251y9911 10/7/99251 (Open this document in 'Page Layout' view!)ECO251 QBA1 Name __________________ FIRST HOUR EXAM SECTION MWF TR 11AM 12:30 OCTOBER 7, 1999 Note that in 2000 all exams will be open book. The exam below is a closed book exam. This means that parts I and II will be changed considerably. Questions like d) and l) in part I and j), k) an l) in part II will still appear. wfFpNLxppp1Part I. Explain or Define the Following (13 Points Maximum)a) Field (1) See diagram at rightb) Cell (1) A location in a fieldc) Stubhead (1) The top area of a stub –see diagram.Table NumberTitleHeadnoteFootnotesSource NoteStub HeadMaster CaptionColumn LabelsROWLABELSCELLSField BoxheadFieldStubd) I have a table describing the grades received by a class (A, B, C, D, F or NG) and their year (Fr,So, Jr, Sr). there are no individuals in the class who are not regularly enrolled undergraduates. Ifwe define the following categories:C1 'Person received A or B' C3 ' Person is Freshman or Sophomore’'C2 'Person received C, D, or F’ C4 'Person is Junior or Senior'Are the following classes: (3)Mutually Exclusive? Collectively Exhaustive?C2 and C3 __n__ ___n___C3 and C4 __y___ ___y___C1, C3, C4 __n___ ___y___C3 and C4 are mutually exclusive because no individual in C3 can also be in C4.C1, C3 and C4 are collectively exhaustive because everyone must be in at least one of theseclasses.e) The mean, median and mode have something in common as to what they measure, which they do not share with , say, the variance. What is it? Make a sketch showing where they would berelative to one another in a distribution that is skewed to the left. (4) They are all measures of central tendency. The sketch should show the mean on the left, the mode on the right and the median between them .f) Frequency Polygon (What does it look like, what does it show? A labeled sketch might workbest.) (1) A line graph with xon the x-axis and frequency on the y-axis.g) Interval Data (1) Quantitative data like temperature where the interval between two values hasa constant meaning and there is no real bottom or top. Contrast it with ordinal or ratio data.251y9911 10/7/99h) Third Quintile (1) A point with 3/5 or 60% of the data below it.i) Mesokurtic (1) Not flat or sharp peaked, or, better, with a zero coefficient of excess, 2.j) Box Plot (2) See text page 85. A double firecracker diagram that shows the median and the quartiles.k) Is the mean of a population a statistic or a parameter? (1) Numbers that describe a populationare parameters.l) My firm has a large number of stores throughout the country with annual sales between 12 and50 million dollars. If this data is to be presented in nine classes, what intervals would you use?Explain your reasoning using the appropriate formula. (3) Use 91250classes of no.lowest-highest 2222.4. So the interval should be above 4.2222, maybe 4.5. You might try 10-14.49, 14.5-18.99, 19-23.49, 2.5-2.99, 28-32.49, 32.5 to 36.99, 37-41.49, 41.5 to 45.99, and 46 to 50.49.m) If I pick an item at random from a very large population with a median of 535, what is theapproximate probability that the item I pick will be above 535? (2) Since half the numbers are above the median, the probability is 50%.n) If you answered question m) and the distribution in m) is skewed to the right and I pick anotheritem from the population, is the chance that it is above the mean greater, less than theprobability you gave in m), or is it unchanged? ( A picture may help you decide) (1)If the distribution is skewed to the right, the mean is above the median. If half the numbers areabove the median, less than half must be above the mean.2251y9911 9/27/99Part II. Give formulas for the following or compute an appropriate answer, showing your work (12 Points maximum):a) Population Variance (Definitional formula for ungrouped data) (2)b) Root-mean-square (2)c) Sample Mean (Grouped data) (1)d) Sample Standard Deviation (Use words!) (1)e) Coefficient of Variation ( For a population)(1)f) Population Skewness (1)g) Sample Variance (Grouped Data - ComputationalFormula (2)h) Kurtosis (Population - Ungrouped) (2)i) Pearson's Measure of Skewness (2)j) Compute the Harmonic Mean of the numbers 4, 40 and 400 (2)k) If a population of 1500 items has a mean of 13555 and a standard deviation of 100, according to Chebyshef's Inequality, what is the minimum number of items that could be between 13355 and 13755? (3)l) If you answered k) and you now learn that the population is unimodal and symmetrical, would youraise or lower your estimate in k), or would you leave it unchanged? (1)Solution: a) Population Variance (Definitional formula for ungrouped data) (2) Nx22b) Root-mean-square (2) 221xnxrms or 21xnxrmsc) Sample Mean (Grouped data) (1) nfxxd) Sample Standard Deviation (Use words!) (1) The square root of the sample variance.e) Coefficient of Variation ( For a population)(1) Cf) Population Skewness (1) 323332311nxxNxNg) Sample Variance (Grouped Data - Computational Formula (2) 1222nxnfxsh) Kurtosis (Population - Ungrouped) (2) Nx44i) Pearson's Measure of Skewness (2) deviationstdmodemeanSK.3 j) Compute the Harmonic Mean of the numbers 4, 40 and 400 (2) xnxh111 so 12001114001113140014001040010031400140141311hx and811.101111200hxk) If a population of 1500 items has a mean of 13555 and a standard deviation of 100, according to Chebyshef's Inequality, what is the minimum number of items that could be between 13355and 13755? (3) Chebyshef’s Inequality says 21kkxP which means that theproportion in the tails outside the interval k to k is at most 21k, so that theproportion within the same interval is at least 211k. In this case 21001355513755k, so theproportion is at least 43411112k, and 1125150043, so the number is at least 1125.3l) If you answered k) and you now learn that the population is unimodal and symmetrical, would you raise or lower your estimate in k), or would you leave it unchanged? (1) The empirical rule says that 95% is within 2 standard deviations, so raise the estimate.251y9911 10/7/99Part III.
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