251y0012 10/11/00 ECO251 QBA1 Name ______KEY__________ FIRST HOUR EXAM SECTION MWF 10 11 TR 11 12:30 OCTOBER 7, 2000 Part I. Multiple Choice (10 points)1.(S-2) Inferential statistics is a. The display of characteristics of a sample in a graph with summary measures. b. The display of characteristics of a population in a graph with summary measures.*c. The process of estimating facts (parameters) about a population from a sample taken from the population. d. A branch of mathematics devoted to the collection, display and analysis of data. e. None of the above.2.(S-3) The Fortune 500 listing of the 500 largest companies in the US in order of their annual sales is an example of *a. Ordinal data. b. Nominal data. c. Interval data. d. Ratio data. e. None of the above.3. A used automobile dealer lists cars in the following classes. A - 100,000 miles or more on the odometer, B - less than 100,000 miles on the odometer, C - Diesel. Are these three categories *a. Collectively exhaustive? b. Mutually exclusive? c. Both mutually exclusive and collectively exhaustive? d. Neither mutually exclusive or collectively exhaustive? e. Can't tell with the information given.4. (D7-9) If a distribution is skewed to the left, we can say that it is likely that a. Mean > median > mode b. Median > mean > mode*c. Mode > median > mean d. Mode > mean > median e. Mode = mean = median (Most people got this backwards - make a diagram!)5. A graph that connects points, each of which represents the cumulative frequency F is called a a. Histogram*b. Ogive c. Frequency Polygon d. Pie chart e. None of the above1251y0012 10/11/00Part II. Compute an appropriate answer, showing your work (except in a)) (15 Points maximum - if you do more than 15 points, only your right answers will be counted.):a) Fill in the following table (3) ClassfrelfF50-59.99 _ .12 __60-69.99 3 __ __70-79.99 _ __ 1280-89.99 7 __ __90-99.99 6 _ __Total 25 __ Solution:ClassfrelfF50-59.99 3 .12 360-69.99 3 .12 670-79.99 6 .24 1280-89.99 7 .28 1990-99.99 6 .24 25Total 25 1.00Note that 25nb) Assume that we have sold 1000 life insurance policies in amounts between $5300 and $9800. If this data is to be presented in seven classes, what intervals would you use? Explain your reasoning using the appropriate formula and make a table showing the class intervals you would actually use. (3)Solution: 86.642753009800so use 650 or 700. This is only a suggestion. Any number somewhat above or equal to 643 will work. Class from toA 5000 5699.99 B 5700 6399.99C 6400 7099.99D 7100 7799.99E 7800 8499.99F 8500 8199.99G 9200 9899.99c) (S-30)If a population of 1000 items with an unknown distribution has a mean of 12 and a standard deviation of 1.5, what is the approximate minimum number of items that must be (i) between 6 and 18? (ii) between 12 and 18? Note: there was an error here - (ii) was a harder question than I intended to give - I will thus give 3 points for a correct answer for (i). (ii) should have read (iic) What is the maximum that could be over 18? (3)Solution: (i) If we use the formula xzk, we find that 45.1126 and.45.11218 According to the Chebyshef inequality, The minimum fraction of the data that must be between 4 is 16151611112k. Fifteen sixteenths of 1000 is about 938. (ii) since we can't pick sides here, the answer can't really be found. (iic) The answer is the opposite to the answer to (i). There are about 1000 - 938 = 62 items left over. All of these could be above 18.2251y0012 10/11/00d) Do c) again assuming that the distribution is unimodal and symmetric.(2)Solution: (i and iic) Since the Empirical Rule says that almost all points must be between3, we would expect almost all of the 1000 points to be between 6 and 18, since these points are 4, and we would be quite surprised if even one point is above 18. (ii) If the distribution is symmetric, we would expect half of the 1000 points or 500 on one side. Again there will be 2 points for a correct answer to (i).e) For the numbers 11.1, 13.2, 15.1 and 11.5, compute the i) Root-mean-square ii) Harmonic mean, iii) geometric mean (2 each)Solution: Note that 9.50x. This is not used in any of the following calculations and there is no reason why you should have computed it!(i) The Root-Mean-Square. 71.6574125.13201.22824.17421.123415.111.152.131.11411222222xnxrms4275.164. So 823.124275.16412xnxrms.(ii) The Harmonic Mean. 086957.0066225.0075758.0090090.0415.1111.1512.1311.11141111xnxh 319029.041079757.0. So 5380.12079757.01111xnxh.(iii) The Geometric Mean. 41198.25443198.254435.111.5`12.131.11441321nnngxxxxxx 25.0198.254436297.12. Or 44234.271469.258022.240695.2415.11ln1.15ln2.13ln1.11ln41)ln(1ln xnxg 53605.214420.1041. So 6297.1253605.2exg. I got the last result by putting 2.53605 into the calculator and pressing 'inverse' and then 'ln x.' Or )log(1log xnxg 5.11log1.15log2.13log1.11log41 10139.140557.44110607.117898.112057.104532.141. So6297.121011217.1gx. I got the last result by putting 1.10139 into the calculator and pressing 'inverse' and then 'log x.'Notice that the original numbers and all the means are between 11.1 and 15.1. In spite of everything that I said, there are many of you who think that: (i) You can find a sum of squares by summing numbers and squaring the sum; (ii) You can find the sum of x1 by adding up the numbers and taking the reciprocal; (iii) You can find an nth by dividing by n. I can only recommend a remedial math class (unless, of course, you want to try listening in class and checking out the homework very carefully.)3251y0012 10/11/00Part III. Do the following problems (25 Points)1. In a period of 7 days you make the following numbers of sales(in millions):Day : 1 2 3 4 5 6 7 Sales: 9.2 10.2 9.2 11.2 19.2 12.2 14.2 Compute the following (assuming that the numbers are a sample):a) Mean
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