Economic Statistics
A continuous random variable can assume the infinitely many values
corresponding to points on the line interval
The researcher faces the question: how should I model a variable X in the
sample?
Examples of variables for which discrete
Suppose = 0.05, n = 16, x N(5.05,0.12), so that the true value of = =
5.05
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Ho : = 5
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Calculate the power of the following test:
Ha : > 5
Properties of the (1 ):
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Smaller (i.e., higher confidence) implies a lower (1 )
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Larger n implies larger (1
Hypothesis Testing: Formal mechanism for drawing conclusions
Statistical process is analogous to the legal system
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1. Assume the defendant is innocent
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2. The prosecution then compiles evidence against that assumption
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3. Original assumption is proved
Given a 100(1 )% confidence interval
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Sampling Error: % of the time, the true value of the population parameter
will not fall in the 100(1 )% confidence interval
Suppose , the population mean is unknown, but we have a large sample n > 30:
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Derive a 100
Consider a binomial random variable X = # successes
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Let the population proportion of successes be p
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If we take a random sample of size n then we can calculate the sample
statistic: = x/n
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The central limit theorem implies that: N(p, (p(1p)/n) if np(
Let X be a random variable of interest. Can be discrete or continuous
Central Limit Theorem: If random samples of size n observations are drawn from
a population with finite mean and standard deviation , then, when n is
sufficiently large, the sampling d
The scores on a national achievement test were approximately normally
distributed, with a mean of 540 and standard deviation of 110.
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If you achieved a score of 680, how far, in standard deviations, did your
score depart from the mean?
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What percentage
Economic Statistics
Parameters: Numerical descriptive measures associated with a population of
measurements
Statistics: Numerical descriptive measures associated with sample
measurements
Arithmetic mean of a set of n measurements is equal to the sum of th
Economic Statistics
Probability is the science of chance.
Two ways to think about probability:
1. Population to Sample: Given a fair coin, probability gives us the chance that
the next flip is heads: 50%.
2. Sample to Population: Test that a coin is fair
Economic Statistics
We need combinatorics to derive the number of simple events in the sample
space and in events.
mn Rule: For any experiment conducted in two stages, with m possible outcomes
in the first stage and n possible outcomes in the second stage
clear all
cap log close
cd "/Users/econlab/Desktop/STATA/"
log using HW9.log, replace
*1(a)*
set obs 8
input y
0.1
0.3
0.5
0.8
1.2
1.8
2.5
3.4
input x
1
2
3
4
5
6
7
8
twoway (scatter y x)
*1(b)*
gen x2=x^2
reg y x x2
*99.85% of the total variation is expl