If a population is believed to be approximately normal, what is the minimum sample size that can be sufficient?

When dealing with a population that exhibits an approximately normal distribution, statistical analysis can be conducted with relatively small sample sizes due to the properties of normality. A sample size of 15 is often considered the minimum threshold necessary to adequately estimate population parameters, such as the mean, while also allowing for the construction of confidence intervals.

A sample of this size typically provides enough data to observe the central tendency and variability inherent in the population. Statistically, when the population is normal, the sampling distribution of the mean will also be normal, regardless of sample size, which means that even small samples can yield reliable results. However, as the sample size increases beyond this threshold, the estimates become more stable and precise.

In practice, researchers sometimes increase the sample size above 15 to enhance the reliability of their findings, especially when conducting hypothesis tests or when the consequences of decision-making are significant. However, the key point remains that a sample size of 15 provides a foundation for conducting analyses under the assumption of normality and is generally accepted as sufficient for initial investigations.