Now we will stop 𝑁 persons and take the mean of their age
We will assume that the average age follows a Normal distribution
(Is this a reasonable hypothesis?)
Find an interval that will contain the outcome with 80% of probability
This time we assume we do not know the population average \(μ\) and we want to estimate it from a sample
This time we know the sample average \(\bar{X}\) and the population standard deviation \(σ\)
Build an interval for the population average
What is the probability of observing \((\bar{X}≥y)\)
if the real average μ is 0?
More precisely \[ℙ(\bar{X}≥y | μ = 0, σ )\]
Here \(y\) is the observed sample average
Are men older or younger or same age as women?
This time we have a sample of men and a sample of women
We assume that both populations are Normal, same variance
Then \((\bar{X}_f - \bar{X}_m)\) follows a normal with \(μ=μ_f - μ_m\)
We want to know if that number is 0. What is \[ℙ(\bar{X}_f ≠ \bar{X}_m | μ = 0, σ )?\]