Question

Select the correct answer for the blank: If everything else stays the same, the required sample size ____ as the confidence level decreases to reach the same margin of error. Answer:

Answer 1

Answer:

The required sample size increases.

Step-by-step explanation:

The margin of error of a confidence interval is given by:

$M = z*\frac{\sigma}{\sqrt{n}}$

In which z is related to the confidence level(the higher the confidence level the higher z), $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

The confidence level decreases, so z decreases.

For the margin of error to stay the same, the sample size also has to decrease.

The required sample size increases.