Confidence Interval homework help

#1
This is the only part of our homework I am not understanding...

A.)If the 95% confidence interval for the population mean is (6,20), what is the sample mean?

B.)Given the 95% CI in part a, would (5,21) be a possible 99% CI for the same sample of data? If not, why not?

C.)Given the 95% CI in part a, would(8,19) be a possible 99% CI for the same sample of data? If not, why not?

D.)Given the 95% CI in part a, would (4,28) be a possible 99% CI for the same sample of data? If not, why not?
 
#2
When you create a CI to estimate a parameter, you take the corresponding statistic as your point estimate, and then you add/subtract some value from that statistic to generate the interval. The value that you add is the same value that you subtract. So the statistic is always the midpoint of the interval. (That should pretty directly give you the answer to A,D, and hopefully will help you piece together the answers to B,C as well)
 
#3
Wouldn't A's answer be 6+20 / 2?

I think what really confuses me is the percentages for B, C, and D. What does the 95% change?
 

CB

Super Moderator
#4
So the statistic is always the midpoint of the interval.
I'm nitpicking here, but this isn't always true. If the sampling distribution that we've assumed for the statistic isn't symmetric, then the point estimate won't necessarily be in the middle of the interval. An example would be a confidence interval for an odds ratio calculated as part of a logistic regression: The point estimate won't usually be in the middle of the interval. In the case of a confidence interval calculated for a sample mean using conventional methods your claim does hold true though.
 
#5
Wouldn't A's answer be 6+20 / 2?

I think what really confuses me is the percentages for B, C, and D. What does the 95% change?
Changing the confidence level changes the value that you are adding/subtracting to your point estimate, therefore it changes the width of your interval.

Switching to a higher level of confidence (e.g. moving from 95 conf --> 99 conf) yields a less precise (i.e. wider) interval.