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Chapter 2: Q58E (page 103)
Calculate the variance and standard deviation for samples where
a.n= 10, 鈭�x2 = 84, 鈭�x= 20
b.n= 40, 鈭�x2 = 380, 鈭�x= 100
c.n= 20, 鈭�x2 = 18, 鈭�x= 17.
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A qualitative variable is measured for 20 companies randomly sampled and the data are classified into three classes, small (S), medium (M), and large (L), based on the number of employees in each company. The data (observed class for each company) are listed below. ______________________________________ SSL M SM M S M S L M S SSS M L S L ----------------------------------------------------------------
a. Compute the frequency for each of the three classes.
b. Compute the relative frequency for each of the three classes.
c. Display the results, part a, in a frequency bar graph.
d. Display the results, part b, in a pie chart.
Professional athletes鈥� salaries.The salaries of superstar professional athletes receive much attention in the media. The multimillion-dollar long-term contract is now commonplace among this elite group. Nevertheless, rarely does a season pass without negotiations between one or more of the players鈥� associations and team owners for additional salary and fringe benefits for allplayers in their particular sports.
a.If a players鈥� association wanted to support its argument for higher 鈥渁verage鈥� salaries, which measure of central tendency do you think it should use? Why?
b.To refute the argument, which measure of central tendency should the owners apply to the players鈥� salaries? Why?
Question: Hull failures of oil tankers.Owing to several major ocean oil spills by tank vessels, Congress passed the Oil Pollution Act, which requires all tankers to be designed with thicker hulls. Further improvements in the structural design of a tank vessel have been proposed since then, each with the objective of reducing the likelihood of an oil spill and decreasing the amount of outflow in the event of a hull puncture. To aid in this development, Marine Technology (Jan. 1995) reported on the spillage amount (in thousands of metric tons) and cause of puncture for 50 major oil spills from tankers and carriers. [Note: Cause of puncture is classified as either collision (C), fire/explosion (FE), hull failure (HF), or grounding (G).] The data are saved in the accompanying file.
a.Use a graphical method to describe the cause of oil spillage for the 50 tankers. Does the graph suggest that any one cause is more likely to occur than any other? How is this information of value to the design engineers?
b.Find and interpret descriptive statistics for the 50 spillage amounts. Use this information to form an interval that can be used to predict the spillage amount of the next major oil spill.
Network server downtime.A manufacturer of network computer server systems is interested in improving its customer support services. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system downtime. The 40 most recent customers were surveyed to determine the amount of downtime (in hours) they had experienced during the previous month. These data are listed in the table.
Customer Number | Downtime | Customer Number | Downtime |
230 | 12 | 250 | 4 |
231 | 16 | 251 | 10 |
232 | 5 | 252 | 15 |
233 | 16 | 253 | 7 |
234 | 21 | 254 | 20 |
235 | 29 | 255 | 9 |
236 | 38 | 256 | 22 |
237 | 14 | 257 | 18 |
238 | 47 | 258 | 28 |
239 | 0 | 259 | 19 |
240 | 24 | 260 | 34 |
241 | 15 | 261 | 26 |
242 | 13 | 262 | 17 |
243 | 8 | 263 | 11 |
244 | 2 | 264 | 64 |
245 | 11 | 265 | 19 |
246 | 22 | 266 | 18 |
247 | 17 | 267 | 24 |
248 | 31 | 268 | 49 |
249 | 10 | 269 | 50 |
a.Construct a box plot for these data. Use the information reflected in the box plot to describe the frequency distribution of the data set. Your description should address central tendency, variation, and skewness.
b.Use your box plot to determine which customers are having unusually lengthy downtimes.
c.Find and interpret the z-scores associated with the customers you identified in part b.
Groundwater contamination in wells. In New Hampshire, about half the counties mandate the use of reformulated gasoline. This has led to an increase in the contamination of groundwater with methyl tert-butyl ether (MTBE). Environmental Science & Technology (Jan. 2005) reported on the factors related to MTBE contamination in public and private New Hampshire wells. Data were collected for a sample of 223 wells. Three of the variables are qualitative in nature: well class (public or private), aquifer (bedrock or unconsolidated), and detectible level of MTBE (below limit or detect). [Note: A detectible level of MTBE occurs if the MTBE value exceeds .2 micrograms per liter.] The data for 11 selected wells are shown in the accompanying table.
Source: Based on J. D. Ayotte, D. M. Argue, and F. J. McGarry, 鈥淢ethyl tert-Butyl Ether Occurrence and Related Factors in Public and Private Wells in Southeast New Hampshire,鈥� Environmental Science & Technology, Vol. 39, No. 1, Jan. 2005, pp. 9鈥�16
a. Use graphical methods to describe each of the three qualitative variables for all 223 wells.
b. Use side-by-side bar charts to compare the proportions of contaminated wells for private and public well classes.
c. Use side-by-side bar charts to compare the proportions of contaminated wells for bedrock and unconsolidated aquifers.
d. What inferences can be made from the bar charts, parts a鈥揷?
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