!!Midterm!1! ! ! ! ! Name:!October!15,2010! ! ! ! Section/TA!!The!exam!is!50!minutes!long.!!If!you!work!after!you!are!told!to!stop,!your!exam!may!be!invalidated.!!You!may!not!speak!to!anyone!during!the!exam!other!than!your!instructor!or!a!proctor.!!If!you!are!caught!looking!at!another!person's!exam!you!will!be!reported!for!academic!misconduct.!!Write!clearly.!!Short!answers!are!best.!!!!!1)!This!histogram!shows!the!distribution!of!the!number!of!reported!Facebook!friends!of!students!who!live!off!campus!(top)!and!on!campus!(bottom).!!a)!(3)!Approximately!what!is!the!median!number!of!Facebook!friends!for!!those!who!live!on!campus?!!Explain!your!reasoning.!!!!!b)(2)!!Indicate!the!location!of!the!median!on!the!histogram!above.!!c)!(4)!Write!a!short!sentence!or!two!comparing!these!two!distributions.!!!!!!!!2.!!A!math!teacher!brags!that!a!majority!of!her!students!scored!above!the!mean!on!her!last!exam.!!This!means!(circle!the!best!response)!!a)!the!teacher!is!crazy!because!this!is!not!possible.!b)!the!distribution!of!scores!was!rightSskewed!c)!the!distribution!of!scores!was!leftSskewed!d)!the!distribution!of!scores!was!symmetric!!3.!In!September,!2010,!the!Pew!Foundation!did!a!survey!and!asked!"All!in!all,!do!you!strongly!favor,!favor,!oppose,!or!strongly!oppose,!allow ing! gays!and!lesbians!to!marry!legally?"!!This!class!(and!the!other!Stats!10!sections)!were!asked!the!same!question.!!The!bar!chart!on!the!next!page!shows!the!distribution!of!responses.!!!!a)!(2)!About!70%!of!the!respondents!were!female.!!Assume!there!is!NO!association!between!gender!and!one's!response!to!this!question.!!By!drawing!on!the!bar!chart!above,!indicate!what!a!segmented!bar!chart!would!look!like!under!this!assumption..!Be!sure!to!indicate!which!regions!represent!male!and!which!female,!and!the!height!of!those!regions.!!!b)!(2)!Below!is!the!actual!ribbon!chart!for!the!data!collected!in!class.!!What!do!you!conclude!concerning!the!relation!between!gender!and!opinions!about!gay!marriage,!and!why?!!Circle!the!best!choice.!!i)!Gender!and!opinion!are!associated,!because!the!distribution!of!gender!is!different!in!different!response!categories.!ii)!Gender!and!opinion!are!independent,!because!the!distribution!of!gender!is!the!same!in!all!but!two!of!the!response!categories.!iii)!Gender!and!opinion!are!associated,!because!the!proportion!of!people!responding!in!each!category!is!not!the!same.!iv)!Gender!and!opinion!are!independent,!because!the!proportion!of!people!responding!in!each!category!is!not!the!same.!!!!!!!4.!The!International!Gini!Index!is!used!to!measure!income!disparity!within!a!country.!!A!country!whose!Gini!Index!is!0!is!one!in!which!all!people!make!the!same!amount!of!money.!!A!country!with!an!Index!of!1!is!one!in!which!one!person!makes!all!of!the!income,!and!everyone!else!makes!nothing.!!Below!is!a!scatterplot!using!income!disparity!to!predict!life!expectancy!for!a!number!of!countries!from!around!the!world.!The!data!are!from!the!CIA!Factbook.!!The!U.S.!is!at!!(45,!78),!to!give!you!some!frame!of!reference.!(The!data!are!about!2!years!out!of!date.)!!a)!(2)!Choose!the!best!interpretation!of!the!value!of!r2.!Circle!your!choice.!i)!About!19%!of!the!data!lie!within!one!standard!deviation!of!the!regression!line.!ii)!About!19%!of!the!total!variation!!in!life!expectancy!is!explained!by!the!regression!line.!iii)!About!19%!of!the!observations!fall!on!the!regression!line.!iv)!Predictions!of!life!expectancy!based!on!the!regression!line!will!be!correct!in!!about!19%!of!the!cases.!v)!About!19%!of!the!total!variation!in!income!disparity!is!explained!by!the!regression!line.!!!b)!(2)!Using!the!regression!line,!what!is!the!predicted!mean!life!expectancy!of!countries!with!an!income!disparity!index!of!40?!!!c)!(2)!True!or!False:!!These!data!tell!us!!that!by!decreasing!the!income!disparity!in!the!U.S.,!we!will!increase!the!life!expectancy.!!(Write!the!WORD!"true"!or!"false".)!!!d)!(2)!The!best!interpretation!of!the!slope!is!(circle!the!best!interpretation)!!i)!Countries!that!are!10!units!higher!!in!income!disparity!have,!on!average,!a!lower!mean!life!expectancy!by!about!4.6!years.!ii)!Countries!with!a!Gini!Index!of!0!(no!income!disparity)!have!an!average!life!expectancy!of!about!88!years.!iii)!All!countries!with!an!income!disparity!10!units!higher!will!have!a!lower!life!expectancy!by!4.6!years.!iv)!Countries!that!are!10!units!higher!in!income!disparity!have,!on!average,!a!higher!mean!life!expectancy!by!about!4.6!years.!!5.!(2)!A!large!number!of!students!reported!the!number!of!hours!they!slept!last!night.!!The!distribution!is!roughly!symmetric!and!the!mean!is!about!!7.5!hours.!!The!minimum!was!2!hours!and!the!maximum!was!10.!!Which!of!the!following!is!the!best!choice!for!the!standard!deviation?!! a)!about!1!hour!! b)!about!2!hours!!
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