Statistical methods for Economics - Semester 1

u = 200 Sigma^2 (S^2) = 2500 n = 100

E(Xbar) = u. This is because: the expectation of the sample mean is the same as the population mean. Therefore E(Xbar) = 200

Std.Dev(Xbar) = RootVar(Xbar) = root(sigma^2,/n) =

Since we already have Sigma^2 = 2500 and n=100, Std.dev(Xbar) = root(2500/100) = root25 = 5

Standardizing

•So if: X~N(μ, σ2) Then:

•We can now use Normal Probability Tables to obtain probabilities. •If for example X~N(10, 36)

Then

Therefore:

Question: 

Find the number z₀ such that if Z~N(0,1)

 a)      P(Z ≥ z₀) = 0.05

 b)      P(Z< z₀)…