1. 1 Midterm Review

2. 2 Econ 240A  Descriptive Statistics  Probability  Inference  Differences between populations  Regression

3. 3 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

4. 4 Stem and Leaf Diagtam  Example: Problem 2.24  Prices in thousands of $ of houses sold in a Los Angeles suburb in a given year

5. 5 Subsample Problem 2.24 Prices in thousands $ Houses sold in a Los Angeles suburb

6. 6 Sorted Data Problem 2.24 Prices in thousands $ Houses sold in a Los Angeles suburb

7. 7 Summary Statistics Problem 2.24 Prices in thousands $ Houses sold in a Los Angeles suburb

8. 8 Problem 2.24 Prices in thousands $ Houses sold in a Los Angeles suburb

9. 9 Box and Whiskers Plots  Example: Problem 4.30  Starting salaries by degree

10. 10 Subsample Problem 4.50 Starting salaries By degree

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14. 14 II. Probability  Concepts  Elementary outcomes  Bernoulli trials  Random experiments  events

15. 15 Probability (Cont.)  Rules or axioms:  Addition rule  P(AUB) = P(A) + P(B) – P(A^B)  Conditional probability  P(A/B) = P(A^B)/P(B)  Independence

16. 16 Probability ( Cont.)  Conditional probability  P(A/B) = P(A^B)/P(B)  Independence  P(A)*P(B) = P(A^B)  So P(A/B) = P(A)

17. 17 Probability (Cont.)  Discrete Binomial Distribution  P(k) = C n (k) p k (1-p) n-k  n repeated independent Bernoulli trials  k successes and n-k failures

18. 18 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?

19. 19 24 28 25 18 29 25 24 23 25 24 29 32 28 30 23 27 21 Subsample

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24. 24 Probability (Cont.)  Continuous normal distribution as an approximation to the binomial  n*p>5, n(1-p)>5  f(z) = (1/2  ½ exp[-½*z 2 ]  z=(x-   f(x) = (1/  (1/2  ½ exp[-½*{(x-   

25. 25 III. Inference  Rates and Proportions  Population Means and Sample Means  Population Variances and Sample Variances  Decision Theory

26. 26 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) =  C(I) +  C(II)

27. 27 Sample Proportions from Polls  Where n is sample size and k is number of successes

28. 28 Sample Proportions So estimated p-hat is approximately normal for large sample sizes

29. 29 Sample Proportions  Where the sample size is large

30. 30 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 company’s appliances

31. 31 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 commercial’s honesty if in a random sample of 400 households, 10% report at least one service call?

32. 32 Problem 9.38 Answer  Null Hypothesis: H 0 : p=0.05  Alternative Hypothesis: p>0.05  Statistic:

33. 33 4.59 Z. Z critical 1.645 5%

34. 34 Sample means and population means where the population variance is known

35. 35 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?

36. 36 Problem 9.26 (Cont.)  Null Hypothesis: H 0 :   Alternative Hypothesis: H A :   Statistic:

37. 37   Zcrit(1%)= -2.33

38. 38 Sample means and population means when the population variance is unknown

39. 39 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.

40. 40 Problems 12.33 (Cont.)  Can we conclude that on average the containers are mislabeled? Use 

41. 41 t crit 5%  

42. 42 Problems 12.33 (Cont.) 7.87.977.92 7.917.957.87 7.937.797.92 7.998.067.98 7.947.828.05 7.757.897.91

43. 43 Mean7.913888889 Standard Error0.019969567 Median7.92 Mode7.91 Standard Deviation0.084723695 Sample Variance0.007178105 Kurtosis-0.24366084 Skewness-0.22739254 Range0.31 Minimum7.75 Maximum8.06 Sum142.45 Count18

44. 44 Problems 12.33 (Cont.)  Can we conclude that on average the containers are mislabeled? Use 

45. 45 Confidence Intervals for Variances

46. 46 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.

47. 47 Problems 12.33 &12.55 (Cont.)  Estimate with 95% confidence the variance in contents’ weight.    variable with n-1 degrees of freedom is (n-1)s 2 /  

48. 48    

49. 49 Problems 12.33 &12.55(Cont.) 7.87.977.92 7.917.957.87 7.937.797.92 7.998.067.98 7.947.828.05 7.757.897.91

50. 50 Mean7.913888889 Standard Error0.019969567 Median7.92 Mode7.91 Standard Deviation0.084723695 Sample Variance0.007178105 Kurtosis-0.24366084 Skewness-0.22739254 Range0.31 Minimum7.75 Maximum8.06 Sum142.45 Count18

51. 51 Problems 12.33 &12.55(Cont.)  7.564<(n-1)s 2 /   <30.191  7.564<17*0.00718/   <30.191  (1/7.564)*17*0.00718>   >(1/30.191)*17*0.00718  0.0161>   >0.0040

52. 52 IV. Differences in Populations  Null Hypothesis: H 0:     or     =0  Alternative Hypothesis: H A :     ≠ 0

53. 53 IV. Differences in Populations Reference Ch. 9 & Ch. 13

54. 54 V. Regression  Model: y i = a + b*x i + e i

55. 55 Lab Five

56. 56 The Financials

57. 57 Excel Chart

58. 58 Excel Regression

59. 59 Eviews Chart

60. 60 Eviews Regression

61. 61 Eviews: Actual, Fitted & residual