# Developing Confidence Intervals DAY 2

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## Objective

SWBAT use a simulation in order to develop a confidence interval.

#### Big Idea

Reporting a point estimate along with a margin of error provides much more information that the point estimate alone. We can use simulations to develop a confidence interval.

## Simulating the Sampling Distribution

75 minutes

In the previous class period, students completed the first page of Reaction Time and are ready to share their statistics with the class.  Each pair of students calculated 5 sample mean reaction times from the Census at School data and I ask them to plot these statistics on the class dot plot on the board.  I direct students to plot each of their five values as "xbars" rather than dots so that we remember that our plot is a distribution of sample means.

I want student to work with our class set of means, so I use the TI NSpire Navigator to collect the five data points from each group and then distribute the entire set to students.  Similar results could be obtained by having each group type their results into a Google Spreadsheet.

Working through the activity Reaction Time, my students discover how repeated samples can be used to informally develop a confidence interval.  They discover that the normal model can be used to estimate a confidence interval and explore the connection between the margin of error and the confidence interval [MP1, MP4, MP6].

Source Url for Sheep Dash
http://www.bbc.co.uk/science/humanbody/sleep/sheep/reaction_version5.swf

## Closure for Confidence Intervals

15 minutes

We end the Reaction Time activity with a class discussion in which we summarize each part of the activity.

1. We gathered our own sample data and calculated the mean time.  Our goal was to compare this to the whole population of students who answered the Census at School survey.
2. We took repeated samples from a population and calculated the means of those samples
3. We looked at the distribution of these means and calculated some summary statistics (mean and standard deviation)
4. We used the summary statistics from the collection of sample means to make a good guess about the parameter (population mean) we were interested in.  Using these statistics we developed an interval that probably contains the population mean.  We were 95% sure that that the mean of the whole population of students would really be in this interval.
5. We considered how our own result related to this interval so that we could compare how our class average compares to the overall population.

To many of my students, this process seems very convoluted. I remind them that we do not know the population values because Census at School does not provide them.  The best we can do is repeated sampling.  This is very often the case when we are trying to estimate population values, so learning how to manage this kind of partial information is important.