In general, the largest sample size gives us the best estimate of the true mean.

Here's why: A larger sample size tends to give a more accurate estimate of the population mean because it reduces the impact of random variation or sampling error. With larger sample sizes, the estimate becomes less influenced by outliers or random fluctuations, leading to a more precise representation of the true mean.

So, for your scenario, the sample size of 80 would likely give the most reliable estimate of the true mean compared to the smaller sample sizes.

Next steps for your understanding:

1. Why does a larger sample size reduce sampling error?
2. How does variability in smaller samples influence the accuracy of the mean?
3. Can sample size alone guarantee an accurate estimate? What else should be considered?
4. What are the statistical methods used to quantify the uncertainty in estimates?
5. How would you interpret the variability of sample means in a large sample versus a small one?

Tip: Even though larger sample sizes generally give better estimates, it's also important to ensure your sample is representative of the entire population to avoid biased results.