The width of the Confidence Interval is inversely related to the Maximum Error of Estimate. T or F? Why or why not?
The answer is false, the width is always 2* maximum error of estimate.
False.
The width of the confidence interval is actually directly related to the maximum error of estimate, not inversely related.
To understand why, let's briefly explain what a confidence interval and maximum error of estimate are.
A confidence interval is a range of values that surrounds a point estimate, such as a mean or proportion, and provides a range within which we can be confident that the true population parameter lies. It is typically expressed as an interval with an upper and lower bound.
The maximum error of estimate, also known as the margin of error, represents the maximum amount of deviation expected between the point estimate and the true population parameter. It provides an indication of the precision of the estimate and is often based on the level of confidence desired.
Now, when we consider the relationship between the width of the confidence interval and the maximum error of estimate, we can see that they are directly related.
If we want to increase the level of confidence, we typically need to widen the confidence interval to capture a larger range of possible values. This increase in width allows for a larger maximum error of estimate, as we are now including a broader range of potential values.
Conversely, if we want to narrow the confidence interval, meaning we want to increase the precision of our estimate, we would need to decrease the maximum error of estimate. This involves reducing the range of possible values the confidence interval covers, which in turn decreases its width.
Therefore, the width of the confidence interval and the maximum error of estimate are directly related, not inversely related, as a wider interval accommodates a larger maximum error, while a narrower interval has a smaller maximum error.