Question

As a manager of a company, you are given 2 estimates for the annual firm’s profits:

1) Estimate A predicting that the mean profit would be between $1 million and $1,5 millions, which is a 95% confidence interval

2) estimate B that the annual profit is between $1.2 million and $1.4 million, a 93% confidence interval.

Which of the two estimates above is more accurate and why?

Answer 1

Higher the confidence level of the confidence interval, higher is the degree of accuracy in the estimate of the mean profit. But a higher confidence level results in a larger (wider interval) of estimate.

Using the estimate A, we are 95% confident that the mean profit of the company would be between $1 million and $1.5 million.

However while using the estimate B, we have only 93% confidence (lower confidence) that the mean profit would be between $12. million and $1.4 million.

Hence although estimate B has a tighter interval (and hence more precise), we have a higher confidence in estimate A and hence estimate A is more accurate.