Stat221 s01 midterm2

Stat221 s01 midterm2 - Al Name Sec g 2'— Stat 221 —...

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Unformatted text preview: Al.. Name: Sec: g 2'— Stat 221 — Midterm 2 May 18, 2001 You have 50 minutes to complete this exam. Two pages of formulas and several tables are provided. Do not write on these pages. You may use a calculator. You are not allowed to use any other books, notes, or other external aides. Please show all of your work and EXPLAIN your answers. Some problems have multiple parts, but generally the parts do not have to be answered in order. If one part of a question does use the answer to an earlier part that you have not been able to answer, you may use a suitable symbol in place of the answer in working the later part of the question. If you made an approximation or an assumption, be sure to note when you have done so and why. Don’t spend too long on one question. Tentative point allocations have been given to each problem to help you manage your time. If any questions arise during the exam, or you need any terminology clariﬁed, please do not hesitate to ask! Please return the formulas page at the end of the exam. One more formula Expected value of discrete random variable, E(X) = E x p(x) Good Luck! .- 1) For problem 1, answer 2 of the 3 questions. Here are several statistical statements. In each case, explain to someone who knows no statistics what the boldface term means. Use just a sentence or two. Relate your explanation to the context provided Be very careful with your wording. (a) (3 pts) A spinning penny has probability .6 of coming up tails. _ 1M. ‘3 (J Li/L/t/LLH j PM“ Lia, WM Low/Mi Wk "lat. i5 {00% 0L m {time , wbqu oust-m3 ct Lemming 15+ch Pit :‘L if“ ) Kyla/Nd! ﬁrm/W51 'tL'I/‘t'ee—AJ bt WLLL MW ‘31?de -ta.t:'.g gt Hp (“V- (got—m 9L. am at ‘t g . .. (b) (3 pts) With 90% conﬁdence we can say that the national unemployment rate for April was between 4.3% and 4.5%. y 0‘; (4 ,t a t-r. . t. L_.\ IN CDMLéthALL 5:444:th autumn-"c: HM yL.\)(,t_{C‘-riton_ pot. target ._Q;--.:+c: >,| WE Wat/(LA be. 901., (‘IME [cutter Wad “ii/LL ulna-re ,3) WLt-d Ci be .. ., _*.- —Pm 9144 P0P»LQCL1,..L (SK/‘1 lac-Wm t- ‘1 +529 A .4 +5 5?? , .l ' '-' -; \\__~1 _gtla,i ., . ‘ (c) (3 pts) The expected winnings on a \$1 lottery ticket are \$0.53. 1 .. 3) Cal Poly is considering switching from quarters to semesters. Suppose that the administration decides to survey student opinion and plans to change to semesters if more than 50% of students indicate they prefer the semester system. SupposéTlTeEEfﬁ proportlon o o y stu EELWHO favor semesters is_4_. (a) (3 pts) The administration is debating taking a sample of n=100 students or n=500 students. The following histograms of sample proportions came from simulations of 1000 repetitions of asking Cal Poly students whether they prefer semesters. Which histogram goes with which sample size? Explain. 8 8 § ‘1 O Nunber of sanples S Number of samples 8 8 8 8 8 _- O 0.30 0.32 0.34 0.35 0.30 0.40 0.42 0.44 0.40 0.43 <———-—-—— ’0 hwﬁpﬁoo n:% \OO_ ‘0' tie. _ mum. Mrtdﬁé "duel; 31mm Scum ild Q_ (b) (2 pts) Which sample size (n=100 or n=500) is more likely to produce a sample proportion eater than .50? . .\ _ ﬂ. _ . _ gr - n :. 6 C) D \ _ i 2 ‘ , r . . r" 3 r 1’ - ' r f 1" “Ali -~. _' ’I_ it ~. ‘ - \‘l l - "I {if I ‘_\,' ‘1 7 _ ‘ ’. .1 1 -.-r -!.~..".-,l ”ll +1.. Ulla?) {I ' i L x H (c) Suppose that Becky and Heather plan to take separate random samples on their own. Heather will use a sample size of 100 but Becky will use a sample size of 250. Both plan to construct a 90% conﬁdence interval from their sample data. 1. (3 pts) Before they collect the data, which woman (Becky, Heather, or the same) has a better chance of obtaining an interval that will contain the true population proportion? Explain Becletc-L Lffdlttiﬁ w ( Lem pndréthzigkt M ”Lil's-“l, Ktt WLLL LC (1; .’C( to “like, WHITE‘LQ H{.‘\»Ll_( (‘lfg [x km" 153m its \. r“ H, Kiln, ”U K K (\Nijflﬂ ‘(\l' l 7? 2. (3 pts) After Collecting their samples, one of them reports the interval (.333 .435), the other ' 3 reports the interval (.350 .402). Explain which interval goes with which woman and how you decided. -«,/ 3 ) , ”5 (.63- ?prtBBCfUL lbw/x ‘lkajlwk bRCﬂ-Muae an. (_ kiltt lira; 910(Saa--Pk>‘l’t( (ttrﬂvfkl V” l ”C iCt/LCQC» \ / - 5) The Survey of Study Habits and Attitudes (S SHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow approximately a normal distribution with {9293—1—1— 5. You suspect that incoming Freshmen have a higher mean since they are often anxious about entering college. You take a simple random sample of 20 incoming freshmen and ﬁnd their mean score to be 116.2 with standard deviation 25. (a) (2 pts) Deﬁne the parameter of interest here in symbols and in words /Vt == mam Seem 5'5 «KS-r \l 5 (b) (2 pts) State the null and alternative hypotheses to test whether freshman score higher on ' 5. average than the college population in general on this exam (in symbols and in words). f'. .'; i l ‘._.A_ ' U L(.( . K7, '. (c) (8 pts) Carry out the appropriate test of signiﬁcance. Make sure you check the technical conditions, include a sketch of the approximate sampling distribution, calculate the test statistic, approximate the p-value, and state your ﬁnal conclusion in English. ' ... D c, ‘ @ ?0 but vie!- .mi‘ f '7.- or“ Eggs—£— ‘7 sic.) ﬁgs. as.) , WV <5: “av—WW2— :2. .4—22. , i" lid/tie .40 Val? H; “Ho 5/ 4 _ 1 (d) (3 pts) Suppose the sample standard deviation had been 10 instead of 25. Which p-value (with standard deviation 10 or standard deviation 25) would be smaller and why does this make sense? (You should not calculate this second p-value.) gm“ d a 1 ("l {jig \,-g [til (51/\ [ 0 We LL} 1;,\ is: (L: . 1‘»!!- (~31: in 'K because, {\1‘ (f5- Chi-L9“ C K ' l b ._j .4‘ vii/ta VM-M’i “no; div-aver: “7‘14 J CELL l at 3 rd 1/; (j ; “HJ -" L/ 1 ‘35 -.n 2) The temperature at any random location in a kiln used in the manufacture of bricks is J normally distributed with a mean of 1000°F and stande deviation of 50°F, (a) (3 pts) If bricks are ﬁred at a temperature above 1125°F,‘ they will crack and must be disposed of. If the bricks are placed randomly throughout the kiln, what proportion of bricks will crack during the ﬁring process? Q _—. -i_~’—‘3«--1~:I.Izr5 P >HZE-D _. W :-, . Lily"J - :5 -.r'l""\ ‘ 'i\ (I Lllé) ”U" [l' Ant». \(ahh‘ "ll, :. ﬂail?) ‘\w‘;i\000 dyL‘ Rt \I‘t\ \lt‘\_.‘0li\\v)\_l't!‘\ E70 . * ﬁg {‘ if‘-")(,\ " ': C J ”2.5—"; {Jul #- % (/ng SID/22's {__Ppto‘g . 4'6 £124) W’ LIL L i\LV 61 C Id... d. that (Cg-l- VJ—Q CU g '3 i.» “1.6 rd ﬂ ' “J (b) (3 pts) If the temperature is too low, the bricks miscolor. Suppose you notice that 3‘% of all bricks miscolor. Use this information to determine the temperature below which thebrlcks miscolor. 1 ‘7 " 2: f(6 NS) 3)—{ U (6 pm) (0—? 48‘ (15 ptS) __(8 pm) 5) I A (15 pts) EC) 7 L IJJ Total (50 pts) ‘l 053 ‘ Extra Credit: Suppose you plan to construct 51conﬁdence intervals. Let X = number of intervals of intervals that capture the population parameter. Name the distribution that this random variable follows. Sat/APR di‘i—‘Tﬁbul i0 V‘\ x 12.34.; ~.../ 4.: continued ﬁom previous page t_/ (d) (4 pts) The student body government decides to pose the question on the school radio station (KCPR) and ask listeners to phone in. Suppose they ﬁnd 90% of 67 voters favor semesters. Give two distinct reasons why it would not be reasonable for them to construct a conﬁdence interval for the proportion of Cal Poly students who favor the semester system based on this sample. 1) @( reasononeim wig—ALE Wlxw CCU/L m QbVLottS WMT 1‘ . (yf CHCL‘leCCi ‘v’r LttttciI us: ﬂiicd / in U! ‘L(_ l. «..Jt'JLi L reasontwo; Usl’ 'Eé. We»? a 33“.. pin Vt (U ‘gcl mitt 33m“. sf} (Q 4) A Gallup poll conducted on October 25-28, 2000 asked a random SW11: “If you were a young man and looking for a bride, which would you prefer — a young woman who is very pretty or a young woman who is not pretty but has a lot of money?” (The interviewers rotated the order in which the two options were presented.) The sample results were that 55% of the respondents said they would prefer a _pretty woman (a) (2 pts) Identify (in symbols and in worm‘lation parameter of interest in this study Ml Kr? :71“ V‘JJEH‘O‘W WM thto {71‘de CL. sit-"LLTT‘I-wjt.“ J ’ c t» (5‘: CL v x (b) (4 pts) Use these sample data to calculate a 90% coriﬁdence interval for the relevant parameter. tﬂ»t.eerte4ewliéiit7iﬁi¥§l .531: .0343 0207., aJ:—=>(.5Il'+/ e 322? 743;) (c) (2 pts) Based on this conﬁdence interval do you think it is plausible that men equally prefer a pretty bride to a rich bride? Explain how you decide. (41)) (It EL ?{0LM4 Lib LC bC (L CLLL,L_QM m M ka ac ii U W?Wm§ a ﬁvuwdfh~osvb go cf _ . vL-"XCY (Li Ltfw HE: 'V'L,-t(L‘\§;1W,L{v—.i “A {M L “I ‘ CL J l t 0’1 a (Z5 {:7 q: x , d K but 3” “3 (it-LC“ Sac , C} \Y“ \(i LX111 ...
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