws a single hand of a fixed size. Which teams produce intervals that capture the deck mean? What fraction of the teams failed to capture the deck mean? Leads to a discussion of confidence intervals.

2). Macro execution MUST be enabled in LibreOffice for the card deck emulator to work properly. To enable macro execution, open LibreOffice, click Tools / Options (on the menu bar), then click on the Security category. Click on the Macro Security button and set the level to Low (Medium will also work but becomes annoying after a while). Close LibreOffice.

4). Open the resulting uncompressed folder from STEP (3). In the uncompressed folder, open the file

"Card Deck Emulator: Statistical Inference.odp"

in LibreOffice. You should be good to go.

5). You may move, copy, reproduce, and/or rename the file "Card Deck Emulator: Statistical Inference.odp" to any location on your hard drive, as needed.

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