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Unformatted text preview: Fall 2009
Statistics 4010 Examination 1 (100 points) ' p '
Name NOTE: I willallow partial credit only if you show all your work. 1. (14) Burning times (in seconds) were recorded for 10 ﬂares of a particular design. In increasing order of
value, these were: I z 3 tr 5. b 7 9 q ~ ~ (0
l3; os ‘65 ~95“ “35‘ "f6 '55 rs ~7s’95 'ga’
56, 59, 64, 65, 67, 69, 71, 74, 79, 8 6 +
(a) Calculate the 0.5 quantile, Q(0.5), of these data. ( (b) Calculate the ﬁrst quartile, Q(O.25), of these data. .
c) Calculate the interquartile range7 IQR, of these data. M .
(d) Estimate the proportion of the above values that are above 7WW'177 (Spa
(e) Calculate Q(0.25)—1.5>< IQR: 311233.. and Q(O.75)+1.5x IQRzﬁfigf
(f) Calculate LAV;___E_é__._ and UAV: “EL”... (g) Draw the Box Plot of these data. W W
45 5O 55 60 65 70 75 80 . 85 2. (14) Suppose that the probability of a customer selecting a national brand of paper towel over the store
brand in a large supermarket is .65 and assume that the customers make their purchase decisions independently. (First, deﬁne the Binomial random variable X XW (n It) W: V ' éy (a) Compute the probability that at least 6 out of 7 customers buying paper towels woul select a
national brand? "We? Pé< 24):. FQCsé)+10€(='7) 0
== ) @és‘jééoaﬂl—l— (Wéés'Yng)
.._ 7x‘o7é'tfzxvs§+ “OHM?? 2 491/762 + o“7‘C/02L :2 0a2338 (b) Use the Normal approximation to the Binomial to ﬁnd the probability that at least 75 out of 100
customers would select a national brand of paper towel? ‘YL s: 1cm WT == 55 720 ha Cardin/wig wam h CI’W a 357 10 .
) lama—7:) :: [O'DK M5“X‘35 X?» N (4521275) =227r‘
Mal PM; 76) =~: Péaggg 3.1 (24) The price of a particular make of an automobile among dealers nationwide is assumed to have a
Normal distribution with mean ,u, = $18, 240 with standard deviation 0' = $1200. (a) What is the probability that a. car of the same make, chosen randomly from a dealer, will cost less
that $17,700? (Show your work). PCX<I77<70>=1 P(Z<—’~m:’ii49> I200 =— PCE (—45) ~
= “Sié‘t (b) Compute the probability that at least 4 out of 5 cars picked randomly will cost less that $17,700?
P (K = ‘7‘) ~+ 230/: 5) = (3M 324?)?1m32éﬂlﬂ
' (3)652479504147‘)”
3. 5x .ouan .4734 + @244)’5 _
1.: . 038.25 + n003705 = vat/93 (c) Approximately, calculate the 90th percentile of the distribution of the price of this make of automobile? Show your work. 9..
\/ m A/(/9)2§L0)(125r3) N&a( (1 5a Mae/6" P(\/>C)=«7 A‘é. (3(2 > c—Mlzq—e)zq I
g.) C "lgﬁw m I’M ‘W'h 3.0—0
“’ W —' t4 7 0: W774: Compute the probability that the average price of 100 randomly selected cars of this make will lie
between $18,000 and $18,400. {3(1ng < \7. < lam)
«taco—191.40 r ‘ Irena ~— t9 {zoo/{r03 (,9 too—(gm z (894064831‘0)
2 P («2 < Z < #35) :O'tme ova/M2— I20
2 =1 4. (24) Suppose that the observed readings of a population of thermometers of a particular brand When the
actual room temperature is 65°F, has mean ,u and variance 02. For the next four parts assume that a
value of a2 = 5.29 is available from past data. (a) Describe the sampling distribution of the sample mean random variable 1—” for a sample of size’
n : 36, assuming that the distribution of readings from the population of thermometers is unknown.
Justify your answer. . ....._ _ f; NCFW’W) MM $93325
@g/ 01:7”) [‘11) “rt 42: “We” (b) If you desire to estimate the population mean ,u, to be Within ilc’F of the true value With 95%
conﬁdence, how many thermoeters should you sample from the above population 7 53/ 04,026, .1 (44 692927 \ ' a“ . 9" , ,—
W 5': 90.39 Sm ’l/Lzsrlj The company statistician obtains a sample of 36 thermometers, and tests each to check for accuracy at
65°F. The sample mean of the readings of the 36 thermometers is 17 = 63.8. (0) Construct a 95% conﬁdence interval estimate of u. You tell the management of the company that
you have 95% conﬁdence that the population mean u is in this interval. Explain in nonstatistical
language how to interpret your statement . INC/~00? C312: g :t 542’ NE,
63.5; + Q44). 4570‘! ...._. tag i wax—93:?— (éa'ogww) 1% 3% say 34, m {—de axe 1420/ “ﬁrm w’ﬁ‘s
W I? b c ‘ 5172241 we, ﬁlial/am?“
ﬁlm WW +0 46“, team 95%415 am. (d) st H0 : u = 65 vs. Ha : u 7é 65 using oz 2 .01. State the rejection region and your decision clearly. “a 77‘... gag—.55 ,
go ‘ 6—7175": 237g 2 ":3 [3 33672;; 2 2'575
4342.1 13I>o9~575
9m {33] w. an, a £49) (.9209 4,, 4%.. no, 5. (24) An auto manufacturer advertises that a new model of an SUV gets at least 30 miles per gallon (mpg)
on highway driving. To test the actual performance of the vehicle, a consumer group used 6
nonprofessional drivers to drive an SUV of the same model from Phoenix to Los Angeles. Based on the
actual mpg obtained for each vehicle, a sample mean of y = 29.42 and a sample standard deviation
.3 = 1.44 were calculated. Assume that the mpg distribution for all SUV’s of this model is approximately Normal with mean mpg [.L. (a) The consumer group wants to determine if the mean mpg is actually less than What the auto
manufacturer claims. Formulate appropriate null and alternative hypotheses needed. Compute a test statistic to test this hypothesis and state your conclusion usin = .05.
Hat/M236 if. a_/IA<3G 16 = “‘ ° amt/2+30maag7 C a
/5 Wu Ira/4x! 4/3
75 :2 219/5 Q‘Q‘: "t 4—,2e0/5
Shhce. “If; ’7—201‘3) 1“ 1‘5 M4212 IQ.R,:>?;7H’CIJD i (b) Explain in words (or deﬁne by a formula) What is meant by the p~value for the test in part (a)
above. Approximately, compute the pvalue of the test statistic calculated in part (a) using an appropriate table, and use it to test the hypotheses you stated in part (a). PVDL(0 Mach/«Inf 19994263257544414 :23:wi «6797 a... PCT; <~W7)r—= P(’Ts>.%vy
ﬂm’ %,M/e) IQDAL/y‘ﬁ. ﬁr GM: 5)
(>01 iglégéz £"VW6‘; ﬁfe<éﬁfog 'ﬂﬁ‘Q/JE :44 0670(‘2'05 ce interval for a. Use this interval to tgst the hypotheses ou gave in part
(a), explaining how you arrived at your conclusion. What is the oz~level of your test? , M s /‘
75; CI} {1 i “13,655 77?} 947%2 i Dad/z; ” iii
529‘s»; :1: ms m7<2¥~2§93a49
A, 2 30 4’3 «Cu MWJ‘ 7%«4 W?
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 Normal Distribution, Standard Deviation, Probability theory, Paper towel, national brand

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