Final answer:
The correct answer is option 2. The distinguishing feature of statistical sampling is its ability to measure the degree of uncertainty when examining part of a population, mathematically. This is best described by option 2 and involves techniques like sampling distribution and standard error to manage sampling variability and assure validity.
Step-by-step explanation:
The distinguishing feature of statistical sampling is best described by option 2, which states: It provides a means for measuring mathematically the degree of uncertainty that results from examining only part of a population. Statistical sampling allows researchers to draw conclusions about populations using smaller, manageable samples while quantifying the accuracy and reliability of the results. Various methods of random sampling, such as simple random sampling, stratified sampling, cluster sampling, and systematic sampling are employed to ensure that the sample represents the population as closely as possible.
In particular, the use of sampling distribution plays a fundamental role in statistical sampling. It involves generating a probability distribution of a statistic (like the mean, proportion, or standard deviation) based on all possible samples of size n from a population. This distribution helps in understanding and quantifying the sampling variability, which refers to how much the sample statistic would vary if we repeatedly took samples from the same population. The concept of standard error is also central in quantifying the sampling variability.
Larger samples generally provide more reliable statistics and can help reduce the sampling variability, thus leading to more accurate estimations of population parameters. Nonetheless, even with larger samples, variability exists due to different individuals making up each sample, highlighting the importance of sound sampling techniques to maximize accuracy and validity in statistical inference.