Answer :
Answer:
There actually isn't a largest possible sample size in this scenario. Here's why:
The formula for margin of error (MoE) in estimating a population proportion considers the sample size (n) alongside the population proportion (p) and the confidence level. It looks like this:
MoE = z * sqrt(p * (1 - p) / n)
where:
z is the z-score for the desired confidence level (1.96 for 95% confidence)
p is the estimated population proportion (which we don't necessarily know beforehand)
n is the sample size (what we're solving for)
As you can see, the equation for MoE has p in the denominator of the square root. Since p has a value between 0 and 1, the smaller the sample size (n), the larger the term p * (1 - p) / n becomes. This, in turn, would lead to a larger MoE.
However, there's a catch. While we can theoretically keep reducing the sample size (n) and get a larger MoE, it becomes increasingly impractical to collect data from very small samples, especially when dealing with real-world populations.
So, in conclusion, there's no technical upper limit on the sample size based on the formula alone. But in practice, you'll need a reasonably sized sample that allows for feasible data collection while achieving the desired level of accuracy (reflected by the margin of error).
Step-by-step explanation:
