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Sec: 2 Stat 221 — Midterm 1
April 27, 2001 You have 50 minutes to complete this exam. A page of formulas and a random number table 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. Good Luck! CLOSE to HOME 1— I) The 1991 World Almanac and Book of F acts contains a section in which it lists “noted
personalities.” One can calculate the lifetimes of these people by subtracting their year of birth from their year of death. A histogram of the distribution of the lifetimes for the 232 people listed
in the “noted politicians of the past” category is given below. 30 40 50 60 70 80 90 100 (a) (1 pt) What do the numbers along the horizontal axis represent? m @1365 01} m ”Pouﬂcmmg %\r'I/L.L (Page 2 (b) (1 pt) What do the numbers along the vertical axis represent? . .
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QC} ‘6. S ‘:__""._Ei"‘,‘,.“ (M' »\‘.\ “'7 y 9/ (c) (2 pts) Roughly what proportion of these politicians lived under 40 years? \ gm" . \ . f .:I_‘._ ‘.\ I“; (1 f3“ 1' J "utJi 1.1 1 . , .ﬂ: 1‘,\ (d) (3 pts) Describe the distribution (remember our “checklist’ﬁ
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879a LC MUN, 65 (323 ((365.33 t it” 2. : ‘ (e) (3 pts) In this data set, which would you expect to be longer, _the mean lifetime or the median lifetime? Explain M WLQ diam _ £5 gm Poulh Mm.” augpi 6LT ..
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bf L0" “’ 0‘2 VJ/C UAWi < Vii 1341' 1}»: r 01.; (12 ruiu (it «TN m i. : (1“le / ‘5’ l! L, u 3) A statistics professor wants to estimate the proportion of women living in San Luis Obispo
county. She randomly selected a page from the 1998—1999 SLO phone book (page 40) and then
randomly selected columns 1 and 4 on that page. She found 166 listings with the following
results: 36 listings had both male and female names, 77 had male names, 14 had female names,
34 had initials only, 5 had pairs on initials. (a) (1 Pt) Identify the population in this study. .
 W0 met/1 m Sam Luff 019: 33,2; 0 .\, (b) (1 pt) Identify the sample in this study. 1 ‘7 {A .~
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, x (d) (3 pts) Do you believe that this sampling technique will give an unbiased estimate for the
proportion of women living in San Luis Obispo? Justify your answer. If you think the estimate
will be biased, explain whether you think the result will be an overestimate or an underestimate ofthepopulationvalue.MS 001le bC biﬁtiz‘cl Mamet LH/Ug fw
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[/ULWU cl 10x 6cm WINA { J 1'. K .  5) (5 pts) You have torn a tendon and are facing surgery to repair it. The orthopedic surgeon
explains the risks to you: Infection occurs in 3% of such operations, the repair fails in 14%, and
both infection and failure occur together in 1%. What is the probability that a randomly selected operation succeeds and is free from infection? _ __ ' __ 12 3.5mm UlePwu : "PU: UP} =
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standard deviation. “Ties” are allowed. Explain youﬁirreaspﬁg:
, , (d) O, 0,10,10,10 (a)0,0,0,10,10 (b)5,5,6,7,7 (c)0,5,
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E g3mallrStE—vLquﬁ : 1030/) u 2) A 10year, 10city research project, ﬁnanced by a branch of the National Institutes of Health, announced results on Friday including that:
children in high—quality day care programs scored better on
language and thinking tests that those who stayed home — Associated Press, 4/20/01 (a) (1 pt) Identify the observational units in this study
0W \dvem u' (b) (1 pt) Identify the explanatory variable in this study (make sure to phrase this as a variable)
when/m v a can cl aﬁr v d 5 day Caz/"C C V Smk/ S how i C) 1,.
(c) (1 pt) Is the explanatory variable quantitative or categorical? CCLTE‘ 301i c etc (d) (1 pt) Identify a response variable in this study.
75 3+ Sam (:7 S (e) (3 pts) Was this an observational study or an experiment? Explain.
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(t) (3 pts) Suggest a potential confounding variable in this study. “P‘ “ll/U2, am i at: in in clctUCm (1:; co vital b1 4,; lairmat U]
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@46 pts) 7) ___ _(8 ptS) Total W" H (50 pts) Total ‘ L} 3 4) Inoculation is the practice of deliberating exposing someone to a disease in the hope that they
would develop a mild case and then be protected from severe cases. On June 26, 1971, Dr.
Zabdiel Boylston conducted one of the ﬁrst inoculations on the American continent. He
inoculated 247 people, six of whom died. By his count there were another 5,759 people in
Boston who were susceptible to smallpox. Of these, 844 died.
(a) (1 pt) Based on the results of Boylston’s inoculations, what is the (empirical) probability that
an inoculated individual would die of small pox?
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BOA Del/Lillircl) ' (b) (1 pt) Based on Boylston’ S data, what is the (empirical) probability that an uninoculated, but
susceptible, individual would die of smallpox? ?(wwmoc g :1 "l
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?( ﬁ>1ﬁ§§blﬁ£ﬁmiykqucy ra)5 (c) (1 pt) Irrespective of whether they were inoculated, what was the probability a susceptible
Boston resident would die of small box during this time? chdl/IS ,_ 860MB _.
ﬁ(§cmpﬂb® / (DOOLQ/ — elfll— 15.1% (d) (3 ptS) Are the events inoculation and death by smallpox independent or dependent based on
these data? Explain. MP6? lCLQl H W ,PCA IB>~ . 1304) j%%,m
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20 lbs. and a standard deviation of 5 lbs. (21) (2 pts) From this information, what is the smallest weight gain you would expect to see for
one of these horses? Be clear how you get the value. 5 “05 J? Tl/llj Wo’vtic'l EC 37 ﬂT'at‘idmv Cl /\
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(b) (3 pts) Between what two values would you expect to see 95% of these weight gains? ”Bax/veers lO amcl Z) 0 lbs . 016“’).. 5b Val/Lu: J”
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l0 (.lo W W VCLAl/L‘LQCL/VLQ a. 1": ) L (c) (3 pts) You are asked to design an experiment to assess whether a new feed improves the
weight gain of horses. You tell the rancher that you will randomly assign the horses to two
groups. Explain to the rancher the primary purpose of this randomization. WUL?HW1CLWJ PvLVPOst O? VCLUICLOYIH:a‘:(L.”'fH'_1..\ [3 %
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\\ Extra Credit. In a rodeo roping contest, a contestant 5 score is the “average” of two times.
Explain why it is more fair to use this combination of two scores instead of relying only on one score. 7“ 'PthJdJ/WATJ ill/KM W VDPCV Willi [(0 WCLL ll ltlttcaml «.1111. to 1111:... $11163 lam}. ,. '1. 11.1'. .f g‘ ‘1 . «I "3.1 ' '41' ‘
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