Question

the results of two random samples of votes for a proposition are given in the table. the samples were selected from the same population, and the margins of error were calculated using the same method which of the following is the most appropriate reason that the margin of error for sample a is greater than the margin of error for sample b? a. sample a had a larger sample size b. sample a had a smaller sample size c. sample a had a smaller number of votes that could not be recorded d. sample a had a lower percent of favorable responses

Explanation:

Step1: Recall margin - of - error formula

The margin of error $E = z\sqrt{\frac{p(1 - p)}{n}}$ (where $z$ is the z - score related to the confidence level, $p$ is the sample proportion, and $n$ is the sample size). For a fixed confidence level (so $z$ is constant) and assuming similar values of $p$, the margin of error is inversely proportional to the square root of the sample size $n$, i.e., $E\propto\frac{1}{\sqrt{n}}$.

Step2: Analyze the relationship between sample size and margin of error

A larger margin of error implies a smaller sample size. Since the margin of error for sample A is larger than that for sample B, sample A must have had a smaller sample size.

Answer:

b. sample A had a smaller sample size