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exam1f09_key - Fall 2009 Statistics 4010 Examination 1 (100...

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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):. FQC-sé)+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 (45212-75) =22-7r‘ 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)z-q 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 69-2927 \ ' 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 p-value 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 19-994263257544414 :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? M 1/0 who? it» Mr” 06: -05 (“Ham/fl W’ (‘3 a Mataxl/ecf’ 74356 Mb PM“) ...
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exam1f09_key - Fall 2009 Statistics 4010 Examination 1 (100...

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