- Create a bootstrap distribution for a sample mean
- Find and describe a bootstrap percentile confidence interval for a population mean
Bootstrap Sample
Let’s learn a new way to construct confidence intervals that involves resampling from the data in a sample from a population. This involves selecting bootstrap samples.
bootstrap sample
A bootstrap sample is a sample that is selected from the values in the original sample.
The bootstrap sample is selected with replacement, and the sample size is the same as the sample size of the original sample.
Let’s practice selecting a bootstrap sample from the sample of the [latex]10[/latex] electric car kWh/[latex]100[/latex] miles ratings.
To create a bootstrap sample from the original sample, we want to select a new sample of size [latex]10[/latex] by sampling with replacement from the original sample. Notice that the observations in the original sample are numbered from [latex]1[/latex] to [latex]10[/latex]. To select the bootstrap sample, we can generate [latex]10[/latex] random numbers between [latex]1[/latex] and [latex]10[/latex] to identify which values are included in the bootstrap sample. Because we are sampling with replacement, we should expect that some of the random numbers generated may be repeated.
Step 2: Enter “10” in the “How many numbers do you want to generate?” box.
Step 3: Select “Yes” for “Sample with Replacement?”
Step 4: Click on the “Generate” button, and the app will display the 10 numbers generated in the box labeled “Current Simulation.”