If a 90%, 95% and 99% confidence interval are found for a population mean, how are the three interval estimates related to each other?
The higher the confidence, the wider the interval
Thanks!
The three confidence intervals, 90%, 95%, and 99%, are related to each other in terms of their level of confidence. A confidence interval is a range of values within which we estimate that the true population parameter lies.
To find a confidence interval, you need to know three key components: the sample mean, the sample standard deviation (or standard error), and the level of confidence.
The level of confidence represents the probability that the true population parameter falls within the interval. A 90% confidence interval means that there is a 90% probability that the true population parameter lies within the interval. Similarly, a 95% confidence interval means there is a 95% probability, and a 99% confidence interval means there is a 99% probability.
Now, let's compare the three intervals:
1. 90% Confidence Interval: This interval is narrower than the other two because it has a lower level of confidence. It means that we are 90% confident that the true population parameter lies within the interval.
2. 95% Confidence Interval: This interval is wider than the 90% confidence interval because it has a higher level of confidence. It means that we are 95% confident that the true population parameter lies within the interval.
3. 99% Confidence Interval: This interval is the widest among the three because it has the highest level of confidence. It means that we are 99% confident that the true population parameter lies within the interval.
In summary, as the level of confidence increases, the width of the confidence interval also increases. This is because a higher level of confidence requires a wider range of values to account for a larger degree of uncertainty.