Which general guideline is used for determining sample size when estimating a population mean?

To determine an appropriate sample size when estimating a population mean, one important guideline is that the sample size should exceed a certain minimum to ensure adequate representation of the population and reliable results. A commonly cited rule is that having a sample size larger than 15 tends to provide a more accurate estimate of the mean, especially when the distribution of the population is unknown or not normal. This guideline helps in achieving a reasonable degree of confidence in the results derived from the sample.

In terms of statistical inference, having a sample that exceeds this threshold allows for better application of the Central Limit Theorem, which states that as sample sizes increase, the sampling distribution of the sample mean approaches a normal distribution, even if the population distribution itself is not normal. This is essential for making valid conclusions about the population mean from sample data.

While other suggested numbers for sample sizes may exist or be used in different contexts, they do not provide a foundational guideline grounded in statistical principles as effectively as the threshold of exceeding 15 does. Therefore, the focus on having a sample size greater than 15 is a widely accepted practice in statistical analysis for estimating population means.