Chapter 8 - Practice Problems 1

Size: px
Start display at page:

Download "Chapter 8 - Practice Problems 1"

Transcription

1 Chpter 8 - Prctice Problems 1 MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. A hypothesis test is to be performed. Determine the null nd lterntive hypotheses. 1) In the pst, the men running time for certin type of flshlight bttery hs been 9.6 hours. The mnufcturer hs introduced chnge in the production method nd wnts to perform hypothesis test to determine whether the men running time hs chnged s result. 1) A) H : μ = 9.6 hours H : μ > 9.6 hours C) H : μ = 9.6 hours H : μ 9.6 hours B) H : μ 9.6 hours H : μ = 9.6 hours D) H : μ 9.6 hours H : μ = 9.6 hours 2) The owner of footbll tem clims tht the verge ttendnce t gmes is over 81,1, nd he is therefore justified in moving the tem to city with lrger stdium. 2) A) H : μ, the verge ttendnce t gmes, is less thn or equl to 81,1 H : μ, the verge ttendnce t gmes, is greter thn 81,1 B) H : μ, the verge ttendnce t gmes, is less thn 81,1 H : μ, the verge ttendnce t gmes, is greter thn or equl to 81,1 C) H : μ, the verge ttendnce t gmes, is greter thn 81,1 H : μ, the verge ttendnce t gmes, is less thn or equl to 81,1 D) H : μ, the verge ttendnce t gmes, is greter thn or equl to 81,1 H : μ, the verge ttendnce t gmes, is less thn 81,1 Clssify the hypothesis test s two-tiled, left-tiled, or right-tiled. 3) At one school, the verge mount of time tht tenth-grders spend wtching television ech week is 21.6 hours. The principl introduces cmpign to encourge the students to wtch less television. One yer lter, the principl wnts to perform hypothesis test to determine whether the verge mount of time spent wtching television per week hs decresed from the previous men of 21.6 hours. 3) A) Two-tiled B) Left-tiled C) Right-tiled 4) A helth insurer hs determined tht the "resonble nd customry" fee for certin medicl procedure is $12. They suspect tht the verge fee chrged by one prticulr clinic for this procedure is higher thn $12. The insurer wnts to perform hypothesis test to determine whether their suspicion is correct. 4) A) Right-tiled B) Two-tiled C) Left-tiled SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Provide n pproprite response. 5) You wish to test the hypotheses shown below. H : μ = 4 H : μ > 4 Would you be inclined to reject the null hypothesis if the smple men turned out to be much smller thn 4? Explin your thinking. 5) 1

2 6) Robert is conducting hypothesis test concerning popultion men. The hypotheses re s follows. H : μ = 5 H : μ > 5 He selects smple of size 35 nd finds tht the smple men is 6. He then does some clcultions nd finds tht for smples of size 35, the stndrd devition of the smple mens is 3.2. Do you think tht he should reject the null hypothesis? Why or why not? 6) MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. The grph portrys the decision criterion for hypothesis test for popultion men. The null hypothesis is H : μ = μ. The curve is the norml curve for the test sttistic under the ssumption tht the null hypothesis is true. Use the grph to solve the problem. 7) A grphicl disply of the decision criterion follows. 7) Determine the rejection region. A).5 B) All z-scores tht lie to the right of C) All z-scores tht lie to the left of D)

3 8) A grphicl disply of the decision criterion follows. 8) Determine the significnce level. A).1 B) C) All z-scores tht lie to the right of D).5 SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Construct grph portrying the decision criterion for the specified hypothesis test. 9) A hypothesis test for popultion men is conducted. The hypotheses re: H : μ = μ 9) H : μ μ The significnce level is.1 nd the criticl vlues re nd Sketch norml curve displying the decision criterion. This curve will represent the norml curve for the test sttistic under the ssumption tht the null hypothesis is true. On your grph indicte the re in ech til, the criticl vlues, the rejection region, nd the nonrejection region. 1) A hypothesis test for popultion men is conducted. The hypotheses re: H : μ = μ 1) H : μ > μ The significnce level is.1 nd the criticl vlue is Sketch norml curve displying the decision criterion. This curve will represent the norml curve for the test sttistic under the ssumption tht the null hypothesis is true. On your grph indicte the re in the til, the criticl vlue, the rejection region, nd the nonrejection region. 3

4 MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. For the given hypothesis test, explin the mening of Type I error, Type II error, or correct decision s specified. 11) In the pst, the men running time for certin type of flshlight bttery hs been 9.8 hours. The 11) mnufcturer hs introduced chnge in the production method nd wnts to perform hypothesis test to determine whether the men running time hs incresed s result. The hypotheses re: H : μ = 9.8 hours H : μ > 9.8 hours Explin the mening of Type I error. A) Concluding tht μ > 9.8 hours when in fct μ = 9.8 hours B) Concluding tht μ < 9.8 hours when in fct μ > 9.8 hours C) Concluding tht μ = 9.8 hours when in fct μ > 9.8 hours D) Concluding tht μ > 9.8 hours when in fct μ > 9.8 hours 12) In 199, the verge mth SAT score for students t one school ws 5. Five yers lter, techer wnts to perform hypothesis test to determine whether the verge SAT score of students t the school hs chnged from the 199 men of 5. The hypotheses re: H : μ = 5 H : μ 5 Explin the mening of Type II error. A) Filing to reject the hypothesis tht μ = 5 when in fct μ 5 B) Concluding tht μ > 5 when in fct μ = 5 C) Concluding tht μ 5 minutes when in fct μ = 5 D) Filing to reject the hypothesis tht μ = 5 when in fct μ = 5 13) At one school, the verge mount of time tht tenth-grders spend wtching television ech week is 21.6 hours. The principl introduces cmpign to encourge the students to wtch less television. One yer lter, the principl wnts to perform hypothesis test to determine whether the verge mount of time spent wtching television per week hs decresed. The hypotheses re: H : μ = 21.6 hours H : μ < 21.6 hours Explin the mening of correct decision. A) Filing to reject the hypothesis tht μ = 21.6 hours when in fct μ = 21.6 hours OR concluding tht μ < 21.6 hours when in fct μ < 21.6 hours B) Filing to reject the hypothesis tht μ = 21.6 hours when in fct μ < 21.6 hours C) Concluding tht μ > 21.6 hours when in fct μ < 21.6 hours D) Concluding tht μ < 21.6 hours when in fct μ = 21.6 hours Clssify the conclusion of the hypothesis test s Type I error, Type II error, or correct decision. 14) At one school, the verge mount of time tht tenth-grders spend wtching television ech week is 21 hours. The principl introduces cmpign to encourge the students to wtch less television. One yer lter, the principl wnts to perform hypothesis test to determine whether the verge mount of time spent wtching television per week hs decresed. The hypotheses re: H : μ = 21 hours H : μ < 21 hours Suppose tht the results of the smpling led to nonrejection of the null hypothesis. Clssify tht conclusion s Type I error, Type II error, or correct decision, if in fct the men mount of time, μ, spent wtching television hs not decresed. 12) 13) 14) A) Type I error B) Correct decision C) Type II error 4

5 15) A helth insurer hs determined tht the "resonble nd customry" fee for certin medicl procedure is $12. They suspect tht the verge fee chrged by one prticulr clinic for this procedure is higher thn $12. The insurer wnts to perform hypothesis test to determine whether their suspicion is correct. The hypotheses re: H : μ = $12 H : μ > $12 Suppose tht the results of the smpling led to rejection of the null hypothesis. Clssify tht conclusion s Type I error, Type II error, or correct decision, if in fct the verge fee chrged by the clinic is $12. 15) A) Correct decision B) Type II error C) Type I error SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Provide n pproprite response. 16) A student performs hypothesis test for popultion men. The hypotheses re: H : μ = 1 H : μ > 1 The significnce level is.5 nd the test sttistic flls in the nonrejection region. The student writes her conclusion s follows: "The test sttistic flls in the nonrejection region so it is sfe to conclude tht the null hypothesis is true; i.e., tht μ = 1." Is this n cceptble wy to write the conclusion? If not, explin why not nd rewrite the conclusion in n cceptble wy. 16) 17) A hypothesis test for popultion men is performed t the.1 significnce level. The results re sttisticlly significnt t the.1 level. Explin the mening of the term sttisticlly significnt. Do you think tht the test sttistic fell in the rejection or nonrejection region? Do you think tht the null hypothesis ws rejected? 17) 18) A phrmceuticl compny hs new drug which relieves hedches. However, there is some indiction tht the drug my hve the side effect of incresing blood pressure. Suppose the drug compny conducts hypothesis test to determine whether the mediction rises blood pressure. The hypotheses re: H : The drug does not increse blood pressure. H : The drug increses blood pressure. Do you think tht for doctors nd ptients it is more importnt to hve smll α probbility or smll β probbility? Why? Do you think tht the phrmceuticl compny would prefer to hve smll α probbility or smll β probbility? Why? 18) MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. A hypothesis test is to be performed for popultion men with null hypothesis H : μ = μ. The test sttistic used will be z = x - μ σ/ n. Find the required criticl vlue(s). 19) α =.8 for two-tiled test. 19) A) ±2.575 B) ±1.75 C) ±1.764 D) ±

6 2) Find the criticl vlue(s) for two-tiled test with α =.2 nd drw grph tht illustrtes your nswer. A) -1.75, ) B) -2.5, 2.5 C) -2.33, 2.33 D)

7 21) Find the criticl vlue(s) for right-tiled test with α =.7 nd drw grph tht illustrtes your nswer. A) ) B) C) 1.48 D) 1.48 SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Perform hypothesis test for the popultion men. Assume tht preliminry dt nlyses indicte tht it is resonble to pply the z-test. 22) The Ntionl Wether Service sys tht the men dily high temperture for October in lrge 22) midwestern city is 56 F. A locl wether service suspects tht this vlue is not ccurte nd wnts to perform hypothesis test to determine whether the men is ctully lower thn 56 F. A smple of men dily high tempertures for October over the pst 37 yers yields x = 54 F. Assume tht the popultion stndrd devition is 5.6 F. Perform the hypothesis test t the α =.1 significnce level. 7

8 23) A mnufcturer mkes steel brs tht re supposed to hve men length of 5 cm. A retiler suspects tht the brs re running short. A smple of 56 brs is tken nd their men length is determined to be 51 cm. Using 1% level of significnce, perform hypothesis test to determine whether the popultion men is less thn 5 cm. Assume tht the popultion stndrd devition is 3.6 cm. 23) 24) A newspper in lrge midwestern city reported tht the Ntionl Assocition of Reltors sid tht the men home price lst yer ws $116,8. The city housing deprtment feels tht this figure is too low. They rndomly selected 51 home sles nd obtined smple men price of $118,9. Assume tht the popultion stndrd devition is $3,7. Using 5% level of significnce, perform hypothesis test to determine whether the popultion men is higher thn $116,8. 25) A resercher wnts to check the clim tht convicted burglrs spend n verge of 18.7 months in jil. She tkes rndom smple of 4 such cses from court files nd finds tht x = 16.7 months. Assume tht the popultion stndrd devition is nd 7.8 months. Test the null hypothesis tht μ = 18.7 t the.5 significnce level. 24) 25) MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. A one-smple z-test for popultion men is to be performed. The vlue obtined for the test sttistic, z = nture of the test (right-tiled, left-tiled, or two-tiled) is lso specified. Determine the P-vlue. 26) A right-tiled test: z = 2.38 A).9826 B).9913 C).174 D).87 x - μ σ/ n, is given. The 26) 27) A two-tiled test: z = 1.31 A).898 B).192 C).951 D) ) 28) A left-tiled test: z = -.58 A).562 B).438 C).281 D) ) SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Perform one-smple z-test for popultion men using the P-vlue pproch. Be sure to stte the hypotheses nd the significnce level, to compute the vlue of the test sttistic, to obtin the P-vlue, nd to stte your conclusion. 29) In the pst, the men running time for certin type of flshlight bttery hs been 8.5 hours. The 29) mnufcturer hs introduced chnge in the production method which he hopes hs incresed the men running time. The men running time for rndom smple of 4 light bulbs ws 8.7 hours. Do the dt provide sufficient evidence to conclude tht the men running time of ll light bulbs, μ, hs incresed from the previous men of 8.5 hours? Perform the pproprite hypothesis test using significnce level of.5. Assume tht σ =.5 hours. 8

9 3) In one city, the verge mount of time tht tenth-grders spend wtching television ech week is 21.6 hours. The principl of Birchwood High School believes tht t his school, tenth-grders wtch less television. For smple of 28 tenth-grders from Birchwood High School, the men mount of time spent wtching television per week ws 19.4 hours. Do the dt provide sufficient evidence to conclude tht for ll tenth-grders t Birchwood High School, the men mount of time spent wtching television per week is less thn the city verge of 21.6 hours? Perform the pproprite hypothesis test using significnce level of.5. Assume tht σ = 7.2 hours. 3) 31) The forced vitl cpcity (FVC) is often used by physicins to ssess person's bility to move ir in nd out of their lungs. It is the mximum mount of ir tht cn be exhled fter deep breth. For dult mles, the verge FVC is 5. liters. A resercher wnts to perform hypothesis test to determine whether the verge forced vitl cpcity for women differs from this vlue. The men forced vitl cpcity for rndom smple of 85 women ws 4.8 liters. Do the dt provide sufficient evidence to conclude tht the men forced vitl cpcity for women differs from the men vlue for men of 5. liters? Perform the pproprite hypothesis test using significnce level of.5. Assume tht σ =.9 liters. 31) MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. Provide n pproprite nswer. 32) A high school biology student wishes to test the hypothesis tht hummingbird feeders cn ffect the men mss of ruby-throted hummingbirds in the re surrounding the feeder. She cptures nd weighs severl femle specimens ner science museum where severl feeders re locted. She obtins the following msses in grms: The student's hypotheses re: H o : μ = 3.65 g H : μ > 3.65 g Use technology to clculte P, then determine if the dt provide sufficient evidence to conclude tht the men mss is greter thn tht of the generl femle popultion. Test t the 5% significnce level nd ssume the popultion stndrd devition is.35 g. A) P =.745; since P > α, ccept the null hypothesis - the mss of hummingbirds in the re surrounding the feeders does not pper to be bove norml. B) P =.255; since P > α, reject the null hypothesis - the mss of hummingbirds in the re surrounding the feeders ppers to be bove norml. C) P =.59; since P > α, reject the null hypothesis - the mss of hummingbirds in the re surrounding the feeders ppers to be bove norml. D) P =.1418; since P > α, ccept the null hypothesis - the mss of hummingbirds in the re surrounding the feeders does not pper to be bove norml. 32) SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Preliminry dt nlyses indicte tht it is resonble to use t-test to crry out the specified hypothesis test. Perform the t-test using the criticl-vlue pproch. 33) Use significnce level of α =.5 to test the clim tht μ The smple dt consists of 33) 15 scores for which x = 42.8 nd s = ) A test of sobriety involves mesuring the subject's motor skills. Twenty rndomly selected sober subjects tke the test nd produce men score of 41. with stndrd devition of 3.7. At the.1 level of significnce, test the clim tht the true men score for ll sober subjects is equl to ) 9

10 35) In tests of computer component, it is found tht the men time between filures is 52 hours. A modifiction is mde which is supposed to increse the time between filures. Tests on rndom smple of 1 modified components resulted in the following times (in hours) between filures At the.5 significnce level, test the clim tht for the modified components, the men time between filures is greter thn 52 hours. 35) MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. Provide n pproprite nswer. 36) Use significnce level of α =.5 to test the clim tht μ = The smple dt consists of 1 scores for which x = 2.1 nd s = 4.1. Stte the null nd lterntive hypotheses, compute the vlue of the test sttistic, nd find the P-vlue for the smple. Stte your conclusions bout the clim. A) H o : μ = 19.6 H : μ 19.6 Test sttistic: t = P-Vlue: P = Reject H o : μ = Since P > α, there is sufficient evidence to support the clim tht the men is different from B) H o : μ = 2.1 H : μ 2.1 Test sttistic: t = P-Vlue: P = Accept H o : μ = 2.1. Since P > α, there is not sufficient evidence to support the clim tht the men is different from 2.1. C) H o : μ = 19.6 H : μ 19.6 Test sttistic: t = P-Vlue: P = Accept H o : μ = Since P > α, there is not sufficient evidence to support the clim tht the men is different from D) H o : μ = 19.6 H : μ 19.6 Test sttistic: t = P-Vlue: P = Accept H o : μ = Since P > α, there is sufficient evidence to support the clim tht the men is different from E) H o : μ = 19.6 H : μ 19.6 Test sttistic: t = P-Vlue: P = Accept H o : μ = Since P > α, there is not sufficient evidence to support the clim tht the men is different from ) A hypothesis test is to be performed for popultion proportion. For the given smple dt nd null hypothesis, compute the vlue of the test sttistic, z = p^ - p p (1 - p )/n 37) Out of 199 observtions, 5% were successes. H: p =.43. A) B).2 C) D) ) 38) A drug compny clims tht over 8% of ll physicins recommend their drug. 12 physicins were sked if they recommend the drug to their ptients. 3% sid yes. H: p =.8. A) B) C) D) ) 1

11 SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Perform hypothesis test for popultion proportion using the criticl vlue pproch. 39) A mnufcturer considers his production process to be out of control when defects exceed 3%. In rndom smple of 85 items, the defect rte is 5.9% but the mnger clims tht this is only smple fluctution nd production is not relly out of control. At the.1 level of significnce, do the dt provide sufficient evidence tht the percentge of defects exceeds 3%? 39) 4) A supplier of 3.5" disks clims tht no more thn 1% of the disks re defective. In rndom smple of 6 disks, it is found tht 3% re defective, but the supplier clims tht this is only smple fluctution. At the.1 level of significnce, do the dt provide sufficient evidence tht the percentge of defects exceeds 1%? 4) 41) In clinicl study of n llergy drug, 114 of the 23 subjects reported experiencing significnt relief from their symptoms. At the.1 significnce level, test the clim tht more thn hlf of ll those using the drug experience relief. 41) MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. Find the P-vlue for the indicted hypothesis test. 42) A medicl school clims tht more thn 28% of its students pln to go into generl prctice. It is found tht mong rndom smple of 13 of the school's students, 39 of them pln to go into generl prctice. Find the P-Vlue for test of the school's clim. 42) A).378 B).1635 C).3461 D) ) In smple of 88 children selected rndomly from one town, it is found tht 8 of them suffer from sthm. Find the P-vlue for test of the clim tht the proportion of ll children in the town who suffer from sthm is equl to 11%. 43) A).5671 B) C).2843 D).2157 SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Perform hypothesis test for popultion proportion using the criticl vlue pproch. 44) A mnufcturer considers his production process to be out of control when defects exceed 3%. In rndom smple of 8 items, the defect rte is 5% but the mnger clims tht this is only smple fluctution nd production is not relly out of control. At the.1 level of significnce, do the dt provide sufficient evidence tht the percentge of defects exceeds 3%? 44) 45) A supplier of 3.5" disks clims tht no more thn 1% of the disks re defective. In rndom smple of 6 disks, it is found tht 3% re defective, but the supplier clims tht this is only smple fluctution. At the.1 level of significnce, do the dt provide sufficient evidence tht the percentge of defects exceeds 1%? 45) 11

12 Answer Key Testnme: CH 8 SET 1 1) C 2) A 3) B 4) A 5) No. The lterntive hypothesis is tht the true men is greter thn 4. A smple men much smller thn 4 does not provide evidence in fvor of this lterntive hypothesis. The null hypothesis should be rejected only if the smple men turns out much lrger thn 4. 6) Answers will vry. Possible nswer. Yes, he should reject the null hypothesis. If H were true, it is not very likely tht the smple men would be s big s 6, since this is more thn three stndrd devitions from 5. So the observed smple men is inconsistent with the null hypothesis. 7) B 8) D 9) 1) 11) A 12) A 13) A 12

13 Answer Key Testnme: CH 8 SET 1 14) B 15) C 16) No; since the test sttistic fell in the nonrejection region, the dt did not provide evidence in fvor of the lterntive, μ > 1. This does not men tht we cn conclude tht μ = 1, only tht we hve no evidence ginst tht hypothesis. In other words, one cn tlk of "filing to reject null hypothesis", but not of "ccepting" it. 17) "Sttisticlly significnt" mens tht the dt provided evidence ginst the null hypothesis. So the test sttistic fell in the rejection region nd the null hypothesis ws rejected. 18) For doctors nd ptients it is more importnt to hve smll β probbility. If the drug relly does increse blood pressure, it is importnt to detect tht. So the probbility of Type II error should be smll. The phrmceuticl compny my prefer to hve smll α probbility since they would lose money if the test concluded tht the drug incresed blood pressure when in fct it didn't. 19) B 2) C 21) C 22) H : μ = 56 F H : μ < 56 F Test sttistic: z = Criticl vlue z = Fil to reject H: μ = 56 F. there is not sufficient evidence to support the clim tht the men is less thn 56 F. 23) H : μ = 5 cm H : μ < 5 cm Test sttistic: z = 2.8. Criticl vlue z = Fil to reject H: μ = 5 cm. There is not sufficient evidence to support the clim tht the men length is less thn 5 cm. 24) H : μ = $116,8 H : μ > $116,8 Test sttistic: z = 4.5. Criticl vlue: z = Reject Ho: μ = $116,8.There is sufficient evidence to support the clim tht the men is higher thn $116,8. 25) H : μ = 18.7 months H : μ 18.7 months Test sttistic: z = Criticl vlues: z = ± Fil to reject H. There is not sufficient evidence to wrrnt rejection of the clim tht the men is 18.7 months. 26) D 27) B 28) C 29) H : μ = 8.5 hours H : μ > 8.5 hours α =.5 z = 2.53 P-vlue =.57 Reject H. At the 5% significnce level, the dt provide sufficient evidence to conclude tht the men running time of ll light bulbs, μ, hs incresed from the previous men of 8.5 hours. 13

14 Answer Key Testnme: CH 8 SET 1 3) H : μ = 21.6 hours H : μ < 21.6 hours α =.5 z = P-vlue =.526 Do not reject H. At the 5% significnce level, the dt do not provide sufficient evidence to conclude tht for tenth-grders t Birchwood High School the men mount of time spent wtching television per week is less thn 21.6 hours 31) H : μ = 5. liters H : μ 5. liters α =.5 z = -2.5 P-vlue =.44 Reject H. At the 5% significnce level, the dt provide sufficient evidence to conclude tht the men forced vitl cpcity for women differs from 5. liters. 32) D 33) H : μ = 32.6 H : μ 32.6 Test sttistic: t = Criticl vlues: t = ± Reject H: μ = There is sufficient evidence to support the clim tht the men is different from ) H : μ = 35.. H : μ 35.. Test sttistic: t = Criticl vlues: t = , Reject the null hypothesis. There is sufficient evidence to wrrnt rejection of the clim tht the men is equl to ) H : μ = 52 hours. H : μ > 52 hours. Test sttistic: t = Criticl vlue: t = Reject H. There is sufficient evidence to support the clim tht the men is greter thn 52 hours. 36) E 37) A 38) D 39) H : p =.3 H : p >.3. α =.1 Test sttistic: z = Criticl vlue: z = Fil to reject the null hypothesis. There is not sufficient evidence t the 1% significnce level to conclude tht the percentge of defects exceeds 3%. 4) H : p =.1 H : p >.1. α =.1 Test sttistic: z = Criticl vlue: z = Reject the null hypothesis. There is sufficient evidence t the 1% significnce level to conclude tht the percentge of defects exceeds 1%. 41) H : p =.5 H : p >.5. α =.1 Test sttistic: z = Criticl vlue: z = Fil to reject H. There is not sufficient evidence t the 1% significnce level to support the clim tht more thn hlf of ll those using the drug experience relief. 42) D 43) A 44) Test sttistic: z = P-vlue =.1472 Fil to reject the null hypotheses. There is not sufficient evidence t the 1% significnce level to conclude tht the percentge of defects exceeds 3%. 14

15 Answer Key Testnme: CH 8 SET 1 45) H : p =.1 H : p >.1. α =.1 Test sttistic: z = P-vlue =. (to four deciml plces) Reject the null hypothesis. There is sufficient evidence t the 1% significnce level to conclude tht the percentge of defects exceeds 1%. 15

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

Unit 29: Inference for Two-Way Tables

Unit 29: Inference for Two-Way Tables Unit 29: Inference for Two-Wy Tbles Prerequisites Unit 13, Two-Wy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike

More information

Distributions. (corresponding to the cumulative distribution function for the discrete case).

Distributions. (corresponding to the cumulative distribution function for the discrete case). Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

Small Businesses Decisions to Offer Health Insurance to Employees

Small Businesses Decisions to Offer Health Insurance to Employees Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers. 2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of

More information

Why is the NSW prison population falling?

Why is the NSW prison population falling? NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

274 Chapter 13. Chapter 13

274 Chapter 13. Chapter 13 74 hpter 3 hpter 3 3. () ounts will be obtined from the smples so th problem bout compring proportions. (b) h n observtionl study compring rndom smples selected from two independent popultions. 3. () cores

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

Numeracy across the Curriculum in Key Stages 3 and 4. Helpful advice and suggested resources from the Leicestershire Secondary Mathematics Team

Numeracy across the Curriculum in Key Stages 3 and 4. Helpful advice and suggested resources from the Leicestershire Secondary Mathematics Team Numercy cross the Curriculum in Key Stges 3 nd 4 Helpful dvice nd suggested resources from the Leicestershire Secondry Mthemtics Tem 1 Contents pge The development of whole school policy 3 A definition

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the

More information

NQF Level: 2 US No: 7480

NQF Level: 2 US No: 7480 NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................

More information

Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 4721 Money and Banking Problem Set 2 Answer Key Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

More information

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define

More information

Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials

Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic

More information

baby on the way, quit today

baby on the way, quit today for mums-to-be bby on the wy, quit tody WHAT YOU NEED TO KNOW bout smoking nd pregnncy uitting smoking is the best thing you cn do for your bby We know tht it cn be difficult to quit smoking. But we lso

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

How To Study The Effects Of Music Composition On Children

How To Study The Effects Of Music Composition On Children C-crcs Cognitive - Counselling Reserch & Conference Services (eissn: 2301-2358) Volume I Effects of Music Composition Intervention on Elementry School Children b M. Hogenes, B. Vn Oers, R. F. W. Diekstr,

More information

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding 1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information

Health insurance exchanges What to expect in 2014

Health insurance exchanges What to expect in 2014 Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount

More information

2015 EDITION. AVMA Report on Veterinary Compensation

2015 EDITION. AVMA Report on Veterinary Compensation 2015 EDITION AVMA Report on Veterinry Compenstion AVMA Report on Veterinry Compenstion 2015 EDITION Copyright 2015 by the All rights reserved. ISBN-13: 978-1-882691-31-9 AVMA Report on Veterinry Compenstion

More information

Health insurance exchanges What to expect in 2014

Health insurance exchanges What to expect in 2014 Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 11/12 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount

More information

Health insurance marketplace What to expect in 2014

Health insurance marketplace What to expect in 2014 Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum

More information

Warm-up for Differential Calculus

Warm-up for Differential Calculus Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

Utilization of Smoking Cessation Benefits in Medicaid Managed Care, 2009-2013

Utilization of Smoking Cessation Benefits in Medicaid Managed Care, 2009-2013 Utiliztion of Smoking Cesstion Benefits in Medicid Mnged Cre, 2009-2013 Office of Qulity nd Ptient Sfety New York Stte Deprtment of Helth Jnury 2015 Introduction According to the New York Stte Tocco Control

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

Contextualizing NSSE Effect Sizes: Empirical Analysis and Interpretation of Benchmark Comparisons

Contextualizing NSSE Effect Sizes: Empirical Analysis and Interpretation of Benchmark Comparisons Contextulizing NSSE Effect Sizes: Empiricl Anlysis nd Interprettion of Benchmrk Comprisons NSSE stff re frequently sked to help interpret effect sizes. Is.3 smll effect size? Is.5 relly lrge effect size?

More information

All pay auctions with certain and uncertain prizes a comment

All pay auctions with certain and uncertain prizes a comment CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 1-2015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin

More information

Estimating Exchange Rate Exposures:

Estimating Exchange Rate Exposures: Estimting Exchnge Rte Exposures: Issues in Model Structure * Gordon M. Bodnr ** Pul H. Nitze School of Advnced Interntionl Studies, The Johns Hopkins University 1740 Msschusetts Avenue NW Wshington, DC

More information

Week 7 - Perfect Competition and Monopoly

Week 7 - Perfect Competition and Monopoly Week 7 - Perfect Competition nd Monopoly Our im here is to compre the industry-wide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between

More information

COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT

COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, cross-clssified

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Active & Retiree Plan: Trustees of the Milwaukee Roofers Health Fund Coverage Period: 06/01/2015-05/31/2016 Summary of Benefits and Coverage:

Active & Retiree Plan: Trustees of the Milwaukee Roofers Health Fund Coverage Period: 06/01/2015-05/31/2016 Summary of Benefits and Coverage: Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge for: Single & Fmily Pln Type: NPOS This is only summry. If you wnt more detil bout your coverge nd costs, you cn get the complete

More information

n Using the formula we get a confidence interval of 80±1.64

n Using the formula we get a confidence interval of 80±1.64 9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge

More information

NOTES. Cohasset Associates, Inc. 2015 Managing Electronic Records Conference 8.1

NOTES. Cohasset Associates, Inc. 2015 Managing Electronic Records Conference 8.1 Cohsset Assocites, Inc. Expnding Your Skill Set: How to Apply the Right Serch Methods to Your Big Dt Problems Juli L. Brickell H5 Generl Counsel MER Conference My 18, 2015 H5 POWERING YOUR DISCOVERY GLOBALLY

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

Anthem Blue Cross Life and Health Insurance Company University of Southern California Custom Premier PPO 800/20%/20%

Anthem Blue Cross Life and Health Insurance Company University of Southern California Custom Premier PPO 800/20%/20% Anthem Blue Cross Life nd Helth Insurnce Compny University of Southern Cliforni Custom Premier 800/20%/20% Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge Period: 01/01/2015-12/31/2015

More information

Enterprise Risk Management Software Buyer s Guide

Enterprise Risk Management Software Buyer s Guide Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

Humana Critical Illness/Cancer

Humana Critical Illness/Cancer Humn Criticl Illness/Cncer Criticl illness/cncer voluntry coverges py benefits however you wnt With our criticl illness nd cncer plns, you'll receive benefit fter serious illness or condition such s hert

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn 33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of

More information

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999 Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,

More information

How To Find Out How A Worker'S Work Ethic Is Related To The Ability To Get A Job

How To Find Out How A Worker'S Work Ethic Is Related To The Ability To Get A Job RtSWD Reserch Notes Reserch Note No. 11 Previously relesed s RtSWD Working Pper No. 15 Popultion Aging nd Trends in the Provision of Continued Eduction Regin T. Riphhn, Prvti Trübswetter 2007 Reserch Notes

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

FUNDING OF GROUP LIFE INSURANCE

FUNDING OF GROUP LIFE INSURANCE TRANSACTIONS OF SOCIETY OF ACTUARIES 1955 VOL. 7 NO. 18 FUNDING OF GROUP LIFE INSURANCE CHARLES L. TROWBRIDGE INTRODUCTION T RADITIONALLY the group life insurnce benefit hs been finnced on yerly renewble

More information

Health Information Systems: evaluation and performance of a Help Desk

Health Information Systems: evaluation and performance of a Help Desk 536 Digitl Helthcre Empowering Europens R. Cornet et l. (Eds.) 2015 Europen Federtion for Medicl Informtics (EFMI). This rticle is published online with Open Access by IOS Press nd distributed under the

More information

10.6 Applications of Quadratic Equations

10.6 Applications of Quadratic Equations 10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,

More information

Integration. 148 Chapter 7 Integration

Integration. 148 Chapter 7 Integration 48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but

More information

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1 PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.

More information

How To Get Low Wage Workers Covered By Insurance Through Their Employer

How To Get Low Wage Workers Covered By Insurance Through Their Employer Stephen H. Long M. Susn Mrquis Low-Wge Workers nd Helth Insurnce Coverge: Cn Policymkers Trget Them through Their Employers? Mny policy inititives to increse helth insurnce coverge would subsidize employers

More information

Small Business Cloud Services

Small Business Cloud Services Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly

More information

Lump-Sum Distributions at Job Change, p. 2

Lump-Sum Distributions at Job Change, p. 2 Jnury 2009 Vol. 30, No. 1 Lump-Sum Distributions t Job Chnge, p. 2 E X E C U T I V E S U M M A R Y Lump-Sum Distributions t Job Chnge GROWING NUMBER OF WORKERS FACED WITH ASSET DECISIONS AT JOB CHANGE:

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Participation and investment decisions in a retirement plan: the influence of colleagues choices

Participation and investment decisions in a retirement plan: the influence of colleagues choices Journl of Public Economics 85 (2002) 121 148 www.elsevier.com/ locte/ econbse Prticiption nd investment decisions in retirement pln: the influence of collegues choices Esther Duflo,b, *, Emmnuel Sez MIT,

More information

Uplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu

Uplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu Uplift Cpcity of K-Series Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid,

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

4.11 Inner Product Spaces

4.11 Inner Product Spaces 314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces

More information

Binary Representation of Numbers Autar Kaw

Binary Representation of Numbers Autar Kaw Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy

More information

Integration by Substitution

Integration by Substitution Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is

More information

STATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY

STATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY Yer STATUS OF LAND-BASED WIND ENERGY Deutsche WindGurd GmbH - Oldenburger Strße 65-26316 Vrel - Germny +49 (4451)/9515 - info@windgurd.de - www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Section 7-4 Translation of Axes

Section 7-4 Translation of Axes 62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the

More information

c. Values in statements are broken down by fiscal years; many projects are

c. Values in statements are broken down by fiscal years; many projects are Lecture 18: Finncil Mngement (Continued)/Csh Flow CEE 498 Construction Project Mngement L Schedules A. Schedule.of Contrcts Completed See Attchment # 1 ll. 1. Revenues Erned 2. Cost of Revenues 3. Gross

More information

Review Problems for the Final of Math 121, Fall 2014

Review Problems for the Final of Math 121, Fall 2014 Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since

More information

Chapter. Contents: A Constructing decimal numbers

Chapter. Contents: A Constructing decimal numbers Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting

More information

ORIGINAL ARTICLE. An Evaluation of the Mars Letter Contrast Sensitivity Test

ORIGINAL ARTICLE. An Evaluation of the Mars Letter Contrast Sensitivity Test 1040-5488/05/8211-0970/0 VOL. 82, NO. 11, PP. 970 975 OPTOMETRY AND VISION SCIENCE Copyright 2005 Americn Acdemy of Optometry ORIGINAL ARTICLE An Evlution of the Mrs Letter Contrst Sensitivity Test BRADLEY

More information

Morgan Stanley Ad Hoc Reporting Guide

Morgan Stanley Ad Hoc Reporting Guide spphire user guide Ferury 2015 Morgn Stnley Ad Hoc Reporting Guide An Overview For Spphire Users 1 Introduction The Ad Hoc Reporting tool is ville for your reporting needs outside of the Spphire stndrd

More information

6.2 Volumes of Revolution: The Disk Method

6.2 Volumes of Revolution: The Disk Method mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

SPECIAL PRODUCTS AND FACTORIZATION

SPECIAL PRODUCTS AND FACTORIZATION MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come

More information

TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING

TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING Sung Joon Kim*, Dong-Chul Che Kore Aerospce Reserch Institute, 45 Eoeun-Dong, Youseong-Gu, Dejeon, 35-333, Kore Phone : 82-42-86-231 FAX

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one. 5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued

More information

COMPONENTS: COMBINED LOADING

COMPONENTS: COMBINED LOADING LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of

More information

Assessing authentically in the Graduate Diploma of Education

Assessing authentically in the Graduate Diploma of Education Assessing uthenticlly in the Grdute Diplom of Eduction Dr Mree DinnThompson Dr Ruth Hickey Dr Michelle Lsen WIL Seminr JCU Nov 12 2009 Key ides plnning process tht embeds uthentic ssessment, workintegrted

More information

I calculate the unemployment rate as (In Labor Force Employed)/In Labor Force

I calculate the unemployment rate as (In Labor Force Employed)/In Labor Force Introduction to the Prctice of Sttistics Fifth Edition Moore, McCbe Section 4.5 Homework Answers to 98, 99, 100,102, 103,105, 107, 109,110, 111, 112, 113 Working. In the lnguge of government sttistics,

More information

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time

More information

The Determinants of Private Medical Insurance Prevalence in England

The Determinants of Private Medical Insurance Prevalence in England The Determinnts of Privte Medicl Insurnce Prevlence in Englnd Derek R. King, Elis Mossilos LSE Helth nd Socil Cre, London School of Economics nd Politicl Science LSE Helth nd Socil Cre Discussion Pper

More information

Techniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist

Techniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist Techniques for Requirements Gthering nd Definition Kristin Persson Principl Product Specilist Requirements Lifecycle Mngement Elicit nd define business/user requirements Vlidte requirements Anlyze requirements

More information

Statistics A B C D E F G H I J K L M N O. Review set 5. Contents:

Statistics A B C D E F G H I J K L M N O. Review set 5. Contents: 5 Sttistics Contents: A B C D E F G H I J K L M N O Descriing dt Collecting informtion Rndom smpling Presenting nd interpreting dt Grouped discrete dt Continuous (intervl) dt Mesures of centres of distriutions

More information

MATH 150 HOMEWORK 4 SOLUTIONS

MATH 150 HOMEWORK 4 SOLUTIONS MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive

More information

persons withdrawing from addiction is given by summarizing over individuals with different ages and numbers of years of addiction remaining:

persons withdrawing from addiction is given by summarizing over individuals with different ages and numbers of years of addiction remaining: COST- BENEFIT ANALYSIS OF NARCOTIC ADDICTION TREATMENT PROGRAMS with Specil Reference to Age Irving Leveson,l New York City Plnning Commission Introduction Efforts to del with consequences of poverty,

More information

ffiiii::#;#ltlti.*?*:j,'i#,rffi

ffiiii::#;#ltlti.*?*:j,'i#,rffi 5..1 EXPEDTNG A PROJECT. 187 700 6 o 'o-' 600 E 500 17 18 19 20 Project durtion (dys) Figure 6-6 Project cost vs. project durtion for smple crsh problem. Using Excel@ to Crsh Project T" llt ffiiii::#;#ltlti.*?*:j,'i#,rffi

More information

Rate and Activation Energy of the Iodination of Acetone

Rate and Activation Energy of the Iodination of Acetone nd Activtion Energ of the Iodintion of Acetone rl N. eer Dte of Eperiment: //00 Florence F. Ls (prtner) Abstrct: The rte, rte lw nd ctivtion energ of the iodintion of cetone re detered b observing the

More information

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl

More information

A COMPARISON OF ALCOHOL SCREENING INSTRUMENTS AMONG UNDER-AGED DRINKERS TREATED IN EMERGENCY DEPARTMENTS

A COMPARISON OF ALCOHOL SCREENING INSTRUMENTS AMONG UNDER-AGED DRINKERS TREATED IN EMERGENCY DEPARTMENTS Alcohol & Alcoholism Vol. 37, No. 5, pp. 444 450, 2002 A COMPARISON OF ALCOHOL SCREENING INSTRUMENTS AMONG UNDER-AGED DRINKERS TREATED IN EMERGENCY DEPARTMENTS THOMAS M. KELLY 1 *, JOHN E. DONOVAN 1, JANET

More information

Business Examples. What is a hypothesis? Recap : Hypothesis Testing. Recap : Confidence Intervals. Hypothesis Testing (intro)

Business Examples. What is a hypothesis? Recap : Hypothesis Testing. Recap : Confidence Intervals. Hypothesis Testing (intro) ypthesis Testing (intr) We hve discussed tw methds f mking inference n prmeters in ppultin bsed n rndm smple (in English, hw d we figure ut the true men r prprtin) Pint estimtes give us single guess Stt

More information

How To Network A Smll Business

How To Network A Smll Business Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Exercises in KS3 Mathematics Levels 7-8. R Joinson

Exercises in KS3 Mathematics Levels 7-8. R Joinson Exercises in KS Mthemtics Levels 7-8 R Joinson Sumbooks Northwy Chester CH 8BB Exercises in KS Mthemtics - Levels 7 nd 8 First Published 00 Copyright R Joinson nd Sumbooks This pckge of worksheets is sold

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information