Question

A sample size of \(x\) is considered to be sufficient to hold the Central Limit Theorem (CLT). The value of \(x\) should be:

• A. less than 20
• B. greater than or equal to 30
• C. less than 30
• D. sample size does not affect the CLT

Answer 1

The Correct Option is B

The Central Limit Theorem (CLT) is a fundamental principle in statistics stating that the distribution of the sample mean of a large number of independent, identically distributed variables will be approximately normally distributed, regardless of the original distribution's shape. The ability to apply the CLT is highly beneficial in statistical analysis for making inferences about population parameters. A general rule of thumb for the CLT to hold is having a sample size of 30 or more, often expressed as \(n \geq 30\). This helps ensure that the sample mean distribution approaches normality.

Hence, among the options provided, the correct answer is: greater than or equal to 30

Answer 2

The Central Limit Theorem (CLT) states that for a sufficiently large sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population’s distribution. Typically, a sample size of \(n \geq 30\) is considered sufficient for the CLT to hold true in practice.

Thus, the correct answer is \(n \geq 30\).