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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. _
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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 tr. . 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 ulnare ,3) WLtd Ci be .. ., _*. —Pm 9144 P0P»LQCL1,..L (SK/‘1
lacWm 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
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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. _ . _
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(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 BecletcL 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. «,/
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kiltt lira; 910(SaaPk>‘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 «KSr \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 pvalue, 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 pvalue
(with standard deviation 10 or standard deviation 25) would be smaller and why does this make
sense? (You should not calculate this second pvalue.) gm“ d a 1 ("l {jig \,g [til (51/\ [ 0 We LL} 1;,\ is: (L: . 1‘»!! (~31: in 'K because, {\1‘ (f5 ChiL9“ C K ' l b ._j .4‘ vii/ta VMM’i “no; divaver: “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 >HZED _. 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 (Cgl 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 2528, 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‘Iwjt.“ 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 (itLC“ Sac , C} \Y“ \(i LX111 ...
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