251y0311 2 19 03 ECO251 QBA1 FIRST HOUR EXAM February 21 2003 Name Key Social Security Number Part I 34 points 1 Which of the following is NOT a reason for the need for sampling a It is usually too costly to study the whole population b It is usually too time consuming to look at the whole population c It is sometimes destructive to observe the entire population d It is always more informative to investigate a sample than the entire population 2 Most analysts focus on the cost of tuition as the way to measure the cost of a college education But incidentals such as textbook costs are rarely considered A researcher at Drummand University wishes to estimate the textbook costs of first year students at Drummand To do so she monitored the textbook cost of 250 first year students and found that their average textbook cost was 300 per semester Identify the population of interest target population to the researcher a All Drummand University students b All college students c All first year Drummand University students d The 250 students that were monitored 3 Which of the following is a continuous quantitative variable a The color of a student s eyes b The number of employees of an insurance company c The amount of milk produced by a cow in one 24 hour period d The number of gallons of milk sold at the local grocery store yesterday 4 If I describe the place where a number is in a table as column 3 row 5 the location of that number is a a Field b Cell c Stub d Label 1 251y0311 2 19 03 TABLE 2 1 An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance A representative from a local insurance agency selected a random sample of insured drivers and recorded X the number of claims each made in the last 3 years with the following results X f fx 1 14 14 2 18 36 3 12 36 4 5 20 5 1 5 50 111 5 Referring to Table 2 1 how many drivers are represented in the sample a 5 b 15 c 18 d 50 6 Referring to Table 2 1 how many total claims are represented in the sample a 15 b 50 c 111 d 250 7 When constructing charts the following is plotted at the class midpoints a frequency histograms b percentage polygons c cumulative relative frequency ogives d All of the above 8 Which of the following is NOT a reason for drawing a sample a A sample is less time consuming than a census b A sample is less costly to administer than a census c A sample is usually a good representation of the target population d A sample is less cumbersome and more practical to administer 2 251y0311 2 19 03 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 Stem Leaves 3 24 4 03478999 5 0112345 6 12566 7 01 8 9 2 9 Referring to Table 2 4 what percentage of the respondents rated overall television quality with a rating of 50 or below a 0 11 b 0 40 c 0 44 11 out of 25 d 0 56 TABLE 2 11 The ordered array below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective Defects 1 2 4 4 5 5 6 7 9 9 12 12 15 17 20 21 23 23 25 26 27 27 28 29 29 Class Frequency f Rel Frequency f rel 0 5 99 4 16 5 9 99 6 24 10 24 99 2 08 15 20 99 2 08 20 24 99 4 16 25 29 99 7 28 Total 25 1 00 10 Referring to Table 2 11 if a frequency distribution for the defects data is constructed using 0 but less than 5 as the first class the frequency of the 20 but less than 25 class would be 4 11 Referring to Table 2 11 if a frequency distribution for the defects data is constructed using 0 but less than 5 as the first class the relative frequency of the 15 but less than 20 class would be 08 3 251y0311 2 19 03 TABLE 2 13 A research analyst was directed to arrange raw data collected on the yield of wheat ranging from 40 to 93 bushels per acre in a frequency distribution 12 If the researcher was directed to present the data in 5 classes what should the class interval be Show your calculations Solution 93 40 10 6 Use 11 or more 5 13 Show the actual intervals you might use I used 12 as my width some used 15 Class A B C D E From 40 52 64 76 88 to 51 99 63 99 75 99 87 99 99 99 14 Which of the following is NOT sensitive to extreme values a The range b The standard deviation c The interquartile range d The coefficient of variation 15 In right skewed distributions which of the following is the correct statement Q2 and the median are the same a The distance from Q1 to Q2 is larger than the distance from Q2 to Q3 b The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3 c The mean is smaller than the median d The mode is larger than the mean 16 In a perfectly symmetrical distribution a the range equals the interquartile range b the interquartile range equals the mean c the median equals the mean d the variance equals the standard deviation 17 Evaluate the following statements i If every individual in the population is equally likely to be chosen to be in the sample we must be taking a simple random sample ii The sum of cumulative frequencies in a distribution always equals 1 iii The Chebyschev inequality says that least 1 9 of the data must be 3 standard deviations or more from the mean a Only the first is true b Only the second is true c Only the third is true d None are true e All are true A simple random sample of n must also have all possible samples of n equally likely The relative frequencies add to 1 At most 1 9 of the data is 3 or more standard deviations from the mean 4 251y0311 2 19 03 Part II My Social Security Number is 265398248 If I write it in clumps of 2 numbers I get 26 53 98 24 8 Write your social security number the same way Compute the following a The Median 1 b The Standard Deviation 3 c The 2nd Quintile 2 Solution The numbers in order are 8 24 26 53 98 x x2 8 64 x1 x2 24 …
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