TABLE 2-2X f_TABLE 2-5RelativeTABLE 2-7251y0312 9/26/03 ECO251 QBA1 FIRST HOUR EXAMOctober 1, 2003 Name: _____KEY____________ Social Security Number: _____________________Part I. (32 points)1. The process of using sample statistics to draw conclusions about true population parameters is calleda) *statistical inference.b) the scientific method.c) sampling.d) descriptive statistics.2. A summary measure that is computed to describe a characteristic of an entire population is calleda) *a parameter.b) a census.c) a statistic.d) the scientific method.3. Which of the following is a discrete quantitative variable?a) the Dow Jones Industrial Averageb) the volume of water released from a damc) the distance you drove yesterdayd) *the number of employees of an insurance companyTABLE 1-1The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products. 4. Referring to Table 1-1, the possible responses to the question "Are you happy, indifferent, or unhappy with the performance per dollar spent on the videocassette recorder?, " if we write downa 1 for ‘happy, ’ a 2 for ‘unhappy’ and a 3 for ‘indifferent, are the following kind of random variable.a) ratiob) *nominalc) intervald) ordinal1251y0312 9/26/03TABLE 2-2At 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 72 53 114 85 95. Referring to Table 2-2, how many regional offices are represented in the survey results?a) 127b) 5c) 15d) *40 fnTABLE 2-5The following are the durations (in minutes) of a sample of long-distance phone calls made within the continental United States, reported by one long-distance carrier:RelativeTime (in Minutes) Frequency 0 but less than 5 0.375 but less than 10 0.2210 but less than 15 0.1515 but less than 20 0.1020 but less than 25 0.0725 but less than 30 0.0730 but less than 35 0.026. Referring to Table 2-5, if 1,000 calls were randomly sampled, how many calls lasted under 10 minutes?a) 220b) 370c) 410d) *590The answer is the cumulative frequency for the 2nd class multiplied by 1000. class relf relF 0 but less than 5 0.37 0.375 but less than 10 0.22 0.5910 but less than 15 0.15 0.7415 but less than 20 0.10 0.8420 but less than 25 0.07 0.9125 but less than 30 0.07 0.9830 but less than 35 0.02 1.007. If I make a graph of the data in table 2-5 (Assume the table represents a sample of 1000 calls) with the following x and y coordinates for the first five points: {(0, 0), (5, 370), (10, 590), (15, 740) , (20, 840)}, a one-word name for this type of graph is _ogive_ , and the last point on the line could be (45, _1000_ ) Explanation: The x points are the upper limits of the class, starting at the last empty class. The y points are the cumulative frequencies, gotten by multiplying therelF column by 1000. When the graph gets to x = 35, y hits 1000 and is 1000 for all subsequentpoints.2251y0312 9/26/03 8. Referring to Table 2-5, what is relF for the percentage of calls that lasted under 20 minutes?a) 0.10b) 0.76c) *0.84 Look at the table.d) None of the above – write in the correct answer.TABLE 2-7The stem-and-leaf display below contains data on the number of months between the date a civil suit is filed andwhen the case is actually adjudicated for 50 cases heard in superior court. Stem Leaves 1 2 3 4 4 4 7 8 9 92 2 2 2 2 3 4 5 5 6 7 8 8 8 93 0 0 1 1 1 3 5 7 7 84 0 2 3 4 5 5 7 95 1 1 2 4 6 66 1 5 89. Referring to Table 2-7, the civil suit with the fourth shortest waiting time between when the suit was filed and when it was adjudicated had a wait of _14__ months. Explanation: The first four numbers are 12, 13, 14, 14.10. Eunice computes the following statistics from a sample 3)2)(1(xxnnn, 33sk, 12nxx, deviationstdmodemean.3 , 243424131321nsnnxxnnnnnk. She thinks the sample represents a population that is skewed to the right. Which of the statistics would show skewness and what sign should she expect from them? (No partial credit on this one.) Answer: Any legitimate measure of skewness would be positive if the population is skewed to theright. From your formula table, the measures of skewness are: (i) 33)2)(1(xxnnnk - skewness, (ii)331skg - relative skewness and (iii) deviationstdmodemeanSK.3 - Pearson’s measure of skewness. The other two are 122nxxs - the sample variance, which is always positive and measures dispersion and 243424131321nsnnxxnnnnnk - the coefficient of excess (in the outline), which measures kurtosis.11. In a perfectly symmetrical distribution with one mode. a) the arithmetic mean equals the median.b) the median equals the mode.c) the arithmetic mean equals the mode.d) *all of the above.e) none of the above.3251y0312 9/26/0312. According to the Bienayme-Chebyshev rule (I called it Chebyshef’s Inequality), at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?a) 1b) 2c) 3d) *4 Explanation: If at least 93.75% are ‘in,’ then at most 6.25% are out in the tails. The rule says that 21k is the proportion in the tails, defined as the points below k and the points above k. If you try out the values here, you will find ,0625.161412sok must be 4. More directly, you could solve 9375.121k, by trying the four values ofk that were given. This is a problem that was done in class.13. Evaluate the following statements. (i) The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.(ii) In a set of numerical data, the value for Q3 can never be smaller than the value for Q1. (iii) In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3. a) (i) and (ii) are false.b) *(i) and (iii) are false.c) (ii) and (iii) are
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