lOMoAR cPSD|25922779 Solution Manual for the questions of the probability and statistics for computer scien tists 2nd edition by Baron with All Chapters 100% Complete Solutions to Exercises 4 Solutions to Exercises 4.1 About these solutions The solutions that follow were prepared by Darryl K. Nester. I occasionally pillaged or plagiarized solutions from the second edition (prepared by George McCabe), but I take full responsibility for any errors that may remain. Should you discover any errors or have any comments about these solutions (or the odd answers, in the back of the text), please report them to me: Darryl Nester Bluffton College Bluffton, Ohio 45817 email: nesterd@bluffton.edu WWW: http://www.bluffton.edu/ ~nesterd 4.2 Using the table of random digits Grading SRSs chosen from the table of random digits is complicated by the fact that students can nd some creative ways to (mis)use the table. Some approaches are not mistakes, but may lead to different students having different right answers. Correct answe rs will vary based on: • The line in the table on which they begin (you may want to specify one if the text does not). • Whether they start with, e.g., 00 or 01. • Whether or not they assign multiple labels to each unit. • Whether they assign labels across the rows or down the columns (nearly all lists in the text are alphabetized down the columns). Some approaches can potentially lead to wrong answers. Mistakes to watch out for include: • They may forget that all labels must be the same length, e.g., assigning labels like 0,1,2,...,9,10,... rather than 00 ,01,02,.... • In assigning multiple labels, they may not give the same number of labels to all units. E.g., if there are 30 units, they may try to use up all the two -digit numbers, thus assigning 4 labels to the rst ten units and only 3 to the remaining twenty. 4.3 Using statistical software The use of computer software or a calculator is a must for all but the most cursory treatment of the material in this text. Be aware of the following considerations: Acknowledgments • Standard deviations: Students may easily get confused by software which gives both the so -called sample standard deviation (the one used in the text) and the population standard deviation (dividing by n rather than n − 1). Symbolically, the former is usually given as sand the latter as σ (sigma), but the distinction is not always clear. For example, many computer spreadsheets have a command such as STDEV(...) to compute a standard deviation, but you may need to check the manual to nd out which kind it is. . As a quick check: for the numbers 1, 2, 3, s = 1 while σ = 0.8165. In general, if two values are given, the larger one is s and the smaller is σ. If only one value is given, and it is the wrong one, use the relationship s . • Quartiles and ve -number summaries: Methods of computing quartiles vary between different packages. Some use the approach given in the text (that is, Q1 is the median of all the numbers below the location of the overall median, etc.), while others use a more complicated approach. For the numbers 1, 2, 3, 4, for example, we would have Q1 = 1.5 and Q3 = 2.5, but Minitab reports these as 1.25 and 2.75, respectively. Since I used Minitab for most of the analysis in these solutions, this was sometimes a problem. However, I remedied the situation by writing a Minitab macro to compute quartiles the IPS way. (In effect, I was dumbing down Minitab, since its method is more sophisticated.) This and other macros are available at my website. • Boxplots: Some programs which draw boxplots use the convention that the whiskers extend to the lower and upper deciles (the 10th and 90th percentiles) rather than to the minimum and maximum. (DeltaGraph, which I used for most of the graphs in these solutions, is one such program. It took some trickery on my part to convince it to make them as I wanted them.) While the decile method is merely different from that given in the text, some methods are (in my opinion) just plain wrong . Some graphing calculators from Sharp draw box charts, which have a center line at the mean (not the median), and a box extending from x − σ to x + σ! I know of no statistics text that uses that method. 4.4 Acknowledgments I should mention the software I used in putting these solutions together: • For typesetting: TEX speci cally, Textures, from Blue Sky Software. • For the graphs: DeltaGraph (SPSS), Adobe Illustrator, and PSMathGraphs II (MaryAnn Software). • For statistical analysis: Minitab, G •Power, JMP IN, and GLMStat the latter two mostly for the Chapters 14 and 15. George McCabe supplied output from SAS for Chapter 15. G•Power is available as freeware on the Internet, while GLMStat is shareware. Additionally, I used the TI -82, TI -85, TI -86, and TI -92 calculators from Texas Instruments. Chapter 1 Solutions Section 1: Displaying Distributions with Graphs 1.1 (a) Categorical. (b) Quantitative. (c) Categorical. (d) Categorical. (e) Quantitative. (f) Quantitative. 1.2 Gender: categorical. Age: quantitative. Household income: quantitative. V oting Democratic/Republican: categorical. 1.3 The individuals are vehicles (or cars ). Variables: vehicle type (categorical), where made (categorical), city MPG (quantitative), and highway MPG (quantitative). 1.4 Possible answers (unit; instrument): • number of pages (pages; eyes) • number of chapters (chapters; eyes) • number of words (words; eyes [likely bloodshot after all that counting]) • weight or mass (pounds/ounces or kilograms; scale or balance) • height and/or width and/or thickness (inches or centimeters; ruler or measuring tape) • volume(cubicinchesorcubiccentimeters; rulerormeasuringtape[andacalculator]) Any one of the rst three could be used to estimate the time required to read the book; the last two would help determine how well the book would t into a book bag. 1.5 A tape measure (the measuring instrument) can be used to measure (in units of inches or centimeters) various lengths such as the longest single hair, length of hair on sides or back or front. Details on how to measure should be given. The case of a bald (or balding) person would make an interesting class discussion.
