4 Solutions to Exercises - Web.LeMoyne.Edu

1 50 Solutions to Exercises4 Solutions to About these solutionsThe Solutions that follow were prepared by Darryl K. Nester. I occasionally pillaged orplagiarized Solutions from the second edition (prepared by George McCabe), but I take fullresponsibility for any errors that may remain. Should you discover any errors or have anycomments about these Solutions (or the odd answers, in the back of the text), please reportthem to me:Darryl NesterBluffton CollegeBluffton, Ohio Using the table of random digitsGrading SRSs chosen from the table of random digits is complicated by the fact that studentscan find some creative ways to (mis)use the table. Some approaches are not mistakes, butmay lead to different students having different right answers. Correct answers will varybased on: The line in the table on which they begin (you may want to specify one if the text doesnot).

2 Whether they start with, , 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 thetext 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, , assigning labels like0;1;2;:::;9;10;:::rather than 00;01;02;:::. In assigning multiple labels, they may not give the same number of labels to all , if there are 30 units, they may try to use up all the two-digit numbers, thus assigning4 labels to the first ten units and only 3 to the remaining Using statistical softwareThe use of computer software or a calculator is a must for all but the most cursory treatmentof the material in this text. Be aware of the following considerations:Acknowledgments51 Standard deviations:Students may easily get confused by software which gives boththe so-called sample standard deviation (the one used in the text) and the populationstandard deviation (dividing bynrather thann 1).

3 Symbolically, the former isusually given as s and the latter as (sigma), but the distinction is not always example, many computer spreadsheets have a command such as STDEV(:::) tocompute a standard deviation, but you may need to check the manual to find out whichkind it a quick check: for the numbers 1, 2, 3,sD1 while :D0:8165. In general, iftwo values are given, the larger one issand the smaller is . If only one value is given,and it is the wrong one, use the relationshipsD qnn 1. Quartiles and five-number summaries:Methods of computing quartiles vary betweendifferent packages. Some use the approach given in the text (that is,Q1is the medianof all the numbers below the location of the overall median, etc.), while others use amore complicated approach. For the numbers 1, 2, 3, 4, for example, we would haveQ1D1:5 andQ3D2:5, but minitab reports these as and , I used minitab for most of the analysis in these Solutions , this was sometimesa problem.

4 However, I remedied the situation by writing a minitab macro to computequartiles the IPS way. (In effect, I was dumbing down minitab , since its method ismore 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 theminimum and maximum. (DeltaGraph, which I used for most of the graphs in thesesolutions, is one such program. It took some trickery on my part to convince it to makethem as I wanted them.)While the decile method is merelydifferentfrom that given in the text, some methodsare (in my opinion) just plainwrong. Some graphing calculators from Sharp draw boxcharts, which have a center line at the mean (not the median), and a box extending fromx toxC ! I know of no statistics text that uses that AcknowledgmentsI should mention the software I used in putting these Solutions together: For typesetting: TEX specifically, Textures, from Blue Sky Software.

5 For the graphs: DeltaGraph (SPSS), Adobe Illustrator, and PSMathGraphs II (MaryAnnSoftware). For statistical analysis: minitab , G Power, JMP IN, and GLMStat the latter twomostly for the Chapters 14 and 15. George McCabe supplied output from SAS forChapter 15. G Power is available as freeware on the Internet, while GLMStat is share-ware. Additionally, I used the TI-82, TI-85, TI-86, and TI-92 calculators from 1 Looking at Data DistributionsChapter 1 SolutionsSection 1:Displaying Distributions with (a)Categorical.(b)Quantitative.(c)Catego rical.(d)Categorical.(e)Quantitative.(f) : categorical. Age: quantitative. Household income: quantitative. VotingDemocratic/Republican: individuals are vehicles (or cars ). Variables: vehicle type (categorical), wheremade (categorical), city MPG (quantitative), and highway MPG (quantitative). 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 (cubic inches or cubic centimeters; ruler or measuring tape [and a calculator])Any one of the first three could be used to estimate the time required to read the book;the last two would help determine how well the book would fit into a book tape measure (the measuring instrument) can be used to measure (in units of inchesor centimeters) various lengths such as the longest single hair, length of hair on sides orback or front.

6 Details on how to measure should be given. The case of a bald (or balding)person would make an interesting class answers (reasons should be given): unemployment rate, average (mean ormedian) income, quality/availability of public transportation, number of entertainmentandculturalevents, housingcosts, crimestatistics, population, populationdensity, numberof automobiles, various measures of air quality, commuting times (or other measures oftraffic), parking availability, taxes, quality of (a), the number of deaths would tend to rise with the increasing population, even ifcancer treatments become more effective over time: Since there are more people, thereare more potential cases of cancer. Even if treatment is more effective, the increasingcure rate may not be sufficient to overcome the rising number of (b), if treatments for other diseases are also improving, people who might havedied from other causes would instead live long enough to succumb to if treatments were becominglesseffective, many forms of cancer are detectedearlier as better tests are developed.

7 In measuring five-year survival rates for (c), if wecan detect cancer (say) one year earlier than was previously possible, then effectively,each patient lives one year longer after the cancer is detected, thus raising the five-yearsurvival (a)1988:94924;800;000:D0:00003827D38:27 deaths per million riders. 1992:90354;632;000:D0:00001653D16:53 deaths per million riders. Death rates are less than half what theywere; bicycle riding is safer.(b)It seems unlikely that the number of riders more thandoubled in a six-year the proportion or percentage of repairs, Brand A is more reliable:294213;376:D0:22D22% for Brand A, and192480D0:4D40% for Brand (a)Student preferences may vary; be sure they give a reason. Method 1 is faster, butless accurate it will only give values that are multiples of 10.(b)In either method 1 or2, fractions of a beat will be lost for example, we cannot observe beats in 6 seconds,only 7.

8 The formula 60 50 t, wheretis the time needed for 50 beats, would give amore accurate rate since the inaccuracy is limited to the error in measuringt(which canbe measured to the nearest second, or perhaps even more accurately). answers are total profits, number of employees, total value of stock, and (a)Yes: The sum of the ethnicgroup counts is 12,261,000.(b)Abar graph or pie chart (not recom-mended) may be used. In orderto see the contrast of the heightsof the bars, the chart needs to befairly of students (thousands)54 Chapter 1 Looking at Data (a)Shown at right. The bars aregiven in the same order as the data inthe table the most obvious way butthat is not necessary (since the vari-able is nominal, not ordinal).(b)Apie chart would not be appropriate,since the different entries in the ta-ble do not represent parts of a of female (a)Below.

9 For example, Motor Vehicles is 46% since41;89390;523D0:4627:::. The Other causes category is needed so that the total is 100%.(b)Below. The bars may bein any order.(c)A pie chartcouldalso be used, since the categories represent parts of awhole (all accidental deaths).CausePercentMotor vehicles46 Falls15 Drowning4 Fires4 Poisoning8 Other causes23 MotorVehicleFalls Drowning FiresPoisonOtherCauses010203040 Percent of accidental (a) is strongly skewed to the right with a peak at 0; Figure (b) issomewhat symmetric with a central peak at 4. The peak is at the lowest value in (a),and at a central value in (b). distribution is skewed to the right with a single peak. There are no gaps or are two peaks. Most of the ACT states are located in the upper portion of thedistribution, since in such states, only the stronger students take the distribution is roughly symmetric.

10 There are peaks at .230 .240 and .270 . middle of the distribution is about .270. Ignoring the outlier, the range is about:345 :185D:160 (or:350 :180D:170). will vary. The distribution of coin years would be left-skewed because newercoins are more common than older (a)Among the women, 200 appears to an outlier. Amongthe men, the two high scores would probably not be consid-ered outliers.(b)The women s median is ; the rangeis 99 (101 to 200). The men s median is ; the range is117 (70 to 187). Generally, women have higher back-to-back stemplot shown has split does not seem to be a substantial difference be-tween the two groups; this is supported by the fact thatthe medians are (calcium) and 112 (placebo) almost identical. Before treatments, the two groups arevery the first two digits are used as stems, bothdistributions appear very spread out and one mightconclude that there are outliers.