What is the minimum sample size considered adequate for making interval estimates of a population mean using standard formulas?

The choice of a minimum sample size of 30 is significant in the context of making interval estimates of a population mean because of the Central Limit Theorem (CLT). The Central Limit Theorem states that, regardless of the population's distribution, the sampling distribution of the sample mean will tend to be normally distributed as the sample size increases, provided the sample size is sufficiently large. While there is no strict rule for what constitutes "sufficiently large," a sample size of 30 is commonly accepted as a threshold that allows statisticians to use normal distribution-based methods when estimating population parameters.

When sample sizes are less than 30, the sample mean may not approximate a normal distribution closely enough for valid interval estimates, especially if the underlying population distribution is skewed or not normal. Thus, having at least 30 observations helps ensure that the sample mean will be approximately normally distributed, which is essential when constructing confidence intervals and conducting hypothesis tests.

Choosing a sample size smaller than 30 could lead to inaccuracies in the estimates derived from the sample data, particularly in the confidence intervals. This is why the convention of n ≥ 30 is widely adopted in statistical practices for making reliable inferences about population parameters.