Question

which of the following conditions must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population?

$\mu \geq 30$

$\bar{x} \geq 30$

$n \geq 30$

$n \geq 30$

Explanation:

To make a statistical inference about a population from a non - normally distributed sample, we rely on the Central Limit Theorem. The Central Limit Theorem states that when the sample size \( n \) is large enough (usually \( n\geq30 \)), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

• \( \mu \) is the population mean, and the size of the population mean has no direct relation to the normality of the sampling distribution for inference from a non - normal population.
• \( \bar{x} \) is the sample mean, and the value of the sample mean does not determine the normality of the sampling distribution for the purpose of inference from a non - normal population.
• \( N \) is the population size, and the population size is not the key factor for the normality of the sampling distribution when making inferences from a sample of a non - normal population. The key factor is the sample size \( n \).

Answer:

C. \( n\geq30 \)