ECO 578 Summer I 2016 Page 1 of 15 Name: ____________________ ID: ____________________ Online Exam I Midterm Exam There are 4 parts: Part A: Answer the following questions (1-10) Part B: True/ False (11-30) Part C: Select the correct answer for the following questions (31-40) Part D: Work Problem (41-55) **All work must be shown step by step** Two different ways to submit your answer sheet 1. Scan your answer sheet and place it in ONE FILE at drop-box. (preferable) **Zipped files are not allowed 2. Use MS-Word and place it in a drop-box. **Excel is not acceptable for this test **Deadline: Sunday, 19th of June 2016 BY 11:59 P.M. (CST) **All work in part D must be shown step by step in order to receive full credit Part A: Answer the following questions (1-10) 1. What are the measures of central tendency? 2. What are the characteristics of mean, median, and mode? 3. What is the sampling error? ECO 578 Summer I 2016 Page 2 of 15 4. Name 6 reasons why we use samples instead of an entire population. 5. Name measures of spread or variability. 6. Explain the concept of error and uncertainty as it relates to decision making. 7. As discussed in the class live, what are 3 ways of calculating R 2? 8. Suppose the classes for an organized set of data are as follows: please fill in the A column and answer the B question. Class A. Mid-Point B. What is the value of class width? 0.235 - 0.875 0.875 - 1.515 1.515 - 2.155 9. Into which class is the value 14.6 assigned? (Circle your answer) Class a. 11.2 - 12.9 b 12.9 - 14.6 . c. 14.6 - 16.3 ECO 578 Summer I 2016 Page 3 of 15 10. What is the standard deviation for these data: 3.784, 3.784, and 3.784 Part B: True or False (11-30) ______11. The random sample is the most important, because statistical theory applies to it alone. ______12. In a frequency distribution, the class mark is the number of observations that fall within that class. ______13. Original class interval frequencies can be obtained by multiplying the respective relative frequencies by the total number of observations. ______14. The sum of the class frequencies is equal to the number of observations made. ______15. Planning is the most important step in statistical studies. ______16. Systematic, stratified and cluster sampling are not approximations to simple random sampling. ______17. A relative frequency distribution describes the proportion of data values that fall within each category. ______18. There would be no need for statistical theory if census, rather than a sample was always used to obtain information about populations. ______19. P( A B) is P ( B| A )P( A) ______20. The median always exists in a set of numerical data. ______21. P ( A B ) =0 means that A and B are mutually exclusive events. ______22.Mutually exclusive events imply that if one event occurs, the other cannot occur. An event (e.g., A ) and its complement are always mutually exclusive. ______23. )=1 P ( A )+P ( A ______24.When events are not mutually exclusive, the rule is: ______25. Rule of addition when event are mutually exclusives: ______26. P ( A B )=P ( A ) + P ( B )P( A B) P ( A B )=P ( A ) + P ( B ) P ( B A ) is not P ( A|B )P(B) ______27. Events are independent when the occurrence of one event has no effect on the probability that another will occur. ______28.The P(x) is always 0 P(x) 1. ______29. The mean of the discrete probability distribution for a discrete random variable is called its expected value. ECO 578 Summer I 2016 Page 4 of 15 ______30. A random variable is a variable that can take different values according to the outcome of an experiment, and it can be either discrete or continuous. Part C: Multiple Choice (31-40) Use the following data to answer question 31-36 : 20 31 45 _____ 31. The Mode is______ a. 33 b. 34 _____ 32. The 50th percentile is______ a. 33 b. 35 _____ 33. The Mean is______ a. 33.89 b. 34.89 _____ 34. The Variance is______ a. 139.43 b. 162.11 _____ 35. The Standard deviation is______ a. 11.81 b. 12.73 _____ 36. The Range is______ a. 25 b. 28 54 38 33 22 45 17 c. 38 d. 45 c. 45.5 d. 45 c. 38.13 d. 32.13 c. 154.27 d. 149.07 c. 12.42 d. 12.21 c. 34 d. 37 Select the best answer for question 37-40 : _____ 37. The simplest measure of dispersion is the a. Standard deviation. b. Variance. c. Quartile deviation d. Range _____ 38. The largest value in a set of data is 240, and the lowest value is 100. If the resulting frequency distribution is to have seven classes of equal width, what will be the class width? a. 12 b. 7 c. 5 d. 20 _____ 39. For the values 10, 20, 30, 40, and 50, the average absolute deviation from the mean is a. 10 b. 15 c. 12 d. 14 _____ 40. A simple random sample for five executives who went on a diet on their doctor's order report the following numbers of pounds lost during their first two weeks on the diet: 5,8,3,7,8. What is the variance for this sample? a. 4.7 b. 3.76 c. 1.94 d. 2.17 ECO 578 Summer I 2016 Page 5 of 15 Part D: Must show all your work step by step in order to receive full credit; Excel is not allowed. (41-55) 41. Use the given information to answer the following questions: X f 0 9 1 1 a. Range b. Variance c. Standard deviation 42. Use the given information to answer the following question Y 3 9 a) Compute the value of b1 c) Interpret the meaning of X 1 5 b) Compute the value of b1 b0 d) Find the regression equation. ECO 578 Summer I 2016 Page 6 of 15 43. The length of stay in a hospital for major surgery is recorded for a sample of 48 patients: (a-h) Length of Stay (Days) Patient Count a) Mean 12 22 13 2 14 8 b) Median c)Mode d) Range e)Variance f) Standard deviation g) 95th Percentile h) 3nd Quartile 15 16 ECO 578 Summer I 2016 Page 7 of 15 44. Use the problem number 3 on page 3-19 to fill and complete table, then answers the following questions (a-h). (**Using D-Method) Score Frequency Mid-point (X) Cf d -2 -1 0 1 2 Total a) Mean b) Median c) Mode d) Range e) Variance f) Standard deviation g) 45th Percentile h) 1st Quartile df d 2 d 2 f ECO 578 Summer I 2016 Page 8 of 15 45. Please fill and complete the following table, then answer the following questions (a-h). (**Using DMethod) Age (in years) 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 Total Frequency 10 19 27 16 10 6 5 3 Mid-point (X) Cf fx d -3 -2 -1 0 1 2 3 4 a) Mean b) Median c) Mode d) Range e) Variance f) Standard deviation g) 45th Percentile h) 1st Quartile df d2 fd2 ECO 578 Summer I 2016 Page 9 of 15 46. Use problem 11 on page 4-11 to answer the following questions (a-e): a) Find b0 c) Interpret the meaning of b) Find b1 b1 d) Find the regression equation e) Predict the average value of Y for X=6 47. Work on problem 33 on page 5-19 (a-d): a) b) c) d) ECO 578 Summer I 2016 Page 10 of 15 48. Use the information from problem 15 on page 4-12 to fill in the given table, then answer the following questions (a-g). Giving that Y=Income, X=Expense Area Y ($1000) Income Rate X ($1000) Average Expense XY X2 Y2 Total a) Compute the value of b1 c) Interpret the meaning of b) Compute the value of b1 e) Compute the Coefficient of determination. b0 d) Find the regression equation. f) Predict the income rate for an area with an average expense of $75 ECO 578 Summer I 2016 Page 11 of 15 g) Interpret the Coefficient of determination 49. Please fill in the blank and answer the following questions: SUMMARY OUTPUT Regression Statistics Multiple R __________ R Square __________ Adjusted R Square 0.125 Standard Error __________ Observations __________ ANOVA F Significance F __________ 0.2308 2.227 MS _________ _ _________ _ Coefficients __________ Standard Error t Stat P-value Lower 95% Upper 95% Intercept 112.413 9.484 11.853 7.52722E-05 88.033 136.793 X -19.137 14.033 -1.364 0.231 -55.211 16.937 Regression Residual Total a) What is df SS 1 0.828 __________ 6 b0 c) Interpret the meaning of b) What is b1 e) What is the coefficient of determination Lower 95.0% _________ _ _________ _ b1 d) What is the regression equation f) What is the coefficient of correlation Upper 95.0% __________ __________ ECO 578 Summer I 2016 Page 12 of 15 g) Interpret the coefficient of determination h) Interpret the coefficient of correlation 50. Work on problem 5 on page 5-13 a) b) c) 51. Work on problem 16 on page 5-15 only part b (1-7). 1) 2) 3) 4) 5) 6) ECO 578 Summer I 2016 Page 13 of 15 7) 52. Work problem number 5 on page 6-13 (a-e). a) b) c) d) e) 53. Work on problem 13 on page 6-15 a) b) c) d) ECO 578 Summer I 2016 Page 14 of 15 e) 54. Use problem number 4 on page 6-22 to fill in the table and answer the following questions (a-c). X P[X=x] (X)(P[X=x]) [X-E(X)] 0 1 2 3 4 5 6 Total a) Expected value c) Standard deviation 55. Work on problem 8 on page 6-14 (a-b): a) b) b) Variance [X-E(X)]2 [X-E(X)]2 P[X=x] ECO 578 Summer I 2016 Page 15 of 15