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

The required sample size increases.

Explanation:

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

`M = z*(\sigma)/(√(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.