Statistical methods for Economics - Semester 1

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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) =

(http://sph.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/SampleStandardDev_Formula.png)

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

Standardizing

So if: X~N(μ, σ2Then:

 (http://davidmlane.com/hyperstat/pictures/image2.gif)

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

Then

(http://i1293.photobucket.com/albums/b593/harry_owen1/Picture1.png)

Therefore:

(http://i1293.photobucket.com/albums/b593/harry_owen1/Picture2.png)

Question: 

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

 a)      P(Z ≥ z0) = 0.05

 b)      P(Z< z0)

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