Question

Using the same mean, standard deviation, and level of confidence, suppose that n were 69 instead of 25. Would the error bound become larger or smaller? How do you know?

Short answer

The error bound will become smaller.

Step-by-step solution

Given Information

Suppose the confidence level was reduced to $90\%$from $95\%$.

Also, the mean, standard deviation, and sample size are the same.

Explanation

As the formuia for error bound is given below

$EBM=z_{\frac{a}{2}}\frac{\sigma }{\sqrt{n}}$

So decrease in confidence level will decrease the error bound because, as the confidence level decreases the area under the curve to capture the true population mean is less.

Hence the error bound will become smaller.

Step # Final Answer

The error bound will become smaller.