Question

c. do you think the mean of the sample means is a better estimate of the population mean than the mean the teacher originally calculated? explain.

Explanation:

The mean of sample means (from sampling distribution) is a better estimate of the population mean due to the Central Limit Theorem. As sample size increases or more samples are taken, the distribution of sample means centers around the population mean, reducing sampling error. The original mean might be from one sample, while the mean of sample means incorporates multiple samples, leading to a more accurate, less variable estimate.

Answer:

Yes, the mean of the sample means is a better estimate. By the Central Limit Theorem, the mean of sample means (from multiple samples) converges to the population mean. It reduces sampling error, as using multiple samples’ means provides a more stable, accurate estimate than a single sample’s mean (the teacher’s original calculation).