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251x0411 2/11/04 ECO251 QBA1 FIRST HOUR EXAM February 18, 2004 Name: _____________________ Social Security Number: _____________________ Part I. (7 points) Use the 5 3-digit numbers that you used in the second problem in the take-home exam. (If you don’t have them – take the numbers (9, 9, 9, 9, 9, 9, 10, 12, 8,1300) and replace the nines with your student number, changing any zeros in your student number to ones, then rewrite the resulting string of numbers as five three-digit numbers. Example: Seymour Butz’s student number is 976500, so he gets 976511101281300 which, as three digit numbers is (976, 511, 101, 281, 300. ) Compute the following: a) The Median (1) b) The Standard Deviation (3) c) The 3rd Quintile (2) d) The Coefficient of variation (1) 1 251x0411 2/11/04 Part II. (At least 35 points – At least 2 points each) 1. Which of the following is a graph of the cumulative distribution? a) Ogive b) Histogram c) Frequency Polygon d) Pie Chart e) None of the above 2. Which of the following is an example of continuous ratio data? a) The Likert Scale rate consumer impression of a product on a 1 to 5 scale with one best and 5 worst. b) The Celsius scale for measuring temperature c) The number of Brittany Spaniels entered in a dog show d) The number of dollars you paid in sales tax last year. 3. Cumulative relative frequency cannot be calculated by a) Taking the cumulative frequency for each class and dividing by the sum of cumulative frequencies for all classes. b) The relative frequency for each class plus the sum of the relative frequencies of all previous classes. c) The relative frequency of each class plus the cumulative relative frequency of the previous class d) The cumulative frequency of each class divided by the sum of the frequencies for all classes. e) All of the above can be used to calculate cumulative relative frequencies. 4. Consider the following formulas (i) x 2 nx 2 n 1 (ii) k 3mean mode (iii) 33 std .deviation s n x 3 3x x 2 2nx 3 .If the sample is skewed to the left, which of these (n 1)( n 2) should be positive? a) (i) b) (ii) c) (iii) d) (iv) e) None should be positive f) All should be positive. (iv) 5. (D-68) From which of the following would it be easiest to calculate the interquartile range? a) Mean, median and mode b) Ogive c) Box Plot. d) Stem-and-leaf plot 6. A summary measure that is computed to describe a characteristic of a sample is called a) a parameter. b) a census. c) a statistic. d) the scientific method. 251x0411 2/11/04 2 7. What is the difference between a field and a cell? Make a diagram of a table and show where one of these is. 8. If a distribution is skewed to the right, we would expect a) mode > mean b) mode < median c) median > mean d) mode > median 9. The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of a) inferential statistics. b) descriptive statistics. c) a parameter. d) a statistic. 10. Which of the following is most likely a parameter as opposed to a statistic? a) the average score of the first five students completing an assignment b) the proportion of females registered to vote in a county c) the average height of people randomly selected from a database d) the proportion of trucks stopped yesterday that were cited for bad brakes 11. Which of the following is most likely a parameter as opposed to a statistic? a) the average score of the first five students completing an assignment b) the proportion of females registered to vote in a county c) the average height of people randomly selected from a database d) the proportion of trucks stopped yesterday that were cited for bad brakes TABLE 2-2 At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. X f_ 1 7 2 5 3 11 4 8 5 9 12. Referring to Table 2-2, across all of the regional offices, how many total employees were supervised by those surveyed? a) 15 b) 40 c) 127 d) 200 3 251x0411 2/11/04 TABLE 2-4 A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. StemLeaves 3 24 4 03478999 5 0112345 6 12566 7 01 8 9 2 13. Referring to Table 2-4, what fraction of the respondents rated overall television quality with a rating of 80 or above? e) 0.00 f) 0.04 g) 0.96 h) 1.00 14. (6 points) On the basis of 100 observations Stock A has a mean rate of return of 7% with a standard deviation of 1% Stock B has a mean rate of return of 9% and a standard deviation of 1.5% For stock A the fraction of observations between 4% and 10% must be at least ______%. If returns on stock A have a symmetrical unimodal distribution, the fraction of observations between 4% and 10% must be approximately _________. According to what you have learned in class, which of these two stocks is riskiest? You must show why for your answer to count. 15. A survey of 47 cities shows that the number of new AIDS cases reported last year varied from 135 to 1337. If these data are to be presented in 5 classes, what intervals would you use? Explain your reasoning using an appropriate formula and use it to fill in the table below. Class From To A B C D E 16. Cities are divided into three classes Class A At least 900 new AIDS cases B Less than 900 new AIDS cases C More than 30% of new AIDS cases also had a chronic contagious disease. Which of the following classes are mutually exclusive? (Circle) (1.5) A and B , B and C, A, B, and C Which of the following classes are collectively exhaustive? (Circle) (1.5) A and B , B and C, A, B, and C 4 251x0411 2/11/04 ECO251 QBA1 FIRST EXAM February 18, 2004 TAKE HOME SECTION Name: _________________________ Student Number: _________________________ Throughout this exam show your work! Please indicate clearly what sections of the problem you are answering and what formulas you are using. Turn this is with your in-class exam. Part III. Do all the Following (11 Points) Show your work! 1. Look at the frequency distribution below. Replace the 9s with your student number. If any digit of your student number is 0, change it to a 1. For example, Seymour Butz’s student number is 976500 so the frequencies he uses are (9, 7, 6, 5, 1, 1, 10, 12, 8). Class $500- 599.99 $600- 699.99 $700- 799.99 $800- 899.99 $900- 999.99 $1000-1099.99 $1100-1199.99 $1200-1299.99 $1300-1399.99 frequency 9 9 9 9 9 9 10 12 8 Assume that this data represents a sample of rents paid in Chester County. a. Calculate the Cumulative Frequency (0.5) b. Calculate The Mean (0.5) c. Calculate the Median (1) d. Calculate the Mode (0.5) e. Calculate the Variance (1.5) f. Calculate the Standard Deviation (1) g. Calculate the Interquartile Range (1.5) h. Calculate a Statistic showing Skewness and Interpret it (1.5) i. Make a histogram of the Data showing relative or percentage frequency (Neatness Counts!)(1) j. Extra credit: Put a (horizontal) box plot below the histogram using the same scale. (1) 5 251x0411 2/11/04 2. Use the frequencies you used in problem 1 in this problem as values of x . Add 1300 at the end. Write the result in clumps of 3 digits. Example: In the last problem, Seymour Butz used (9, 7, 6, 5, 1, 1, 10, 12, 8). If we add 1300 at the end, we have 976511101281300. In 3 digit clumps this gives him (976, 511, 101, 281, 300). For these five numbers, compute the a) Geometric Mean b) Harmonic mean, c) Root-mean-square (1point each). Label each clearly. If you wish, d) Compute the geometric mean using natural or base 10 logarithms. (1 point extra credit each ). While you’re at it, compute the sample mean and bring it to the exam (no credit – but it won’t hurt). 6