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Section 8.5 Using Computers to Make New Estimation Methods Possible Bootstrap Confidence Interval Why use it? 
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Used when sampling distribution or standard error is difficult to derive mathematically for a statistic. It can also be used for example to find a confidence interval for the population mean when the assumption of normality is in question. How does it work? 
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This methods resamples with replacement from the original sample many times. Each time a sample is made. A new sample statistic is calculated. This process of resampling and re‐calculating a statistics happens thousands of times. To find the 95% confidence interval, using the bootstrap method, find the 2.5th and 97.5th percentiles of the simulated bootstrap distribution. 95% CI: (2.5th percentile, 97.5th percentile). To find the 90% confidence interval, using the bootstrap method, find the 5th and 95th percentiles of the simulated bootstrap distribution. 90% CI: (5th percentile, 95th percentile). Example: Estimating the variability of a thermometer. A mother was interested in determining how much variability existed in measurements from a thermometer. She decided to test her thermometer and take her body temperature ten times. 98.55 98.45 98.85 98.40 98.25 98.60 98.40 98.20 98.65 98.50 Find the 95% confidence interval for the population standard deviation using the bootstrap method. Example: A cell phone sales person is trying to estimate the average number of text messages sent by students per day. Here is the data set that she collected from 14 randomly selected students. 0 50 100 60 0 30 30 50 15 200 5 2 5 500 a.) Are the assumptions met for a confidence interval for the population mean, using the formula from the previous chapter? b.) Why might the median be a good measure to use in this case? c.) Find the 90% confidence interval for the population median using the bootstrap method.