Question

You have just completed a study and found a 95% confidence interval with a width of 8 points. A colleague suggests that they would like to see a 99% confidence interval. The width of the 99% CI would be:

1) 0

2) less than 8 points

3) 8 points

4) more than 8 points

Answer 1

A 99% confidence interval would be wider than a 95% confidence interval. Since a 95% interval has a width of 8 points, a 99% interval will have a wider width, more than 8 points, to account for the increased certainty. The correct option is 4.

Step-by-step explanation:

When comparing confidence intervals at different confidence levels, the interval with the higher confidence level will be wider. This is because a higher confidence level means that there is a greater degree of certainty that the interval will contain the true population parameter, thereby requiring a broader range of values to increase the likelihood of inclusion.

In essence, if we increase the confidence level from 95% to 99%, we seek to exclude only 1% of the distribution, as opposed to 5%, effectively making the interval wider to ensure that more of the distribution is captured within it.

Given a 95% confidence interval with a width of 8 points, moving to a 99% confidence interval would mean that the new interval must be greater than 8 points. To be more certain that the confidence interval contains the true value of the population parameter, the range of the interval must expand.

Therefore, the correct response to the question is that the width of a 99% confidence interval would be more than 8 points (option 4).