Significance Test and Confidence Intervals In General:
The article contains a 95% confidence interval. Would the margin of error
in a 99% confidence interval computed from the same data be less, the same,
or greater?
http://en.wikipedia.org/wiki/Confidence_interval
To understand the relationship between a confidence interval and the margin of error, let's first define what they are.
A confidence interval is a range of values that we are fairly confident contains the true value of a population parameter, such as a mean or proportion. It is calculated based on sample data and provides a range rather than a specific point estimate.
The margin of error, on the other hand, is the amount of error or uncertainty we allow for in our estimation. It is typically represented as a plus/minus value around the point estimate.
In general, when we increase the level of confidence (e.g., going from a 95% confidence interval to a 99% confidence interval), the margin of error will increase. This means that the range of values in the confidence interval will be wider.
The reason for this is that when we aim for a higher level of confidence, we need to be more conservative or have greater certainty about our estimate. To achieve this greater certainty, we need to allow for more error or variability in our estimation.
Therefore, if you computed a 99% confidence interval from the same data, the margin of error would be greater compared to a 95% confidence interval computed from the same data. This means that the 99% confidence interval would be wider, providing a larger range of values that might capture the true population parameter.