Question

what does the central limit theorem state about the sampling distribution of sample means? (1 point)
○ the sampling distribution of sample means is skewed.
○ the sampling distribution of sample means is approximately normally distributed.
○ the sampling distribution of sample means is uniform.
○ the sampling distribution of sample means is the same as the population distribution.

Explanation:

The Central Limit Theorem (CLT) states that for a sufficiently large sample size (usually \( n \geq 30 \), or for any sample size if the population is normal), the sampling distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution.

• The first option is incorrect because the CLT implies the sampling distribution of sample means is not skewed (it's approximately normal).
• The third option is incorrect because the sampling distribution of sample means is not uniform (it's approximately normal).
• The fourth option is incorrect because the sampling distribution of sample means is not the same as the population distribution (it's approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size).

The correct statement is that the sampling distribution of sample means is approximately normally distributed.

Answer:

B. The sampling distribution of sample means is approximately normally distributed.