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Sampling is a fundamental concept in statistics, especially when conducting surveys or studies. Here, sampling refers to the selection of a smaller group, or a subset, from a larger population to understand the entire population's behavior or characteristics. In the context of our Facebook study, a sample of 92 students was chosen from a private university's student body.

The way we choose this sample affects the accuracy of our results. Common methods include random sampling, where every student would have an equal chance of being selected, and stratified sampling, where the student population might be divided into subgroups (such as year of study or major) before sampling from each subgroup.

Using a well-chosen sample allows researchers to make inferences about the broader population without having to survey everyone, saving time and resources. However, it's crucial to ensure the sample is representative to avoid biases in the results.

Proportion is a term used to describe the relationship between parts of a whole. In statistics, it is often expressed as a fraction, showing the part of the data that fits a certain category.

In our exercise, we calculate the proportion of students who use Facebook to pass the time by dividing the number of students who answered 'yes' by the total number of students surveyed. This is represented mathematically as \( \frac{23}{92} \).

This fraction can also be converted to a percentage by multiplying by 100, providing a more relatable expression of the data. Understanding proportions helps us grasp how prevalent a certain behavior or characteristic is within a specific group and is essential for making data-driven decisions.

Data analysis involves examining, cleaning, and modeling data to discover useful information, draw conclusions, and support decision-making. In our Facebook usage study, analyzing the proportion of students using Facebook to pass time provides insights into student behaviors.

Once the data is gathered, it’s important to process it correctly: identify any outliers, ensure data consistency, and then compute desired statistics such as averages, proportions, or variances. In our case, calculating the proportion gives a direct insight into a common student behavior.

Data analysis transforms raw data into meaningful results. It allows us to answer hypotheses, validate assumptions like whether Facebook is a popular pastime activity among students, and can contribute to further research or policy developments in educational environments.