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Points Stat/Math 390, Spring, Test 3 (Final Exam), June 5, 2009; lVlaeran 1 1% esearcher A performs a twosided, twosample ttest, computes the p—value, and ﬁnds it to be less than
04. Researcher B performs the same type of test on the same data set, but has labeled the two populations
opposite to A. Which of the following is most true? a) The two p—values will have opposite signs. c) Depends on the data.
he two p—values will be equal, period. d) None of the above.
{2‘ 2. A computer printout gives the number 13 as the 95% lower conﬁdence bound for a population mean (/1). Circle all the correct interpretations.
3, here is 95% probability that the corresponding interval covers [1.
Q We can be 95% conﬁdent that n is larger than 13.
c We can be 95% conﬁdent that n is less than 13.
There is 95% probability that ,u is larger than 13. d)
1 . The sample mean and sample standard deviation (8) for a quantity are computed to be 370.69 and 24.36, respectively. Suppose you had believed a priori that the true mean ,u would be at most 360. Does
this data contradict this prior belief? on’t answer that! Just circle the one with the correct hypotheses.
a)H0:§§360,H1:§>360. éHOZ/LS360,H11M>360.
b)H0:EZ360, H1:E<360. d)H0:,uZ360, H1:,u<360. 1 An article “Agronomic Performance of Winter versus Spring Wheat,” presented the results of an ex— periment to compare the yield (kg/ha) of Sundance Winter wheat and Manitou Spring Wheat. Data
on mean yield from 4 test plots is given in the Table. What kind of test must one perform to see
if the true average yield for the winter wheat is more than 500kg/ha higher than for Spring Wheat? Lot 1 2 3 4
Sundance 3201 3095 3297 3644 aired 2—sample t.test c) Chi—sqd test of homogeneity
Manitou 2386 2011 2616 3094 b) Unpaired 2—sample t—test d) Anova F—test {2 u want to test to see if two population means are egfial or not. Circle all the appropriate tests. a) 2—sample 1—sided t—test —sample 2—sided t—test NOVA with 2 populations d) chi—squared 1 6. A regression model of the form log(y) 2 04 + ﬁlm + 62m2 + 63m4 is used to ﬁt 100 cases of data. The
degree of freedom for the resulting sum of squared errors (or residuals) is a) 100 — 2 b) 100 — 3 @100 — 4 d) cannot be determined, because of the log. 2 "l7. n investigator wishes to estimate the difference between population mean lifetimes of two different rands of batteries under speciﬁed conditions. If the population standard deviations are 3 hours and 4 hours respectively, and equal sample sizes are to be selected, what value of mthe common sample
size n will be necessary to estimate the difference to within 0.5 hour with 95% conﬁdence? Show work! ._ I L L
mag): HL +3711 :7 AM J— 314.4” = 0.;
W n
:DS ‘. ['754— 5/: 7 %> M: l‘l.b z) VL:38L[.,Z J? ’o
‘ 2‘
4.25 8. Suppose sample of size 711,712, and 713 are independently selected from three different populations with means lab/12, M3, and standard deviations 01, 02, 03, respectively. It can be shown that the quantity 0 2 T1 — %:r—2 — 5’73 has a normal distribution with mean given by 6 2 ,ul — $112 — $113.
2 a) What is the variance or standard deviation of that normal distribution (in terms of the notation deﬁned
here)? 2 b) What is the 95% conﬁdence interval for 6? You do NOT need to derive the answer; simply write it
down. If 9. sample of 319 font—seat occupants involved in head—on collisions in a certain region resulted in 95 I" who sustained no injuries. Does this data suggest that less than one third of all such accidents result in
no injuries? State the relevant hypotheses in welldeﬁned notation, compute the pvalue, and state the conclusion in words (04: 0.01). 77 s fVafaV—hrg A .a‘/ S‘qu [Haj“Ink;  (Q) “a 32% z = P‘W = (“lg/M)“ V3 43; “MS” W
_' Wlassﬁwflv, “v.70. 7‘” 9 9—,
I f 5 J47) Hr. ego—12g) w w w. \LvJu: lev(%<—\H7 : 0.033>’>°4 —7 Gwﬂ—Hjuﬂ’ra "‘4 lam/W #H, (D X LELlO. A regression analysis carried out to study the effect, on the surface area of a cobalt hydroxide catalyst
y) é , of the mole contents of cobalt (m1) and calcination temperature (m2), resulted in the following print
out. The regression model used was y = 04 + ﬁl $1 + ﬁg $2 + ﬁg m1 m2. WITHOUT any calculation, answer a)—c) AND refer (by drawing arrows, for example) to the speciﬁc entry/ entries in the printo SHOW all work. Useﬂiﬂﬂﬁ
Predictor Par Est Std Err T p Interc 185.5 21.2 8.7
cob —45.97 10.6 A .3 e interaction term useful for predicti
b) What is the typical de ' uncertainty) in 33?
c) Suppose e conﬁrmed that there is o linearity; does it follow that cobalt area
decreases with temperature? [VDJ bccqu)‘ e is)? Analysis of Variance: “V, 1.0,“ ‘j—\'s_._‘ ‘
Source DF SS F p (1) According to the regression equation, a future value of MS
Model 3 15223.5 5 4.5 18.92 0.0001 cobalt area, when all the predictors are set at their
\ ) Error 4290.5 268.2 55 E respective means, is predicted to be 49.5. Compute an
0" Tota 19514.0
A appropriate 2—sided interval for this prediction that
conveys information about preCiSion and reliability. Pr: +— ‘tu'J 951+ 1’ .L( p {if=5? . 001
0.0005
—5.9 0.0001 temp —0.30 0.5
a) g, cobtemp 0.09 @ 3.50<0.0035 => 41.5”: lam/2.5 .7, (—L
8 +21) 'L II “’1
“6: 2.u.o\\~= 35;, = 2487. M‘Lﬁ 3m 3 ...
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 Spring '08
 Statistics, Standard Deviation, Sample standard deviation, spring wheat, Manitou spring wheat, population mean lifetimes

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