Python Tutorial : Bootstrap confidence intervals

Want to learn more? Take the full course at https://learn.datacamp.com/courses/case-studies-in-statistical-thinking at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- You have now used graphical exploratory data analysis, or EDA, to investigate the active bouts of the zebrafish. I remind you of one of my favorite quotes from John Tukey. Exploratory data analysis can never be the whole story, but nothing else can serve as a foundation stone--as the first step. In this course, and throughout your data science endeavors in general, it is important to heed Tukey's advice and start with EDA. Now that we have done some EDA, let's start progressing toward the whole story. We saw in the previous exercises that the active bout lengths are roughly Exponentially distributed. The Exponential distribution has a single parameter that describes the characteristic time between arrivals of a Poisson process. The value of that parameter that best describes the data is computed from the mean of all of the active bout lengths. Thus, the mean computed from the data is the optimal parameter value. Let's look at how this is done with the nuclear incident data. We can use the np.mean() function to compute the mean of all inter-incident times, which is 87 days, indicated by the vertical gray line on the plot. But how confident are we in this value? What if we could somehow measure a collection of inter-incident times again? What would we get for the mean? We can simulate this by drawing a bootstrap sample. Specifically, we resample the data with replacement using the `np.random.choice()` function. We can plot the ECDF of the resampled data, along with the mean inter-incident time computed from this resampled data set. We get a slightly different value than we got from the original data. We can do this procedure again and again and again and again and again and again. Each value of the mean inter-incident time is a bo