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## Estimation via Bootstrapped Confidence Intervals

.large[Kelly McConville | Math 141 | Week 8 | Fall 2020]

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## Announcements/Reminders

* No lab due this week.

* PA 2 by end of day Friday.

* Note: Updated the [due dates for PA 3 and the Final PA on the website](https://reed-statistics.github.io/math141f20/due_dates.html).

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## Week 8 Topics

* Estimation

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## Goals for Today

* Percentile method bootstrapped confidence intervals

* Constructing CIs in `R`

* Interpretation of confidence

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### Sampling Dist Versus Bootstrap Dist

* Data needed:

* Center:

* Spread:

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### Bootstrapped SE-Method Confidence Intervals

**95% CI Form**:

$$
\mbox{statistic} \pm 2\mbox{SE}
$$

We approximate `$\mbox{SE}$` with `$\widehat{\mbox{SE}}$` = the standard deviation of the bootstrapped statistics.

Caveats:

* Assuming a random sample

* Even with random samples, sometimes we get non-representative samples.  Bootstrapping can't fix that.

* Assuming the bootstrap distribution is bell-shaped and symmetric

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### Percentile Method Confidence Interval

If I want a P% confidence interval, I find the bounds of the middle P% of the bootstrap distribution.

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### Let's see how to calculate these confidence intervals in R with the confidenceIntervals.Rmd handout.

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### What do we mean by confidence?

CI: Interval of plausible values for the parameter

I am P% confident that the true parameter is in the computed interval.