midterm-1-102-s09-solutions

midterm-1-102-s09-solutions - Ecn 102 Analysis of Economic...

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Ecn 102 - Analysis of Economic Data University of California - Davis April 23, 2009 Instructor: John Parman Midterm 1 - Solutions You have until 10:20am to complete this exam. Please remember to put your name, section and ID number on both your scantron sheet and the exam. Fill in test form A on the scantron sheet. Answer all multiple choice questions on your scantron sheet. Choose the single best answer for each multiple choice question. Answer the long answer questions directly on the exam. Keep your answers complete but concise. For the long answer questions, you must show your work for full credit. Name: ID Number: Section: (POTENTIALLY) USEFUL FORMULAS ¯ x = 1 n n i =1 x i s 2 = 1 n - 1 n i =1 ( x i - ¯ x ) 2 CV = s ¯ x skew = n ( n - 1)( n - 2) n i =1 ( x i - ¯ x s ) 3 kurt = n ( n +1) ( n - 1)( n - 2)( n - 3) n i =1 ( x i - ¯ x s ) 4 - 3( n - 1) 2 ( n - 2)( n - 3) μ = E ( X ) z = ¯ x - μ σ n t = ¯ x - μ s n Pr [ T n - 1 > t α,n - 1 ] = α Pr [ | T n - 1 | > t α 2 ,n - 1 ] = α n i =1 a = na n i =1 ( ax i ) = a n i =1 x i n i =1 ( x i + y i ) = n i =1 x i + n i =1 y i s 2 = ¯ x (1 - ¯ x ) for proportions data t α,n - 1 = TINV (2 α, n - 1) Pr ( | T n - 1 | ≥ | t * | ) = TDIST ( | t * | , n - 1 , 2) Pr ( T n - 1 t * ) = TDIST ( t * , n - 1 , 1) (POTENTIALLY) USEFUL EXCEL OUPUT TINV(.01,499)=2.59 TINV(.02,499)=2.33 TINV(.025,499)=2.25 TINV(.05,499)=1.96 TINV(.10,499)=1.65 TINV(.20,499)=1.28 TINV(.01,399)=2.59 TINV(.02,399)=2.34 TINV(.025,399)=2.25 TINV(.05,399)=1.97 TINV(.10,399)=1.65 TINV(.20,399)=1.28 TINV(.01,299)=2.59 TINV(.02,299)=2.34 TINV(.025,299)=2.26 TINV(.05,299)=1.97 TINV(.10,299)=1.65 TINV(.20,299)=1.28
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2 Midterm 1 - Solutions SECTION I: MULTIPLE CHOICE (55 points) 1. Suppose you have annual observations of obesity rates for the past fifty years and you want a graph of the data that shows the trend in obesity over time. The best graph for this purpose would be: (a) A bar chart. (b) A pie chart. (c) A line chart. (d) A histogram. (c) A line chart would allow us to see how obesity rates are changing over time. The other types of charts would show us frequencies of particular values for obesity but wouldn’t tell us which values were more frequent at different points in time. 2. The probability of a Type II error occurring depends on: (a) The true population mean. (b) The significance level, α . (c) The sample size. (d) All of the above. (d) The further the true population mean is from μ 0 , the less likely we are to obser- vae a sample mean that leads us to fail to reject the null hypothesis. The significance level determines the range of sample means over which we would fail to reject the null hypothesis so changing the significance level will change the probability of in- correctly failing to reject the null. The sample size influences the distribution of ¯ X . As the sample size gets larger, the probability of getting a ¯ x close to the true mean goes up, so the likelihood of failing to reject the null hypothesis will go down.
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