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When we talk about random sampling, we're referring to the technique of selecting a subset of individuals from a population in such a way that every individual has an equal chance of being chosen. This method is critical for obtaining a sample that represents the whole population without bias.

In our example, a group of 20 students at a university has been randomly selected to estimate the percentage of all students who are registered to vote. It is crucial that the students were chosen without any pattern or predetermined criteria to ensure that the findings can be generalized to the entire student body. Random sampling is used in various fields, including statistics, research, and polling, and is foundational to the integrity of estimating proportions and conducting statistical analysis.

Proportion calculation is a fundamental aspect of many statistical analyses. It involves determining the ratio of a subset of a group to the entire group. This ratio provides insights into characteristics of populations and helps in making predictions and decisions.

To calculate the proportion of university students registered to vote, we first count the number of 'R' responses (registered students). For example, if there are 15 'R' responses out of 20 students, the calculation would use the formula:
\[ p = \frac{{\text{{number of 'R' responses}}}}{{\text{{total number of responses}}}} \]
Given 15 'R' responses and 5 'N' responses, the proportion of students registered to vote would be calculated as:
\[ p = \frac{15}{20} = 0.75 \]
This result means that 75% of the sampled students are estimated to be registered to vote. Please note that for accuracy, the sample must be random, as mentioned in the previous section about random sampling.

Descriptive statistics is a branch of statistics that deals with organizing, summarizing, and presenting data in an informative way. It involves using measures such as mean, median, mode, and proportion, among others, to describe the main features of a data set concisely.

In the context of our voting example, after using random sampling and proportion calculation, descriptive statistics allows us to communicate the estimated proportion of voters in a meaningful way. It tells us not only about the particular sample but also gives us an understanding of the larger population. However, it's important to remember that descriptive statistics do not allow us to make hypotheses about the data or infer conclusions beyond the data we have. It's simply a way to describe what we observe in the dataset.