Simulation: A trial consists of a single infant choosing a toy. How many trials must we simulate?

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BlackTom AI · Accepted Answer

Question restatement: A simulation task asks, “Simulation: A trial consists of a single infant choosing a toy. How many trials must we simulate?” There are no answer options provided for this numerical question, so we cannot critique specific choices.

Because no target probability or precision is stated, the required number of trials depends on what you want to estimate and how precise you want that estimate to be. In general, for estimating a probability p with a Monte Carlo simulation, the standard error (SE) of the estimate is sqrt(p(1-p)/n), where n is the number of trials.

Key idea: without knowing p, you can’t compute the exact n needed for a desired SE. However, you can explore typical scenarios:
- If you expect p around 0.5 (the most variable case), and you aim for a standard error of about 0.125, then n = p(1-p)/SE^2 ≈ 0.25 / 0.015625 = 16. This yields SE ≈ 0.125 and a rough margin of error on the order of ±0.25 at a 95% confidence interval, depending on the z-score used.
- If you want tighter precision, say SE ≈ 0.05, you’d need n ≈ 0.25 / 0.0025 = 100 trials. If SE ≈ 0.01, you’d need n ≈ 2500 trials.

Thus, the value 16 could reflect a deliberately coarse estimate with p near 0.5 and a target SE of about 0.125, representing a small, quick run to get a rough sense of the probability.

If your goal is simply to determine the frequency with which an infant chooses a particular toy, and you’re constrained to a rough approximation, 16 trials might be a reasonable starting point. If, instead, you require a precise estimate of p, you should plan for a larger n based on the desired SE.

Important caveat: because the problem statement does not specify the target probability p or the desired precision, any specific numeric answer (such as 16) is inherently ambiguous. Different goals yield different required numbers of trials.

In summary, without a stated p or precision, there is no unique correct n. The figure 16 could correspond to a rough estimate with p ≈ 0.5 and SE ≈ 0.125, but for more accurate estimation or different assumed p, a different n would be appropriate.

Su25-STATS-141-01/BIO-141-01 Homework 2: Normal Distributions & Hypothesis Tests

Simulation: A trial consists of a single infant choosing a toy. How many trials must we simulate?

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