A. The 95% confidence interval is:
(a) Larger than the 99% confidence interval
(b) Smaller than the 99% confidence interval
(c) The same as the 99% confidence interval
You did not post any data to create a confidence interval from.
The correct answer is (b) Smaller than the 99% confidence interval.
To understand why the 95% confidence interval is smaller than the 99% confidence interval, we need to understand what these two confidence levels mean.
A confidence interval is a range of possible values within which the true value of a population parameter is estimated to lie, based on a sample from that population. It indicates the uncertainty surrounding the estimated parameter.
The confidence level is the level of certainty or confidence we have in the estimated interval. It represents the probability (expressed as a percentage) that the true parameter value falls within the estimated interval, based on repeated sampling.
So, a 95% confidence interval means that if we were to take multiple samples from the population and calculate a confidence interval for each sample, then about 95% of those intervals would contain the true population parameter. Similarly, a 99% confidence interval means that about 99% of the intervals would contain the true population parameter.
Since the 99% confidence level provides a higher level of certainty, it needs to account for a larger range of possible values. Therefore, the 99% confidence interval will be wider or larger than the 95% confidence interval. In other words, we can be more confident that the true parameter falls within the 99% confidence interval, but in order to achieve that higher level of confidence, the interval needs to be larger.
In summary, the 95% confidence interval is smaller than the 99% confidence interval because it provides a lower level of certainty or confidence in estimating the true population parameter.