The sample that will result in a proportion of girls closest to ½ would likely be the one with the largest sample size, as larger samples tend to yield proportions closer to the true population proportion due to the Law of Large Numbers. This is because larger samples tend to average out individual variations and give a result that more closely represents the true distribution in the population.

In this case, the answer is:

D. A collection of 100 kids in the 9th grade.

A larger sample size (100) will reduce the effects of randomness and increase the likelihood that the observed proportion of girls will be closer to ½, assuming the true proportion in the population is around that value.

Would you like more details or have any questions?

Here are 5 related questions:

1. How does the Law of Large Numbers help in determining sample accuracy?
2. Why might a smaller sample size result in more variability in proportions?
3. What factors besides sample size can affect the proportion in a sample?
4. How would the results change if the true proportion of girls in the population was not close to ½?
5. How can we calculate the margin of error in proportion estimates for different sample sizes?

Tip: When estimating population proportions, larger sample sizes reduce random variation, making your estimates more reliable.