STAT\t200\tHomework\t9 Due\tDate:\tNov\t11,\t2016 1. A\tnational\trepresentative\tsurvey\tof\tstudents\tin\tgrades\t7-12\tasked\tabout\tthe experience\tof\tthese\tstudents\twith\trespect\tto\tsexual\tharassment.\tThe students\twere\tasked\twhether\tor\tnot\tthey\twere\tharassed\tin\tperson\tand whether\tor\tnot\tthey\twere\tharassed\tonline.\tHere\tare\tthe\tdata\tfor\tthe\tboys: Harassed\tonline Harassed\tin\tperson Yes No Yes 183 154 No 48 578 (a) What\tis\tthe\tsample\tproportion\tof\tbeing\tharassed\tin\tperson\tgiven\tbeing harassed\tonline?\t(call\tit\t" )\tWhat\tis\tthe\tsample\tproportion\tof\tbeing harassed\tin\tperson\tgiven\tnot\tbeing\tharassed\tonline?\t(call\tit\t# ) (b) Is\tthere\ta\tdifference\tbetween\tthe\ttwo\tsample\tproportions?\t(Conduct\ta two\tsample\tproportion\ttest\twith\tsignificance\tlevel\t0.05) (c) Is\tthere\tan\tassociation\tbetween\tbeing\tharassed\tonline\tand\tin\tperson? (significant\tlevel\t0.05) (d) What\tdo\tyou\tfind\twhen\tyou\tcompare\tyour\tstatistics\tin\tpart\t(b)\tand\t(c)? [Check\tthe\tsquared\tz\tstatistic\tin\tpart\t(b)] 2. A\tPew\tInternet\tsurvey\tasked\tcollege\tpresidents\twhether\tor\tnot\tthey\tbelieved that\tonline\tcourses\toffer\tan\tequal\teducational\tvalue\twhen\tcompared\twith courses\ttaken\tin\tthe\tclassroom.\tThe\tpresidents\twere\tclassified\tby\tthe\ttype\tof educational\tinstitution.\tHere\tare\tthe\tdata: Response Yes No 4-year\tprivate 36 62 Institution\tType 4-year\tpublic 2-year\tprivate 50 66 48 34 For\tprofit 54 45 (a) Show\tthe\tdistribution\tof\tresponse\tusing\tbarplots\tfor\teach\tof\tthe\tinstitution type. (?barplot\tin\tR,\tcheck\tthe\targument\t'beside') (b) Is\tthere\tan\tassociation\tbetween\tthe\tpresidents'\topinion\tto\tthe\tquestion above\twith\ttheir\tinstitution\ttypes?\t(significant\tlevel\t0.05) 3. A\tsurvey\tof\t13,691\tCanadian\tstudents\twho\tenrolled\tin\tprivate\tcareer\tcolleges was\tconducted\tto\tunderstand\tstudent\tparticipation\tin\tthe\tprivate postsecondary\teducation\tsystem.\tStudents\twere\tasked\tabout\ttheir\tfield\tof study\tand\thow\tthey\tpaid\tfor\ttheir\teducation.\tA\tmajor\tsource\tof\tfunding\twas government\tloans.\tHere\tare\tthe\tsurvey\tpercents\tof\tCanadian\tprivate students\twho\tuse\tgovernment\tloans\tto\tfinance\ttheir\teducation\tby\tfield\tof study: Field\tof\tstudy Number\tof\tstudents Percent\tusing government\tloans Trades 942 45% Design 599 53% Health 5234 55% Media/IT 3238 55% Service 1378 60% Other 2300 47% (a) Construct\tthe\t6\tby\t2\ttable\tof\tcounts\tfrom\tabove\ttable.\t(No\tneed\tto\tround up\tto\tintegers) (b) Test\tthe\tnull\thypothesis\tthat\tthe\tpercent\tof\tstudents\tusing\tgovernment loans\tto\tfinance\ttheir\teducation\tdoes\tnot\tvary\twith\tfield\tof\tstudy.\tWhat\tis your\tconclusion?\t(significant\tlevel\t0.05) 4. Recall\tthe\texample\tof\tlongleaf\tpine\ttrees\tin\tthe\tWade\tTract.\tWe\twant\tto examine\twhether\tthe\tdistribution\tof\ttrees\tin\tthe\ttract\tis\trandom\tor\tnot.\tFirst, we\tdivide\tthe\ttract\tinto\tfour\tequal\tparts,\tor\tquadrants,\tin\tthe\teast-west direction.\tCall\tthe\tfour\tpars\tQ1\tto\tQ4.\tThen\twe\ttake\ta\trandom\tsample\tof trees\tand\tcount\tthe\tnumber\tof\ttrees\tin\teach\tquadrant.\tHere\tare\tthe\tdata: Quadrant Q1 Q2 Q3 Q4 Count 40 18 24 22 (a) If\tthe\ttrees\tare\trandomly\tdistributed,\twe\texpect\tto\tfind\t26\ttrees\tin\teach quadrant.\tWhy?\tExplain\tyour\tanswer. (b) However,\twe\tdo\tnot\treally\texpect\tto\tget\texactly\t26\ttrees\tin\teach\tquadrant. Why? (c) Perform\tthe\tgoodness-of-fit\ttest\tfor\tthese\tdata\tto\tdetermine\tif\tthese\ttrees are\trandomly\tscattered.\tWhat\tis\tyour\tconclusion. (significant\tlevel\t0.05) 5. Kiplinger's\t\"Best\tValues\tin\tPublic\tColleges\"\tprovides\ta\tranking\tof\tU.S.\tpublic colleges\tbased\ton\ta\tcombination\tof\tvarious\tmeasures\tof\tacademics\tand affordability.\tWe'll\tconsider\ta\trandom\tcollection\tof\t40\tcolleges\tfrom Kiplinger's\t2011-2012\treport\tand\tfocus\ton\tthe\taverage\tdebt\tin\tdollars\tat graduation\t(AvgDebt)\tand\tthe\tpercent\tof\tstudents\twho\tborrow\t(PercBorrow). Below\tis\tthe\toutput\tfrom\tR\tfor\tthe\tsimple\tlinear\tregression\tof\tAvgDebt\ton PercBorrow. (a) State\tthe\tleast-squares\tregression\tline. (b) Construct\ta\t95%\tconfidence\tinterval\tfor\tthe\tslope.\tWhat\tdoes\tthis\tinterval tell\tyou\tabout\tthe\tchange\tin\taverage\tdebt\tfor\ta\tchange\tin\tthe\tpercent\twho borrow? (c) At\tMiami\tUniversity,\t51%\tof\tthe\tstudents\tborrow,\tand\tthe\taverage\tdebt\tis $27,315.\tWhat\tis\tthe\tresidual