Suppose the following data represent the amount of time (in hours) a random sample of students enrolled in College Algebra spent working on a homework assignment: 3.2, 4.1, 1.2, 0.6, and 2.5. Below are three bootstrap samples. For each bootstrap sample, determine the bootstrap sample mean.


Bootstrap Sample 1: 1.2, 0.6, 3.2, 3.2, 1.2
Bootstrap Sample 2: 0.6, 4.1, 4.1, 0.6, 4.1
Bootstrap Sample 3: 4.1, 3.2, 3.2, 0.6, 1.2

Verified step by step guidance

1. Recall that the bootstrap sample mean is calculated by summing all the values in the bootstrap sample and then dividing by the number of values in that sample.
2. For Bootstrap Sample 1, list the values: 1.2, 0.6, 3.2, 3.2, and 1.2. Calculate the sum of these values.
3. Divide the sum obtained in the previous step by 5 (since there are 5 values) to find the mean of Bootstrap Sample 1.
4. Repeat the process for Bootstrap Sample 2: sum the values 0.6, 4.1, 4.1, 0.6, and 4.1, then divide by 5 to find the mean.
5. Finally, for Bootstrap Sample 3, sum the values 4.1, 3.2, 3.2, 0.6, and 1.2, and divide by 5 to find the mean.

Key Concepts

Bootstrap Sampling

Bootstrap sampling is a resampling technique where samples are drawn with replacement from the original data set. It allows estimation of the sampling distribution of a statistic, such as the mean, without relying on strict assumptions about the population. This method helps assess variability and confidence intervals.

Sample Mean

The sample mean is the average value of a data set, calculated by summing all observations and dividing by the number of observations. It serves as a measure of central tendency and is often used to estimate the population mean. In bootstrap samples, the mean is recalculated to understand variability.

Random Sampling with Replacement

Random sampling with replacement means each data point can be selected multiple times in a sample. This process is essential in bootstrap methods because it mimics the original sampling variability and allows repeated values, which helps approximate the sampling distribution of statistics.