Confidence Intervals Help

[Aaddiittyyaa]

Hey everyone!

Hope everyone's holidays are going well. I was wondering whether anyone could help me understand confidence intervals in regards to probability? I was going through it in the 'A+ Mathematical Methods Notes' book, but was confused by their explanation. I know this is a large area, but can anyone please indicate to me the gist it? I think I'll be able to understand it from there.

Thanks a lot! 

A

[VanillaRice]

Hey there! I'll try and give you a semi-realistic application of CIs

Say you are working as a data analyst in a village somewhere in remote Africa with a population of a few hundred, and you wish to find the average (mean) age of everyone in the village, but it isn't feasible to go around and asking the age of every single person living there. The only thing you know is that the ages in the population is normally distributed. So, what you can do instead is select a random person, and ask for their age (this is called a point estimate, and is your p hat value). You can calculate say, a 95% confidence interval around this person's age. Say we get (20, 60) as our 95% confidence interval. The non-technical interpretation is that we are 95% confident that the true population value (i.e. the true mean age of the population) lies somewhere within this interval.

In summary, a confidence interval is essentially an interval in which we are *relatively* confident that the true population value lies. We calculate it by taking a sample from the population, which we use as the 'centre' of our interval.

Hope this helps

[Aaddiittyyaa]

Thanks a lot! That makes A LOT more sense than my book!

[Sine]

Here is a basic outine of the technical interpretation that VanillaRice alluded to if anyone is interested:
Continuing on from VanillaRice's example

Our 95% confidence interval (C.I) is (20,60) that actually means that 95% of C.I produced will contain the the population value (true mean age). So this means say we took 20 different samples and hence produced 20 different C.I with different values on average 19 of them will contain the population value  (true mean age) and on average 1 C.I will not contain the population value (true mean age).

Good to know both interpretations and apply whichever is necessary, the "less technical" one is definitely more likely to be required by VCAA.