A large sample consists of how many or more observations?

The definition of a large sample in statistics often hinges on the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. A sample size of 30 or more observations is generally considered large because it provides a good approximation for this normality. This threshold allows for more reliable inferences to be made from the sample regarding the population parameters.

In many statistical analyses, such as hypothesis testing and confidence interval estimation, a sample size of 30 is recognized as sufficiently large to enable the application of various statistical techniques without significant concern for the underlying distribution of the data. This benchmark ensures that the variability in estimates decreases and that the estimates themselves become more stable and robust.

Sizes lower than 30 (like 10 or 20) may lead to increased variability and less reliable inferences. Consequently, option C, which indicates a sample size of 30 or more, aligns with standard practices in statistics regarding what constitutes a "large sample."