Question

ch 16 you plan to construct a confidence interval for the mean, μ, of a normal population with (known) standard deviation σ. which of the following will reduce the size of the margin of error? use a lower level of confidence. reduce sigma. increase the sample size.

Explanation:

The margin - of - error formula for a confidence interval of the mean of a normal population with known standard deviation is $E = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, where $z_{\alpha/2}$ depends on the confidence level, $\sigma$ is the standard deviation, and $n$ is the sample size. A lower confidence level corresponds to a smaller $z_{\alpha/2}$ value. Reducing $\sigma$ directly decreases the margin of error as it is in the numerator. Increasing the sample size $n$ decreases the margin of error because it is in the denominator.

Answer:

Use a lower level of confidence, Reduce sigma, Increase the sample size.