Question

1. repeated reasoning what happens to the margin of error as a sample size increases? the margin of error. correct answer: decreases. use the margin of error formula to justify your answer.

Explanation:

Step1: Recall margin - of - error formula

For a proportion in a simple random sample, the margin of error $E = z\sqrt{\frac{p(1 - p)}{n}}$, where $z$ is the z - score corresponding to the desired level of confidence, $p$ is the sample proportion, and $n$ is the sample size.

Step2: Analyze the effect of $n$ on $E$

The sample size $n$ is in the denominator of the square - root fraction. As $n$ increases, the value of $\frac{p(1 - p)}{n}$ decreases. Since the square - root function is an increasing function, $\sqrt{\frac{p(1 - p)}{n}}$ also decreases. And since $E = z\sqrt{\frac{p(1 - p)}{n}}$ and $z$ is a constant for a fixed confidence level, the margin of error $E$ decreases.

Answer:

Decreases