5. A formulae page and two tables are provided at the end of Part A of the examination PART A
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1 Istructios: 1. You have bee provided with: (a) this questio paper (Part A ad Part B) (b) a multiple choice aswer sheet (for Part A) (c) Log Aswer Sheet(s) (for Part B) (d) a booklet of tables. (a) I PART A the umber of marks possible is 4. It is suggested that you first complete the questios o the questio paper by choosig the BEST aswer out of five i each case; the trasfer your aswers to the multiple choice aswer sheet by blackeig the appropriate space with a pecil. ONLY ONE space should be blackeed; otherwise, the questio will be marked wrog. The questios are of equal value. There is o correctio made for guessig; therefore, all questios should be attempted. (b) PART B is worth 11 marks ad cosists of two log aswer questios which are to be aswered i the space provided. 3. At the ed of the examiatio period, had i your multiple choice aswer sheet, together with Part B of the examiatio. Be sure to write your NAME ad STUDENT NUMBER o the MULTIPLE CHOICE ANSWER SHEET for Part A ad o the PART B sectio. 4. Calculators are permitted. 5. A formulae page ad two tables are provided at the ed of Part A of the examiatio PART A 1. Which of the followig statemets about cofidece itervals is INCORRECT? (A) (B) (C) (D) (E) If we keep the sample size fixed, the cofidece iterval gets wider as we icrease the cofidece coefficiet. A cofidece iterval for a mea always cotais the sample mea. If we keep the cofidece coefficiet fixed, the cofidece iterval gets arrower as we icrease the sample size. If the populatio stadard deviatio icreases, the cofidece iterval decreases i width. If the 94% cofidece iterval for a mea cover 5.6 the two tailed test of H 0 : µ = 5.6 at level.06 will ot reject H 0.
2 . The diameter of ball bearigs are kow to be ormally distributed with ukow mea ad variace. A radom sample of size 5 gave a mea of.5 cm. The 95% cofidece iterval had legth 4 cm. The (A) The sample variace is (B) The sample variace is (C) The populatio variace is (D) The populatio variace is (E) The sample variace is A turkey producer kows from previous experiece that profits are maximized by sellig turkeys whe their average weight is 1 kilograms. Before determiig whether to put all their full grow turkeys o the market this moth, the producer wishes to estimate their mea weight. Prior kowledge idicates that turkey weights have a stadard deviatio of aroud 1.5 kilograms. The umber of turkeys that must be sampled i order to estimate their true mea weight to withi 0.5 kilograms with 95% cofidece is: (A) 35 (B) 6 (C) 65 (D)5 (E) A radom sample of 4 Herefords, each with a frame size of three (o a oe-to-seve scale), gave a sample mea weight of 45 kg ad a sample stadard deviatio of 1 kg. A 95% cofidece iterval for the average weight of all Herefords of this frame size is : (A) (435.3, 468.7) (B) (43.9, 471.1) (C) (440., 463.8) (D) (48.5, 475.5) (E) (436.6, 467.4)
3 5. The average yield of grai o 9 radomly picked experimetal plots of farm was foud to be 150 bushels. The yield i bushels per plot i previous studies was foud to be approximately ormally distributed with a variace of 400 bushels. A 98% cofidece iterval for the mea yield is: (A) (130.7, 169.3) (B) (144.8, 155.) (C) (13.8, 167.) (D) (134.5, 165.5) (E) (145.7, 154.4) 6. Auditor A is faced with a populatio of 1,000 accouts (Populatio A). He is goig to select a radom sample of 30 accouts from Populatio A ad he is goig to use the average amout owig i these sampled accouts as a estimate of the average amout owig i Populatio A. Auditor B is faced with a populatio of 10,000 accouts (Populatio B). He is goig to select a radom sample of 30 accouts from Populatio B ad he is goig to use the average amout owig i these sample accouts as a estimate of the average amout owig i Populatio B. Other thigs beig equal: (A) (B) (C) (D) (E) Auditor A's estimate will be about 10 times more accurate tha Auditor B's estimate. Auditor B's estimate will be about 10 times more accurate tha Auditor A's estimate. Auditor A's estimate will be about 3.16 times more accurate tha Auditor B's estimate. Auditor B's estimate will be about 3.16 times more accurate tha Auditor A's estimate. the accuracy of the two estimates will be about the same. 7. I a test of H0: µ=100 agaist Ha: µ 100, a sample of size 10 produces a sample mea of 103 ad a p-value of Thus, at the 0.05 level of sigificace: (A) there is sufficiet evidece to coclude that µ 100. (B) there is sufficiet evidece to coclude that µ=100. (C) there is isufficiet evidece to coclude that µ=100. (D) there is isufficiet evidece to coclude that µ 100. (E) there is sufficiet evidece to coclude that µ=103.
4 8. I a test of H0: µ=100 agaist Ha: µ 100, a sample of size 80 produces Z = 0.8 for the value of the test statistic. The p-value of the test is thus equal to: (A) 0.79 (B) 0.40 (C) 0.9 (D) 0.4 (E) 0.1 The ext questios refer to the followig situatio A Caadia railway compay claims that its trais block crossigs o more that 8 miutes per trai o the average. The actual times (miutes) that 5 radomly selected trais block crossigs were recorded: The value of a appropriate test statistic for testig the claim is: (A).43 (B).97 (C) 6.19 (D) (E) ot withi +.01 of ay of the above 10. The p-value is: (A) less tha.005 (B) betwee.005 ad.01 (C) betwee.01 ad.05 (D) betwee.05 ad.05 (E) larger tha.05
5 1. A appropriate 95% cofidece iterval for µ has bee calculated as ( -0.73, 1.9 ) based o = 15 observatios from a populatio with a ormal N(µ, ) distributio. The hypotheses of iterest are H0: µ = 1.6 versus Ha: µ 1.6. Based o this cofidece iterval, (A) (B) (C) (D) (E) we should reject H0 at the = 0.05 level of sigificace. we should ot reject H0 at the = 0.05 level of sigificace. we should reject H0 at the = 0.10 level of sigificace. we should ot reject H0 at the = 0.10 level of sigificace. we caot perform the required test sice we do ot kow the value of the test statistic 13. The Federal govermet periodically tests packaged products to check that the maufacturer is ot short-weightig the product (i.e., uderfillig products). To allow for variatio i the fillig process, the Federal govermet takes a sample of 16 bottles of beer with omial capacity of 344 ml, (i.e. the label o the bottle says 344 ml.). If the mea volume i the bottles is less tha 340 ml, the maufacturer is fied( i.e. the govermet cocludes that the maufacturer is uderfillig). Suppose a uscrupulous brewer sets the machie to fill, o average, 34 ml. The machie has a stadard deviatio of 4 ml. The probability that a Type II error will be made is: (A).477 (B).08 (C).977 (D).1915 (E).3085 Restig pulse rate is a importat measure of the fitess of a perso's cardiovascular system with a lower rate idicative of greater fitess. The mea pulse rate for all adult males is approximately 7 beats per miute. A radom sample of 5 male studets curretly erolled i the Faculty of Agriculture ad ow takig 5.00 was selected ad the mea pulse restig pulse rate was foud to be 80 beats per miute with stadard deviatio of 0 beats per miute. The experimeter wishes to test if Agriculture studets are less fit, o average, tha the geeral populatio.
6 14. The appropriate ull ad alterate hypotheses are: (A) H0: µ = 7 Ha: µ < 7 (B) H0: x = 7 Ha: x < 7 (C) H0: µ = 80 Ha: µ = 7 (D) H0: x = 7 Ha: x > 7 (E) H0: µ = 7 Ha: µ > 7 The ext three questios refer to the followig situatio The Excellet Drug Compay claims its aspiri tablets will relieve headaches faster tha ay other aspiri o the market. To determie whether Excellet's claim is valid, radom samples of size 15 are chose from aspiris made by Excellet(E) ad the Simple(S) Drug Compay. A aspiri is give to each of the 30 radomly selected persos sufferig from headaches ad the umber of miutes required for each to recover from headache is recorded. The sample results are: Variace Mea Excellet Simple A test at the 5% sigificace level is performed to determie whether Excellet's aspiri cures headaches sigificatly faster tha Simple's aspiri The appropriate hypothesis to be tested is: (A) H 0 : µ E -µ S = 0 vs. H A : µ E -µ S > 0 (B) H 0 : µ E -µ S = 0 vs. H A : µ E -µ S 0 (C) H 0 : µ E -µ S = 0 vs. H A : µ E -µ S < 0 (D) H 0 : µ E -µ S < 0 vs. H A : µ E -µ S = 0 (E) H 0 : µ E -µ S > 0 vs. H A : µ E -µ S = 0
7 16. The absolute value of the appropriate test statistic ad its degrees of freedom are: (A).37 with 14 d.f. (B).37 with 8 d.f. (C).64 with 14 d.f. (D).64 with 8 d.f. (E) oe of the above 17. The absolute value of the critical value for this test is: (A) (B) (C).048 (D).145 (E) A idustrial psychologist wishes to study the effects of motivatio o sales i a particular firm. Of 4 ew salesperso, 1 are paid a hourly rate ad 1 are paid a commissio. The 4 idividuals are radomly assiged to the two groups. The followig data represet the sales volume (i thousads of dollars) achieved durig the first moth o the job. Hourly Rate Commissio Usig JMPi we obtai:
8 Suppose the populatio variaces are equal. The edpoits of a 98% cofidece iterval for the differece i mea sales volume(µ C - µ H ) are: (A) ±.01 (B) ± (C) ±.074 (D) ± [ ] [ ] 1 (38.84) 1 (54.81) (E) oe of the above
9 Part B Name: Marks Studet Number: PART A (out of 4) PART B (out of 11) TOTAL (out of 35) Aswer all questios i the space provided 1. The Natioal Associatio of Realtors reported that the price of previously owed, sigle-family homes rose 5% o average i the third-quarter 1997, from the third-quarter 1996 (USA today, November 14, 1997, 6B). The followig are prices (i thousads of dollars) of a sample of seve homes House Third-Qtr 97 Price Third-Qtr 96 Price Usig JMPi we obtai:
10 diff('97-'96) Quatiles Momets Mea Std Dev Std Error Mea Upper 95% Mea Lower 95% Mea N Sum Weights
11
12 (a) At the.05 level of sigificace, is there ay evidece of a icrease i the average of media prices over the 1-year period? You should defie ay parameters i your hypotheses i terms of this problem. (b) What assumptio(s) is/are ecessary to perform this test?
13 . A experimet was coducted that was cocered with the tesile stregth of yar spu for textile [6.5] usage. Suppose a researcher wishes to examie the effect of air-jet pressure (i psi) o the breakig stregth of the yar. Three differet levels of air-jet pressure are to be cosidered: 30 psi, 40 psi ad 50 psi. A radom sample of 18 homogeeous/similar fillig years are selected from the same batch ad the yars are radomly assiged, 6 each, to the three levels of air-jet pressure. The breakig stregths are as follows: Air-Jet Pressure 30 PSI 40 PSI 50 PSI Usig JMPi we calculate: Aalysis of Variace Source DF Sum of Squares Mea Square F ratio Model 4.04 Error C Total.89 Prob > F a) What are the appropriate hypotheses for the statistical test i this situatio? You should defie ay parameters i your hypothesis i terms of this problem. b) Fill i the missig values i the table as completely as you ca. Complete the test. Let α =.05
14 Fill i the Blaks c) I aalysis of variace we have used graphs to check of the assumptios. The assumptio of was checked by. The assumptio of was checked by.
15 Selected Formulae for (y i y) = y 1 i i=1 i=1 i=1 y i = y i y i=1. s y = 3. r = 1 1 i=1 (y i y) 1 x i x y i y -1 s x s = y x i y i 1 x i ( 1) s x s y ( )( y i ) 4. b = r s y s x = x i y i x i ( )( y i ) ( ) x i x i a = y b x 5. If X has a biomial distributio with parameters ad p, the the mea of X is p ad the variace of X is p(1-p). 6. The samplig distributio of p^ has a mea of p ad a stadard deviatio of 7. The samplig distributio of x _ has a mea of µ ad a stadard deviatio of p(1 p) σ.. 8. Z = x µ 0 σ / x ± z * σ = z * σ m 9. Z = p p 0 p 0 (1 p 0 ) p ± z p(1 p) = z p (1- p ) m 10. t = x µ 0 s / _ x ± t * s
16 11. t = x 1 x (µ 1 µ ) s p s p = ( 1 1)s 1 + ( 1)s ( x 1 x ) ± t * s p with df = 1 + ad σ 1 = σ 1. t = x 1 x (µ 1 µ ) s s with df = smaller of 1 1 ad 1 ( x 1 x ) ± t * s 1 + s Z = p 1 p 1 s p = p(1 p) + 1 p = x 1 + x s p ( p 1 p ) ± z * s D s D = p 1 (1 p 1 ) 1 + p (1 p ) 14. Biomial Probability Distributio: P(X = k) = Error!) perror! k = 0, 1,..., 15. χ = over all cells (Observed cout Expected cout) Expected cout
INSTRUCTIONS (A) 1.22 (B) 0.74 (C) 4.93 (D) 1.18 (E) 2.43
PAPER NO.: 444, 445 PAGE NO.: Page 1 of 1 INSTRUCTIONS I. You have bee provided with: a) the examiatio paper i two parts (PART A ad PART B), b) a multiple choice aswer sheet (for PART A), c) selected formulae
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