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Unformatted text preview: SD\WJ<'\\OV\S "(‘0 %a%”w Pix/\aﬂ. &W 1 (5 points) Consider the set of points {(—2, 5), (—3, 7), (—4, 9), (—5, 11), (~10, n)}. What should 7?.
be so that the correlation between the x— and y—values is l ? II
p g=—2x+\ {Es image‘slobe. “\‘D \ht‘mﬁe. Pf: _‘_ 2. (5 points) Let X denote the number of customers who enter a bank in an hour. Suppose X has a
Poisson distribution, and that P(X = 0) = 0.05. What is the average number of customers entering this
bank in one hour? ?(X=07 = 65* =— 0.05 m: ~ QnCO.o%3>”=> 3 3. (5 points) In a study of high school students, a positive correlation was found between hours
spent per week doing homework, and scores on standardized achievement tests. In fact the correlation
coefﬁcient was 0.95. The investigators concluded that doing homework helps prepare students for these
tests. Does the conclusion follow from the data? Answer yes or no, and explain brieﬂy. no. CDWQUJHOW CLOQS has": “NW“! Cat LiSCLHO“ , 4. (20 points) An article in a medical journal found that percutaneous nephrolithotomy (PN) had a
success rate in removing kidney stones of 240 out of 300 patients. a) Find a 95% conﬁdence interval for the true success rate of the PN procedure. 9: 140/500 2 0,8 — Sowwph— Vocal—Run
0k. 655? (:1 got TL L Qerch—chx quom‘w)
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500 b)How many patients do they need to survey to estimate the true success rate of PN to within ::2% with 95% conﬁdence?
C... (5': catnip]? in?) \l/ 0.02. 2. \. (be
‘‘> in: PCPP) (“BE—i)
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Y “3° P©~V~> 9 n: act—0 5. (20 points) The sodium content of twenty 300—gram boxes of organic cornﬂakes was determined.
The sample mean and sample standard deviation (in milligrams) are: :T: = 129.75 and s = 0.88. The
manufacture claims that mean sodium content of this brand of cornﬂakes is 130 milligrams. Conduct a
test of signiﬁcance at or = 0.05 to determine if the the sodium content is different from 130 milligrams. a) State the hypotheses H0: ,LL=I5D
Ha «LL. 7E £50 b) Calculate the test statistics and determine the pvalue «(x.20, a§=xq asp. +~Te$+ 32 Hex {7.an  s30
: =. 2 —. L27
S/m 0.2.3 /’r—.a_o Pwvoaltwa: PCltl> is 71) "= ixou {OS 7*" (9.1l "POL do «dc Maud .Ho 6) Write the conclusion in terms of this problem. TM is \t‘xc QU‘wLWm swecawﬁeg) ﬂed:
m SDCLLULM comm Es. &W* Mm \°> O W‘ ‘5.
d) Described the type I and type II errors in the context of this situation. Type I error '. Con exuding 46A? m’eQ‘n BWLK'WM
GDVYlTe/‘N’c is NoT V60 ”mg vim ‘1“ $31" K’V‘BS TYPQ‘I «cure—r: QaanLLOLi‘Mv‘) *le WW Sodiwm
COMM is (50 Mg mm H‘ is. not. 6. (15 points) In an article in Statistics and Computing authors investigated the age (x) and length (y) of 25 captured dugongs (sea cows). Use the accompanying SAS output to answer the following
questions. The HEB Procedure
Model: MﬂDELl
Dependent Variable: length Number of ﬂbservations Head 25
Number of ﬂbservations Used 25
Number of Observations with Missing Values 1 ﬁnalysis of Variance Sum of Mean Source DF Squares Square F Value Pr ) F
Model 1 1.31333 1.31383 43.43 (.0001
Error 23 0.32331 0.02?10
Corrected Total 24 1.33?14 Hoot MSE 0.16462 RSquare EEEEEE Dependent Mean 2 .33180 ﬂdj HSq W Eoeff Var ?.08043 Parameter Estimates Parameter Standard
Variable DF Estimate Error t Value Pr > it:
Intercept 1 2.01175 0.05352 3§FE$ £23001 age I me (am
5 lo a) Obtain the equation of the least square line for predicting length from age. 320.02% 'x ~l— 9.9011
.. a052,, \f 2—. \wojt’k. b) Predict the length of a sea cow when its age is 5.
A \3 (‘53 = 2\‘S_l c) The observed length of a dugong at age 5 is 2.02. What is value of the residual?
e = 2.09. —. 248—1 2—. — 0437 (1) What proportion of the observed variation in length can be attributed to the linear relationship
between the length and age? 1* 15“!
R " iaa‘l emsz b‘g “\‘ka— {3wa Variedtam in D’s/423:“
CM be WHOM 4:0 HQ. \NW Y‘Q‘Q‘Hma3 t. e) Roughly what is the size of a typical deviation of points in the scatter plot from the least square '
line? 04578 A
6 = 200T M315 = 0.465 i) What is a 95% Conﬁdence Interval for the true regression slope 6? Interpret the resulting interval. b=o.ca¢l d§=n_2 =25~2=23
353:0.0443 8‘: 2.066?
b i(.t*)° 3b :COtol‘l) i (2.0667)XC0.O4'5’3 (0.02044, 0903772)
We're 652 W'aﬂmi that F.) 6(0‘020‘4‘9‘, 99.03773) 7 7. (30 points) Regression method were used to analyzed the data from a study investigating the
relationship between compressive strength :1: and intrinsic permeability y of various concrete mixes and
cure. Summary quantities are n = 14 Zm=% 2 as? = 157.42
2 yz = 572
Z yf = 23, 530
Z (actya = 1697.80
a) Assuming that the variables are related by the simple linear regression model, determine the equa— tion of the estimated least square regression line that you would use to predict the intrinsic permeability
from compressive strength. s
Sm =2 25“. e5 19: 3“; = ~— 2.33
SW 2189."! a = if b; .; 4.39:)! 5x1 t. .— 53,06 b) Estimate the error standard deviation 0. §$E= Sva‘bsyy 7 22057 . SSE _...
8=JM$E :JT * “33$ c) Calculate a 95% conﬁdence interval for the slope 5;
_ \o' =  .2 .. 53
A
Sb SXX $1.5, 35 if“ dﬁrltt1= {2. => 12’": 2.,th
235 :i: (14760x 0.2:? ~133i0ﬂ5‘1 —> 02.612. 4.74) ) d) What proportion of the observed variation in intrinsic permeability can be attributed to the linear
relationship between the compressive strength and intrinsic permeability? see 2205! “
R1: \*"' :— \""' .———“"' — CL
SST itself? 86 6) Carry out a test of appropriate hypotheses to see whether there is in fact a linear relationship
between the two variables. State the hypotheses, calculate the test statistic, and write the conclusion in
terms of this problem. He: P10
Hoe: {titO 9—... T— ‘io.8(> .112. t
t: Y m 2 :; :~—8;6 37177 i (J {no.8étS 01" Ho‘ @220
Hn‘ 94:0 rt: b/Sb =— 2‘33/e.2'l Crg'gw p—UaﬂML =:.. o ) 1—,) W97} Ho
TM c9—a:\~a Sou—QM W9§3 0‘ new QLW
Miss—HmsﬂA/Cy‘o WW Hon. ‘JYLUO Umiaﬁslﬂg 8. (10 points) . A tutoring service offered by a statistics department has been staffed with the expecn
tation that 1/6 of its clients would be from the business statistics course, 18 from engineering statistics,
1/3 from the statistics course for social science students, and the other 1/6 from the course fer agriculture
students. A random sample of 228 clients revealed that 45, 70, 83, and 30 students from the four courses. Does the data suggest that the percentages on which stafﬁng was based are not correct? State and test
the relevant hypotheses using 0: = 0.05. a) State the hypotheses . _L_ __L_
Ho:Tf—1="G:ll2."‘Jgrﬁa= '33; Tia": C: HM Ho ts, Moi don/UL b) Calculate the test statistics and determine the pvalue Obs 4‘3 ' ’70  853 30 n=1za
eye 38 74:: 7(3 3 8
ategz’ 72 Ga ‘11 39‘
([1 : 31 + at; 4M 69 0) Do you reject 1%? Write the conclusion in terms of this problem. Din UJVMLM 3+4;ngva was bamji Me Mai 10 ...
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 Spring '08
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 Statistics

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