Other things being equal, it is better to have more confidence than less. We would also rather have a smaller margin of error. However, there is a trade off. If we increase the level of confidence, we must increase critical value, which in turn increases

Answer 1

the margin of error. This trade-off can be explained as follows:

When we want to increase our confidence level, say from 95% to 99%, we are essentially saying that we want to be more certain that the true parameter lies within our confidence interval. To achieve this higher level of confidence, we need to use a larger critical value (for instance, from 1.96 to 2.576 for a normal distribution). This larger critical value widens the confidence interval, thereby increasing the margin of error.

The relationship can be summarized as follows:

• Higher Confidence Level → Larger Critical Value → Wider Confidence Interval → Increased Margin of Error.

Therefore, while higher confidence is desirable, it leads to a trade-off with precision, as we end up with a less precise estimate (i.e., a wider margin of error). This is a crucial consideration in statistical analysis when deciding on the appropriate level of confidence for estimating parameters.