Question

question 10 (1 point) increasing the confidence level while keeping the same sample size has what effect on the margin of error? decreases the margin of error and hence decreases the precision decreases the margin of error and hence increases the precision increases the margin of error and hence decreases the precision increases the margin of error and hence increases the precision

Explanation:

Step1: Recall margin - of - error formula

The margin of error $E = z\times\frac{\sigma}{\sqrt{n}}$ for a confidence interval of the population mean (when $\sigma$ is known). Here, $z$ is the z - score related to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. When $n$ is fixed, as the confidence level increases, the value of $z$ increases.

Step2: Analyze the effect on margin of error

Since $E = z\times\frac{\sigma}{\sqrt{n}}$ and $n$ and $\sigma$ are constant, an increase in $z$ (due to increasing the confidence level) will cause an increase in $E$. Also, a larger margin of error means less precision.

Answer:

Increases the margin of error and hence decreases the precision