Statistics 1040, Section 009, Midterm 2 (200 Points) Your Name:

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1 Statistics 1040, Section 009, Midterm 2 (200 Points) Friday, March 31, 2006 Your Name: Instructions: Carefully check whether you have to provide an explanation or not. In case you have to provide an explanation, keep it short. Just 1 sentence (or 2 sentences at most) will be fine. If you do not have to provide an explanation, do not waste your time giving an unneeded explanation. Question 1: Sampling (20 Points) -. ~t (Hypothetical) A survey is carried out by the finance department to determine the distribution of household size in a certain city. They draw a simple random sample of 1,000 households. After several visits, the interviewers find people at home in only 653 of the sample households; Rather than face such a high non-response rate, the department draws a new batch of households, and uses the first 347 completed interviews in the second batch to bring the sample up to its planned strength of 1,000 households. The department counts 3,087 people in these 1,000 households, and estimates the average household size in the city to be about 3.1 persons. Is this estimate likely to be too low~or about Circle your answer and explain clearly! 1

2 ~., j(i {{)qrj, 1~ 2fJd.5', ~~2., ~~ 2 t ~,A- I Question 2: Probability (40 Points) Professor J.S. recently experimented with homegrown chili plants. From 4 seeds that were planted, one seed germinated. Use this chance (25%) as the basis for all calculations in this question and assume that seeds germinate independently from each other. Show your work! -1 f:r uj... ~.ia-rri' C(fl""~~ ~ ~ r"j - 10 ru"::>i(}uto (,-1 %c tj% In a second experiment, J.S. planted 4 more seeds. Determine the following chances: 1. (15 Points) The chancethat all 4 ofthese 4 seeds will germinate is about ' 0.. 3' %. 3. (10 Points) The chance that at least 1 of these 4 seeds will germinate is about CE,3( %. ' '4., J III If..I _J ~, ". Nt XlA4t I Iv? ~~!{i ot ~.. wi ~ l~: \ - (ty;: 1- O. 3( {~= O. {g 3{=: tl..]. (10.If\. '-~4 2

3 A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving. The results can be summarized as follows: -l-m ~~.vnry -1 Average sodium = 240 mg; SD = 131 mg; X Average calories = 149 calories; SD = 62 calories; r = Show' your work! --l~kfd f~ ~ 4{))'b -..t /JIj!Mftvt 1. (10 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories., SO'. l3/ G).~~ -r,.~. ::,' CJ~t;) ~ ~ r.. l2.. 4 SD 6.l.. )(.~:;.~"o-~ '~X;:; l'to 'f(~::. iso- lu.tt ~ B.n_ G) ~,,",~...: I",~:= B./2 tc.l2 ~I G) err I-<0::: B. /1-1" U 2'Y I 2. (10 Points) ~redict the number of mg sodium in an one-cup serving of cereals that _ IJ-L has 200 calones per cup. -:1 ;1.% ~ ~turrd~. -1 ~DlJ,.~~.~~ ~ lui) (,~~~.?ul.(~-= t 3~ II f L12., lou ~ 1- ~.12 t ~J. V :=..2.' J. ~ 'L -Iif4 ~ ~~~~J-J.l 3. (10 Points) Find the r.m.s. error for predicting mg sodium from calories. r...u. ~ ;;, VI-Til. S/)"'1 z: VO.t-I'?J/ 1 f3 ( -~ ~ Uri ~~ I ::: \/1- IiS~ 2. I /3 ( ~ o. 111'1' 13/ i ea s;{)x ~4J..J.. vf... rod I - 1. _ I J1..1-~'oI.y~ =- 'JI-o~180j # lsi - die I 4- -t: L uk. 4. (10 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup.

4 Question 4: EV, SE, Normal Curve & Sampling (70 Points) Time reported in its March 20, 2006, issue on page 30: «74% Proportion offemale college students and graduates who said women on spring-break trips use drinking as an excuse for behavior like public display of nudity and table dancing." Assume that 74% indeed is the true percentage of all female college students and graduates in the US who share this opinion. Suppose an independent researcher wants to do some follow-up study and draws a simple random sample of 400 female college students and graduates in the US..-J. fr~ cj.~~ l/r1r/f Show your work! 1. (10 Points) Indicate the box model. -3 fvrr)h~~~~ c11~{ 11] ts ~,~ - s 4ke't'~ "" Lk'J ID I~. t ~ /J~ Jt;, ~.~. o:~~k~~ -t~.~uj~,~~~.tl.l. ~ I! /[J 'j -141 #~~~(If~ecmJ 2. (20 Points) The expected number of these 400 females in the follow-up study who share the opinion given above is 2. ~, with a standard error of about tg9 <B ~l frj.mi/fhmvrr.~~ lex fvw\_= ~ 4- m~ :: ll-::: 0_ tv. -S,Lr.tJ..~~.k{vf~ 6 r-----~. 7'" _ ~~I J.. ' / L..,J.'vr\. J _.6fp\.. lli.. J1:1_1.,_. I...,_ I\J'rK. SD- V ~ -=. V 108 lor) - V11- }q VO./J t«- 0.1(1.( E II~I(W\. -: ~o,\ O. H ::. ).~ if 54~ = ~.. F), ttlt -= 10 0& Itt ~ t..! ~ 3. (20 Points) The chance that at least 310 of these 400 females in the follow-up study who share the opinion given above is about f. '~K %.' -'q fr~~ ~ 1\ t S.lI.: ~O- J.~C - I~ I ~j ~(~'J,.~~JhL ~ - tr =: # ~ EIt, I~OS{; ~ I ~, 3ib ~.g :5~ ~ Eu.. tj -I( Y ~~ ~(,{ f 5il~ tvrt'\. 1d~ -/.(0 o-oj (. Co: 3'j, Oq 1. - ~ 4-r;"'~ A...tt.~ I '" I to ~ (dar, - (.10~% _ r: u fr1/ -~ fvr ~~ evre... ~ b ' ].. - ~ ~AMJvAit 4 L~

5 4. (10 Points) (Hypothetical) Suppose Time would have asked the female college students and graduates in their study: "On your spring-break trips, do you use drinking as an excuse for behavior like public display of nudity and table dancing?" Other things being equal, the percentage of women who would have answered yes f7:\ to is uestion would have been (a) higher than 74%, (b) about 74%, or ~ c much less t an 4 o. Circle your answer and explain clearly! JJ;, ~~~~~. -w~;;lh ~~ ir~ G) ;{kr~~aj.~~~,~~~ ~ IrJ.,J.~ ~ JI40 ~J 5. (10 Points) (Hypothetical) Suppose that you were asked by the independent researcher to conduct this follow-up study for him. It is up to you to determine how to draw a sample of 400 females that are representative for all female college students and graduates in the US and obtain their opinion regarding the question originally asked by Time. If you have the choice, the best possible way to draw this sample is: (a) Travel to South Padre Island in Texas at the start of Spring Break, go to the beach, ask women (as they arrive on the beach) whether they are college students or graduates, and then ask the first 400 of those for their opinion. (b) To avoid travel, get a list of all current female USU students and female USU graduates, draw a simple random sample of 400 female USU students/graduates, contact them by phone, cell phone, or at home, and ask them for their 0 (c) Get lists of current female students and female graduates from all colleges (and universities) in the US, draw a simple random sample of 400 female students/graduates, contact them by phone, cell phone, or travel across the country if necessary to reach them at home (this may take weeks!), and ask them for their opinion. Circle your answer and explain clear?,! IJ..L..IJ rio _ J L" ;f/., fk ~ w.k/... s J U ~ d1. ~ d4f ~J ~ upakq/q-:; JI" &{S ~ ~tj.. i: Cd. O~[J j;, ~ A~ fnjt ~ ~{ W ~ M-Amntl~Ul\i~ ~, ~A ~(A(tl ~'rrnlx~ ~~ v{ ~ f,{sbt ~f f lak ( ",.).. j4d. ~ _/tvif ~,.l.'y(, ~..v, i:» f,ts tilarm I ~~), P.S.: ifyou hav~;;~~~ been to South Padre Island or a similar location during Spring Break, take a look at Web pages such as htm and think again whether the percentage reported in Time might be true or whether it is totally far-fetched... r::.j 5

6 C~.. ~*~J ~:~~00~1 ~,I) L_; fpp ~'J.fJ, p. 312, ~1- ~""d-~ - I.f -O.h~l')/. ~l YM(oLf.0 J j~~ 1004 ~~1, ~firl «i; So- Jooo{j 'b.(j{jo '~ Question 5: Chance Errors in Sampling'(30 Points) - ~.~, = V it.,~. --=----- es V,"'fN oc>~ OIlu Five hundred draws are made at random from the box '" ~:: O. i{~:). 1 60,000 x []:::I 20,000 x [IJ~ E~"" =: ::;;!l{..... tt True or false? aircle. our answers. No explanation IS,l!eeded...'I:"":J-, d,''9,. ~sc(n\.. : V SOc) V~3 ~ is, " 1. (5 Points) u "" false: The expected value for the percentage of l's among the draws is exactly 25%.. EV% z: 2.s"ro. /).Q~,. 5E«= ~J.6g '(Odd ::r.~~% s, ) ((1 '$"(JO I Vt::..15% (f) '. ~ l% 2. (5 Points) True /QTheexpected value for the percentage of l's among the draws is around 25%, give or take 2% or so. '}v{ L.-r~ Jk.~~ f<ia ~ 4- ID~ ~ ~~ (wial.. i, 2 5 "fo --M ~rrr ilw4) 3. (5 Points)~alse: The percentage of 1's among the draws will be around 25%, give or take 2% or so. /)ll Ca.L~:. ( ~.~ Jt,r ev% ~ 2~~fo 1M ~ lr1:a~ 0( ~ Sf %~ J %).~ 4. (5 Points) True ~he percentage of l's among the draws will be exactly 25%. ' Au ~ 01- [fjl ~ ~ l.:!!o ~Jl!:i±:~~ J. 510 (tj;.j.~.k ~ ~ tr 1S1,,) 5. (5 points~alse: The percentage of l's in the box is exactly 25%. -".~, rj.jl ~~, ( i.; ~ ~~. cr1- l1t~ =1 ') '1") '. t 6. (5 Points) True / false: The percentage of l's in the box is around 25%, give or. 'take 2% or so. '. '1A-t Ln-N ~ Jf4 ~ u? [fj'5 ~ 1A~W\{/l'.(.Jnt) (,J;.J..;" 2«;1, - ~'r<~;f"k)

Part 1. For each of the following questions fill-in the blanks. Each question is worth 2 points.

Part 1. For each of the following questions fill-in the blanks. Each question is worth 2 points. 1. The bell-shaped frequency curve is so common that if a population has this shape, the measurements are