Is this valid? Determine whether each of the following...

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer. (a) According to a recent poll, $75 \%$ of American adults regularly recycle. To simulate choosing a random sample of 100 U.S. adults and seeing how many of them recycle, roll a 4 -sided die 100 times. A result of $1,2,$ or 3 means the person recycles; a 4 means that the person doesn't recycle. (b) An archer hits the center of the target with $60 \%$ of her shots. To simulate having her shoot 10 times, use a coin. Flip the coin once for each of the 10 shots. If it lands heads, then she hits the center of the target. If the coin lands tails, she doesn't.

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer. (a) According to a recent poll, $75 \%$ of American adults regularly recycle. To simulate choosing a random sample of 100 U.S. adults and seeing how many of them recycle, roll a 4 -sided die 100 times. A result of $1,2,$ or 3 means the person recycles; a 4 means that the person doesn't recycle.
(b) An archer hits the center of the target with $60 \%$ of her shots. To simulate having her shoot 10 times, use a coin. Flip the coin once for each of the 10 shots. If it lands heads, then she hits the center of the target. If the coin lands tails, she doesn't.

Key Concepts

Random Sampling

Random sampling is the process of selecting individuals or outcomes from a population in such a way that each member has an equal probability of being chosen. This concept is fundamental in simulation design because it ensures that the sample is representative of the entire population, thereby reducing bias and enhancing the applicability of the results to the real-world scenario being modeled.

Independent Trials

Independent trials refer to the characteristic where the outcome of one trial does not affect the outcome of another. This is essential in simulation experiments because it allows the use of probability distributions like the binomial distribution, where the assumption of independence underlies many of the theoretical results governing the behavior of the simulated process.

Probability Matching

Probability matching involves aligning the assigned probabilities in the simulation with the actual probabilities of the event occurring. In the context of simulation design, it is crucial that the random mechanism (such as a die or coin) accurately reflects the intended probability of success. Failure to do so may lead to simulations that do not correctly mirror the underlying statistical process being studied.

Appropriate Use of Random Tools

The selection of an appropriate random tool (e.g., coins, dice, or random number generators) is critical in designing valid simulations. The chosen tool must be capable of representing the desired probabilities accurately; for example, using a coin to simulate an event with a 60% chance of occurring is inappropriate if it inherently provides a 50% chance for each outcome.

Transcript

Please give Ace some feedback