Name:
Stat 1040, Spring 2006
_
Final Test, May 4, 1:30pm-3:20pm
100 -)
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. Show your work. The test is out of 100 poin~you have 110 minutes to finish.
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.
The following is part of an article from Newsweek, April 24, 2006. This question concerns the
Women's Health Study, described in the second paragraph.
.
Take an Aspirin and •••
BYJULIE BU~"GJ'je~D~j AND
NANCV:FERR4"-1 ~'.'.;;.<' .: ,
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. ·,.spirili'i$~;W6~d~~t1OJg,plain
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and
. ..... ; s. sliitp.".~~i:I1ii$~~~. it quells .
·inllanim~jIQiJ;:!atriie.dium doses, it
.........~;'J'!. ...:. ~Vl~$.;~~~~pai~relief; ,at low
'dosesj Itredu¢es:the'bliO(t~~:iIDmw toclot by
inhibiting·the~aCiiOnilf·tinY~biood ce'lIs called
··platelets~Jtmak.es ~eii$,e,;tn~n~tba(aspirin
might ~~Ip .ptev~~:cloi-"rel~:te~·cardiovascu­
larevents'suth as.·hearfa1ta~1( ~nd stroke,
even in: h~ithy:peopl&. (il"1988, thePhysi­
cians' Health S1\Jdyshowed exactly that. In
heatthYin~, 325mgof.aspirin taken every
other day formeyears reduced the risk ofa
I!l
firstheart attack by 44 percent. That was
great news. For men.
Itwasn't until March 2005thatthe
'WomertsJ~~~hStudy a"ddressed'aSpirin's'
benefits·forWorrien. H~w.ofuen~who
wereatleasi.4~Ye3rs oI~'at~startofthe .
study-who ·participated.in:th~StUdjtook ei­
ther100mg'ofaspirin ora'pla~bo every oth­
erday for' 10years. Surprisingly, thewomen.
taking aspirin e'xpenenced noreduction in "
heart~ attackrisk. However, aspirilltakers
were 17 percenfless likely-to have astroke.
(a) (2 points) Is the study controlled? How do you know?
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@(b) (2 points) Is the study blind? How do you know?
(8 points) The following table summarizes the number of milligrams of sodium per serving for
18 types' of breakfast cereal. Class intervals include the left endpoint but not the right.
Sodium
(milligrams)
tt
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Number of
cereals
120 to 160
4
160 to 200
3
200·to 240
6
240 to 280
3
280 to 320
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~ ~ 1Ifl3. (4 points) Suppose a jury of 12 peo'pi{ is randomly chosen from a large city's adult residents,
of whom 50% are female. What is the chance that at least one pW~on ~ ju;#J female?
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('O-:?e. For 167 college students the average handspan size is 20.9 inches, with an SD of 1.9 inches.
8.Q1. (a)
(5 points) Using the normal curve, approximately what percentage of the students have
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a handspan Of. more than 23 inches?
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(b) (5 points) If 90 percent of the students have a smaller handspan than the teacher, what
~ is the teac~r's handspan?
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(1f~5. For the 167 college students in question 4, the relationship between he~ght and handspan size
is summarized as follows: ~i~
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X height:
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handspan size:
@ (a)
average
average
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68.0 inches SD = 4.0 inches
20.9 inches SD = 1.9 inches
r
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=
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(4 points) Six scatter diagrams are printed on the back ~t the formula sheet. Which of
the scatter diagrams is the correct one for these data? Circle the correct one below:
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@ (b)
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(4 points) Using the summary statistics above, what is the regression estimate for
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handspan for a student who is 60 inches tall?
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(3 points) Find the rms error for your 8Jlswer in part (b).
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(3 points) What would the correlation coefficient be if we changed all the handspan
measurements to centimeters? (There are 2.54 centimeters in an inch).
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(4 points) I have 20 batteries, of which 15 workand theother 5 don't. I choose 4 batteries at
random from all 20 to put in my camera. What is the chance that all 4 batteries work?
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(8 points) In 2002, 17.5% of US tax forms reported incomes under $25,000. If the IRS takes
a random sample of 500 t.~ forms from 2002, what is the chance that between 17% an11iJ8~ .
of the sampled forms reported incomes of under $25,000?
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The 2002 General Social Survey asked "What do you think is the ideal number of children
for a family to have?" For the 497 females who responded, the average was 3.02 with a
standard deviation of 1.81. Suppose these 497 women were like a simple random sample of
adult American females.
~(a)
(7 points) Find a 95% confidence interval for the average response of all adult American
. . female.s.
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(b) (2 points) Is your confidence interval valid even though the answers don't follow the
normal curve? Explain briefly.
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II ~9. ¢' points) The following table comes from a simple random sample of high school seniors from
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a large city, each of whom was asked whether they had ever smoked cigarettes and whether
they had ever drunk alcohol.
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No Yes
Cigarettes
No
Yes
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281 500 781
46 1449 1495
·327 1949 2276
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.Test to see whether there is an association between smoking and drinking alcohol. You should
clearly state the null and the alternative hypotheses, find a test statistic and an approximate
Pvvalue, and state your conclusions in everyday language.
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(.il' points) In the aspirin study described in question 1, there were 19,934 women in the
aspirin group and 19,942 in the placebo group. There were 477 major cardiovascular events
in the aspirin group and 522 in the placebo group. Assuming the women were assigned to the
.aspirin and placebo groups appropriately, perform a statistical significance test to determine
whether or not aspirin prevents major cardiovascular events forwomen like these. You should
clearly state the null and the alternative hypotheses, find a test statistic and an approximate
r-,a;1-L-r-tr/-J-2-­
P-va1u.e, and state your con~lllsions in everyday languagEj.. I (J IJ~
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l~~ll. The long-held standard for normal body temperature is 98.6 degrees.
A group of researchers
believe that normal body. temperature is actually lower than 98.6 degrees. To test this, they
take the temperatures of 10 healthy people. They find the following: -J fr.wJ. cJ.~",,- ~
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98.2
97.8
99.0 98.697.8
98.4 99.7
98.2
f!~AtA
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Suppose this is a simple random sample of all healthy people and that tlie temperatures of
healthy people follow the normal curve.
!!l (a.) (2
p.
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normal curve, would your hypothesis test still be valid? Explain briefly.
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