Let's begin by recalling that the margin of error tells us about a limit on how much the responses of the sample would be different from the responses of the whole population. Having this in mind, let's take a look at the given graph that presents the sample proportions from 3 simulations.
Looking at the graph, we can see that sample a has the least standard deviation σ because its distribution is the most narrow. On the other hand, the distribution of sample c has the most wide distribution, so this sample has the largest standard deviation.
σ_a<σ_b<σ_c
When sample data values differ from each other a lot, we can suspect that the responses of the sample can also differ a lot from the responses of the population. Therefore, samples with the greatest standard deviations will have the greatest margins of error ME.
σ_a<σ_b<σ_c ⇓
ME_a
