To determine which condition must be met in order to make a statistical inference about a population based on a sample, especially when the sample does not come from a normally distributed population, consider the principle known as the Central Limit Theorem (CLT).
The Central Limit Theorem states that when the sample size is sufficiently large, the sampling distribution of the sample mean will be approximately normally distributed regardless of the population's distribution, allowing for valid statistical inferences.
According to the Central Limit Theorem, the sample size [tex]\( n \)[/tex] should be 30 or greater to achieve this approximation under most circumstances. By having a sample size [tex]\( n \geq 30 \)[/tex], the sampling distribution of the sample mean will approximate a normal distribution, making it possible to apply inferential statistical methods.
Thus, the correct condition that must be met is:
[tex]\[ n \geq 30 \][/tex]
This ensures that even if the population distribution is not normal, the distribution of the sample mean can be treated as approximately normal, allowing accurate statistical inference about the population.
