RESAMPLING
a. In general, what does it mean to “resample” the following data set consisting of wait times (minutes) of customers waiting in line for the Space Mountain ride at Walt Disney World: 50, 25, 75, 35, 50?

Verified step by step guidance

1. Resampling refers to the process of repeatedly drawing samples from a given data set, either with or without replacement, to make statistical inferences or to estimate properties of the population. In this case, the data set consists of wait times: 50, 25, 75, 35, 50.
2. To resample with replacement, you would randomly select values from the original data set, allowing the same value to be chosen multiple times. For example, a possible resampled set could be {50, 50, 25, 75, 50}.
3. To resample without replacement, you would randomly select values from the original data set without repeating any value. For example, a possible resampled set could be {75, 50, 35, 25, 50}.
4. Resampling is often used in methods like bootstrapping (with replacement) to estimate the sampling distribution of a statistic, or in permutation tests (without replacement) to test hypotheses.
5. In this context, resampling the wait times could help estimate the variability of the mean or median wait time, or test hypotheses about the distribution of wait times.

Key Concepts

Resampling

Resampling is a statistical technique that involves repeatedly drawing samples from a dataset and analyzing the results. This method is often used to estimate the distribution of a statistic (like the mean or variance) when the underlying population distribution is unknown. In the context of the given dataset, resampling could help assess the variability of wait times and provide insights into customer experiences.

Sampling Distribution

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a specific population. It describes how the statistic (e.g., sample mean) varies from sample to sample. Understanding sampling distributions is crucial for making inferences about the population based on sample data, particularly when resampling techniques are applied.

Bootstrap Method

The bootstrap method is a specific resampling technique that involves taking repeated samples, with replacement, from the original dataset to estimate the sampling distribution of a statistic. This approach allows for the estimation of confidence intervals and hypothesis testing without relying on strong parametric assumptions. In the context of the wait times dataset, bootstrapping could provide a robust way to analyze the variability and reliability of the average wait time.