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14.30 Introduction to Statistical Methods in Economics
Spring 2009
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View Full DocumentProblem Set
#7
14.30

Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Tuesday, April 14, 2009
Question One
We just learned about the standard Normal distribution with PDF 4(z) and CDF @(z).
Let's familiarize ourselves with it, as we will be using it a lot in the future.
1. Find u
=
@(z) for z
=
(3, 2.5, 2, 1.5,
1,
0.5,0,0.5,1,1.5,2,2.5,3).
2. Find
u
=
1

Pr(lZ1
5
z) for z
=
{0,0.5,1,1.5,2,2.5,3) using your answers from part
(1).Explain (via math or words) how you obtained your answers. We call these values
of u "pvalues" which stands for "probability values" of a result at least that extreme
occuring. Memorize these seven valuesyou will certainly use them in the future.
3. Find z
=
@I (u) for
u
=
{0.001,0.005,0.01,0.02,0.05,0.10,0.20).
4. Use the results from part (3) to obtain z
=
W1(l

u) for each u.
5. Use the results and/or methods from part (3) and (4) to obtain z where
1

Pr(lZ1
<
z)
=
u for each u in part
(3).
These values of z are called the "twosided alevel critical
values" where
a
=
u in this example. For example, we say, "The (twosided) 10%
critical value of the standard normal distribution is z
=
.
. ."
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 Fall '10
 jones
 Normal Distribution, Variance, Probability theory, critical values

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