# Stat101 95% Confidence Interval

#### aenyiema

##### New Member
One compared the fertility rate of frogs in two ponds. Suppose p1 denotes fertility rate in Pond1 and p2 denotes fertiliity rate in Pond2. which of the follow 95% confidence intervals would best support the hypothesis that the fertility rate is higher in p1? Please explain your choice.
-0.15<p1-p2<-0.03
-0.07<p1-p2<0.03
-0.03<p1-p2<0.07
0.05<p1-p2<0.12

#### BrenH

##### New Member
Heart of confidence

This goes to the heart of what a confidence interval is.

You could think of a confidence interval as the error bounds on the estimated mean. That is, we are 95% confident that the real value is somewhere between the bounds. For example, below is the confidence interval around the estimate of the mean, x (black arrow ^). The red arrow (^) below is the true population mean, which 95% of the time will fall within the interval.

|------------x------------|
.................^.....^.........

When looking at a difference of means, if the confidence interval of the difference goes through zero, then (to 95% confidence given the current sample) you cannot tell whether one is different to the other. If, however, the entire interval is on one or other side of zero, then there is a detectable difference. This should give you enough to work out the rest.

#### aenyiema

##### New Member
I think it seems like the 3rd answer from what you just said, but I'm still not sure. If you can, please tell me and explain your answer.

#### BrenH

##### New Member
Well, not quite. The question is - what supports the hypothesis that p1 is higher than p2? The third answer states that the difference between p1 and p2 is between -0.3 and 0.7. So this interval includes 0, therefore covers the possibility that there is no difference between the two. That is not what you are wanting to prove. So which is the correct answer?

#### aenyiema

##### New Member
Ok, I'm leaning towards the Answer1 option then. Another one that seems probable is Answer4 based on your explanation. Both options don't include 0. Or am I totally off-track here?

#### BrenH

##### New Member
That is fine now. But you need to ask yourself, what are they asking? I.e. which is bigger than which? If so, should p1-p2 be positive or negative?

#### aenyiema

##### New Member
Ok, it seems like it would be positive. So does that mean Answer4?