Question

Why would the error bound change if the confidence level were lowered to$95\%$?

Short answer

The error bound will become smaller if the confidence level were lowered to$95\%$,

Step-by-step solution

Given information

Given in the question that, One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of $151$hours each month with a standard deviation of $32$hours. Assume that the underlying population distribution is normal.

Explanation

Assume the confidence level is lowered to $95\%$.

The formula for error bound is given below,

$EBM=t_{n-1}\left(\frac{\alpha }{2}\right)\frac{s}{\sqrt{n}}$

So decline in confidence level will reduce the error bound because, as the confidence level declines the area under the curve to capture the true population means is less.