Midterm Review

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Midterm Review
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Econ 240A

• Descriptive Statistics
• Probability
• Inference
• Differences between populations
• Regression

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I. Descriptive Statistics

• Telling stories with Tables and Graphs
• That are self-explanatory and esthetically
  appealing
• Exploratory Data Analysis for random variables
  that are not normally distributed
• Stem and Leaf diagrams
• Box and Whisker Plots

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Stem and Leaf Diagtam

• Example Problem 2.24
• Prices in thousands of of houses sold in a Los
  Angeles suburb in a given year

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Subsample
Problem 2.24 Prices in thousands Houses sold
in a Los Angeles suburb
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Sorted Data
Problem 2.24 Prices in thousands Houses sold
in a Los Angeles suburb
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Summary Statistics Problem 2.24 Prices in
thousands Houses sold in a Los Angeles suburb
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Problem 2.24 Prices in thousands Houses sold
in a Los Angeles suburb
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Box and Whiskers Plots

• Example Problem 4.30
• Starting salaries by degree

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Subsample
Problem 4.50 Starting salaries By degree
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II. Probability

• Concepts
• Elementary outcomes
• Bernoulli trials
• Random experiments
• events

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Probability (Cont.)

• Rules or axioms
• Addition rule
• P(AUB) P(A) P(B) P(AB)
• Conditional probability
• P(A/B) P(AB)/P(B)
• Independence

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Probability ( Cont.)

• Conditional probability
• P(A/B) P(AB)/P(B)
• Independence
• P(A)P(B) P(AB)
• So P(A/B) P(A)

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Probability (Cont.)

• Discrete Binomial Distribution
• P(k) Cn(k) pk (1-p)n-k
• n repeated independent Bernoulli trials
• k successes and n-k failures

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Binomial Random Number Generator

• Take 50 states
• Suppose each state was a battleground state, with
  probability 0.5 of winning that state
• What would the distribution of states look like?
• How few could you win?
• How many could you win?

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28
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30
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Subsample
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Probability (Cont.)

• Continuous normal distribution as an
  approximation to the binomial
• npgt5, n(1-p)gt5
• f(z) (1/2p)½ exp-½z2
• z(x-m)/s
• f(x) (1/ s) (1/2p)½ exp-½(x-m)/s2

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III. Inference

• Rates and Proportions
• Population Means and Sample Means
• Population Variances and Sample Variances
• Decision Theory

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Decision Theory

• In inference, I.e. hypothesis testing, and
  confidence interval estimation, we can make
  mistakes because we are making guesses about
  unknown parameters
• The objective is to minimize the expected cost of
  making errors
• E(C) aC(I) bC(II)

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Sample Proportions from Polls

• Where n is sample size and k is number of
  successes

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Sample Proportions
So estimated p-hat is approximately normal for
large sample sizes
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Sample Proportions

• Where the sample size is large

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Problem 9.38

• A commercial for a household appliances
  manufacturer claims that less than 5 of all of
  its products require a service call in the first
  year. A consumer protection association wants to
  check the claim by surveying 400 households that
  recently purchased one of the companys appliances

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Problem 9.38 (Cont.)

• What is the probability that more than 10
  require a service call in the first year?
• What would you say about the commercials honesty
  if in a random sample of 400 households, 10
  report at least one service call?

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Problem 9.38 Answer

• Null Hypothesis H0 p0.05
• Alternative Hypothesis pgt0.05
• Statistic

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Z critical
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Z .
4.59
1.645
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Sample means and population means where the
population variance is known
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Problem 9.26, Sample Means

• The dean of a business school claims that the
  average MBA graduate is offered a starting salary
  of 55,000. The standard deviation of the offers
  is 4600. What is the probability that in a
  sample of 38 MBA graduates , the mean starting
  salary is less than 53,000?

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Problem 9.26 (Cont.)

• Null Hypothesis H0 m 55,000
• Alternative Hypothesis HA m lt 55,000
• Statistic

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Zcrit(1) -2.33
0.0037
-2.68
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Sample means and population means when the
population variance is unknown
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Problems 12.33

• A federal agency responsible for enforcing laws
  governing weights and measures routinely inspects
  packages to determine whether the weight of the
  contents is at least as great as that advertised
  on the package. A random sample of 18 containers
  whose packaging states that the contents weighs 8
  ounces was drawn.

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Problems 12.33 (Cont.)

• Can we conclude that on average the containers
  are mislabeled? Use a 0.1.

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t crit 5
1.74
-1.74
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Problems 12.33 (Cont.)
7.8 7.97 7.92
7.91 7.95 7.87
7.93 7.79 7.92
7.99 8.06 7.98
7.94 7.82 8.05
7.75 7.89 7.91
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Mean 7.913888889
Standard Error 0.019969567
Median 7.92
Mode 7.91
Standard Deviation 0.084723695
Sample Variance 0.007178105
Kurtosis -0.24366084
Skewness -0.22739254
Range 0.31
Minimum 7.75
Maximum 8.06
Sum 142.45
Count 18
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Problems 12.33 (Cont.)

• Can we conclude that on average the containers
  are mislabeled? Use a 0.1.

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Confidence Intervals for Variances
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Problems 12.33 12.55

• A federal agency responsible for enforcing laws
  governing weights and measures routinely inspects
  packages to determine whether the weight of the
  contents is at least as great as that advertised
  on the package. A random sample of 18 containers
  whose packaging states that the contents weighs 8
  ounces was drawn.

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Problems 12.33 12.55 (Cont.)

• Estimate with 95 confidence the variance in
  contents weight.
• c2 variable with n-1 degrees of freedom is
  (n-1)s2 /s2

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30.191
7.564
2.5
2.5
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Problems 12.33 12.55(Cont.)
7.8 7.97 7.92
7.91 7.95 7.87
7.93 7.79 7.92
7.99 8.06 7.98
7.94 7.82 8.05
7.75 7.89 7.91
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Mean 7.913888889
Standard Error 0.019969567
Median 7.92
Mode 7.91
Standard Deviation 0.084723695
Sample Variance 0.007178105
Kurtosis -0.24366084
Skewness -0.22739254
Range 0.31
Minimum 7.75
Maximum 8.06
Sum 142.45
Count 18
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Problems 12.33 12.55(Cont.)

• 7.564lt(n-1)s2 /s2lt30.191
• 7.564lt170.00718/s2lt30.191
• (1/7.564)170.00718gts2gt(1/30.191)170.00718
• 0.0161gts2gt0.0040

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IV. Differences in Populations

• Null Hypothesis H0 m1 m2, or m1 - m2 0
• Alternative Hypothesis HA m1 - m2 ? 0

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IV. Differences in Populations
Reference Ch. 9 Ch. 13
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V. Regression

• Model yi a bxi ei

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Lab Five
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The Financials
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Excel Chart
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Excel Regression
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Eviews Chart
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Eviews Regression
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Eviews Actual, Fitted residual