Question

A beef rancher randomly sampled $42$cattle from her large herd to obtain a $95\%$confidence interval to estimate the mean weight of the cows in the herd. The interval obtained was $\left(1010,1321\right)$. If the rancher had used a $98\%$confidence interval instead, the interval would have been

(a) wider and would have less precision than the original estimate.

(b) wider and would have more precision than the original estimate.

(c) wider and would have the same precision as the original estimate.

(d) narrower and would have less precision than the original estimate.

(e) narrower and would have more precision than the original estimate.

Short answer

Wider and would have been less precision than original.

Step-by-step solution

Given information

We have been given$98\%$confidence interval instead of a $95\%$confidence interval.

Explanation

As the confidence level increases, we will be more sure about the true mean thus it needs to contain more possible values which implies that confidence level is much wider.

As the confidence interval is wider , our estimate is less accurate.