When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean, µ will be narrower than the 95% confidence interval for µ?

Using the equation for the margin of error, it is found that the 99% confidence interval will be wider than the 95% confidence interval for µ.

What is the margin of error of a confidence interval?

The margin of error of a confidence interval is given by an equation in the following format:

In which:

t is the critical value, which increases as the confidence level increases.s is the standard deviation of the sample.n is the sample size.

In this problem, a 99% confidence interval will have a higher value of t than a 95% confidence interval, hence a higher margin of error, and thus will be wider.

You can learn more about the margin of error of a confidence interval at link

A 99% confidence interval will be wider compared to a 95% confidence interval. This is because while you don't know what the true value of mu is, you are more confident that the parameter is in the interval.

In essence, you are casting a wider net which leads to the higher level of confidence. Imagine if there was a 100 mile stretch of straight land, and somewhere on this line was a special rock that you are looking for. You would be 100% confident if you said "the rock is somewhere on that piece of land", and less confident the more you shrunk the interval.