274 Chapter 13. Chapter 13

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "274 Chapter 13. Chapter 13"

Transcription

1 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 will be obtined from the smples so th problem bout compring mens (verge scores). (b) h n experiment becuse the reserchers n imposing tretment nd mesuring response vrible. ince these re volunteers we will not be ble to generlize the results to ll gmers. 3.3 () wo smples. he two segments re used by two independent groups of children. (b) Pired dt. he two segments re both used by ech child. 3.4 () ingle smple. he smple men will be compred with the known concentrtion. (b) wo smples. he men concentrtion in bekers with the new method will be compred to the men concentrtion in different bekers with the old method 3.5 () H : = : >, where nd re the men improvement of reding bility of the tretment nd control group respectively. (b) he tretment group slightly left-skewed with greter men nd smller stndrd devition ( x =5.48, s=.) thn the control group ( x =4.5, s= 7.5). he htogrms below show no serious deprtures from ormlity for the tretment group (on the left) nd one unusully lrge score for the control group (on the right) ount 3 ount DRP score (tretment group) DRP score (control group) 8 he boxplot (on the left below) lso shows tht the medin DRP score higher for the tretment group nd the IQR higher for the control group. otice tht the unusully high score not identified s n outlier by initb. he combined orml probbility plot (on the right below) shows n overll liner trend for both sets of scores, so the orml condition stfied for both groups.

2 ompring wo Popultion Prmeters retment Percent ontrol DRP score DRP score 6 8 (c) Rndomiztion ws not possible, becuse exting clsses were used. he resercher could not rndomly ssign the students to the two groups without drupting clsses. 3.6 () he two popultions re brest-feeding women nd other women. We wnt to test H : = : <, where nd re the men percent chnge in minerl content of the spines over three months for brest-feeding nd other mothers, respectively. (b) Dotplots (on the left) nd boxplots (on the right) re shown below. oth dtributions pper to be resonbly orml. rest rest Other inerl content (% chnge).6 3. Other inerl content (% chnge) rest-feeding mothers hve lower men minerl content ( x = 3.587, s=.56) with more vribility thn other mothers ( x =.34, s=.97). (c) h n observtionl study so we cnnot mke cuse nd effect conclusion, but th effect certinly worth investigting becuse there ppers to be difference in the two groups of mothers for some reson () he hypotheses should involve nd (popultion mens) rther thn x nd x (smple mens). (b) he smples re not independent. We would need to compre the scores of the boys to the scores for the girls. (c) We need the P-vlue to be smll (for exmple, less thn.5) to reject. A lrge P-vlue like th gives no reson to doubt H. H 3.8 () Answers will vry. Exmine rndom digits, if the digit even then use Design A, otherwe use Design. Once you use design 3 dys, stop nd use the other design for the remining dys in the study. he first three digits re even, so the first three dys for using Design A would be dys,, nd 3. (ote, if Design A used when the digit odd, then the first three dys for using Design A re dy 5, dy 6, nd dy 8.) (b) Use two-sided lterntive ( H : A = : A ), becuse we (presumbly) hve no prior suspicion tht one

3 76 hpter 3 design will be better thn the other. (c) oth smple sizes re the sme ( n = n = 3 ), so the pproprite degrees of freedom would be df = 3 = 9. (d) ecuse.45 < t <.5, nd the lterntive two-sided, ble tells us tht.4 < P-vlue <.5. (oftwre gives P =.485.) We would reject H nd conclude tht there difference in the men dily sles for the two designs. 3.9 () We wnt to test H : = : >. he test stttic t =.3,. < P-vlue <. with df = (I clcultor gives P vlue =.3 with df = nd initb gives P-vlue =.3 with df=37). At the 5% significnce level, it does not mtter which method you use to obtin the P-vlue. he P-vlue (rounded to.3) less thn.5, so the dt give good evidence tht the new ctivities improve the men DRP score. (b) A 95% confidence intervl for ± = (.97, 8.94) with df = ; (.33, 8.68) on I clcultor with df = 37.86; nd (.637, ) using initb with df = 37. We estimte the men improvement in reding bility using the new reding ctivities compred to not using them over n 8-week period to be between.3 nd 8.68 points. 3. We wnt to test H : = : <. he test stttic t = 8.5, P-vlue <.5 with df = (the I clcultor nd initb give P-vlues very close to ). he smll P-vlue less thn ny resonble significnce level, sy %, so the dt give very strong evidence tht nursing mothers on verge lose more bone minerl thn other mothers. (b) A 95% confidence intervl for O ± = ( 4.86,.95) with df = ; ( 4.86,.986) on I clcultor with df =66. (see the screen shots below); nd ( 4.863,.98633) using initb with df = 66. We estimte the difference in the men chnge in bone minerl for brestfeeding mothers when compred to other mothers to be between bout 3% nd 5%, with brestfeeding mothers losing more bone density. 3. () ecuse the smple sizes re so lrge, the t procedures re robust ginst non- ormlity in the popultions. (b) A 9% confidence intervl for F ± = ($4.68, ) using df = ; ($43.54, $634.7) using df = 6; ($43.6, ) using df = 49.. We re 9% confident

4 ompring wo Popultion Prmeters 77 tht the difference in men summer ernings between $43.6 nd $ higher for men. (c) he smple not relly rndom, but there no reson to expect tht the method used should introduce ny bis. h known s systemtic smpling. (d) tudents without employment were excluded, so the survey results cn only (possibly) extend to employed undergrdutes. Knowing the number of unreturned questionnires would lso be useful. hese students re from one college, so it would be very helpful to know if th student body representtive of some lrger group of students. It very unlikely tht you will be ble to generlize these results to ll undergrdutes. 3. Answers will vry. 3.3 () We wnt to test H : R = W : R > W, where R nd W re the men percent chnge in polyphenols for men who drink red nd white wine respectively. he test stttic t = 3.8 with df = 8 nd.5 < P-vlue <.5. (b) he vlue of the test stttic the sme, but df = 4.97 nd the P-vlue.85 (initb gives. with df = 4). he more complicted degrees of freedom give smller nd less conservtive P-vlue. (c) h study ppers to hve been well-designed experiment, so it does provide evidence of custion. 3.4 () A 95% confidence intervl for R W ± = * (.8%, 8.45%). (b) With df = 4.97, t =.3 nd the confidence intervl.3% to 8.%. (initb gives.34% to 8.9% with df = 4.) here very little difference in the resulting confidence intervls. 3.5 () We wnt to test H : = : >, where nd re the men knee velocities for skilled nd novice femle competitive rowers, respectively. he test stttic t = nd the P-vlue =.5. ote tht the two-sided P-vlue provided on the A output, so to get the pproprite P-vlue for the one-sided test use.4/ =.5. ince.5 <., we reject H t the % level nd conclude tht the men knee velocity higher for skilled rowers. (b) Using df = 9., the criticl vlue t* =.86 nd the resulting confidence intervl for (.498,.8475). With 9% confidence, we estimte tht skilled femle rowers hve men ngulr knee velocity of between.498 nd.847 units higher thn tht of novice femle rowers. (c) king the conservtive pproch with ble, df = 7 nd the criticl vlue t* =.895. ince.895 >.86, the mrgin of error would be lrger, so the confidence intervl would be slightly wider. 3.6 () he msing t stttic t = (b) We wnt to test H : = :, where nd re the men weights of skilled nd novice femle competitive rowers, respectively. he test stttic t =.543 nd the P-vlue =.665. ince.665 >.5, we cnnot reject H t the 5% level. here no significnt

5 78 hpter 3 difference in the men weights for skilled nd novice rowers. (c) he more conservtive pproch would use df = 7. he t dtribution with df = 7 hs slightly hevier tils thn the t dtribution with df =., so the conservtive P-vlue would be lrger. 3.7 () wo-smple t test. (b) Pired t test. (c) Pired t test. (d) wo-smple t test. (e) Pired t test. 3.8 () he summry tble shown below. he only vlues not given directly re the stndrd devitions, which re found by computing s= E. (b) Use df = 9. Group retment n x s IDX Untreted (c) h completely rndomized design with one control group nd one tretment group. he esiest wy to crry out the rndomiztion might be to number the hmsters (or their individul cges) from to. Use the R pplet nd put blls in the popultion hopper. elect blls from the hopper. he hmsters with these numbers will be injected with IDX. he other hmsters will serve s the control group. 3.9 () Yes, the test stttic for testing H: = : > t = With either df = 9 or df =.5, we hve significnt result (P-vlue <. or P-vlue <.5, respectively), so there strong evidence tht IDX prolongs life. (b) If using df = 9, the 95% confidence intervl for ± = (4., 4.88). With 95% confidence we estimte tht IDX hmsters live, on verge, between 4. nd 4.88 dys longer thn untreted hmsters. If using df =.5, the intervl (4.49, 4.5). 3. () h two-smple t stttic, compring two independent groups (supplemented nd control). (b) Using the conservtive df = 5, t =.5 would hve P-vlue between.3 nd.4, which (s the report sid) not significnt. 3. We wnt to test H : = :. he test stttic 4..3 t = 3.74 nd the P-vlue between. nd. (df = 5) or (df =.95), greeing with the stted conclusion ( significnt difference). 3. () hese re pired t stttics: For ech bird, the number of dys behind the cterpillr pek ws observed, nd the t vlues were computed bsed on the pirwe differences between the first nd second yers. (b) For the control group, df = 5, nd for the supplemented group, df = 6. (c) he control t not significnt (so the birds in tht group did not dvnce their lying dte in the second yer ), while the supplemented group t significnt with one-sided P-vlue =.95 (so those birds did chnge their lying dte).

6 ompring wo Popultion Prmeters Answers will vry, but here n exmple. he difference between verge femle (55.5) nd mle (57.9) self-concept scores ws so smll tht it cn be ttributed to chnce vrition in the smples (t =.83, df = 6.8, P-vlue =.4). In other words, bsed on th smple, we hve no evidence tht men self-concept scores differ by gender. 3.4 () If the loggers hd known tht study would be done, they might hve (consciously or subconsciously) cut down fewer trees, in order to reduce the impct of logging. (b) Rndom ssignment llows us to mke cuse nd effect conclusion. (c) We wnt to test H : U = L : U > L, where U nd L re the men number of species in unlogged nd logged plots respectively. he test stttic t =. with df = 8 nd.5 < P vlue <.5. Logging does significntly reduce the men number of species in plot fter 8 yers t the 5% level, but not t the % level. (d) A 9% confidence intervl for U L ± = (.46, 7.). (initb gives n intervl from to 7.73.) We re 9% confident tht the difference in the mens for unlogged nd logged plots between.46 nd 7. species. 3.5 Let p denote the proportion of mice redy to breed in good corn yers nd p denote the proportion of mice redy to breed in bd corn yers. he smple proportions re p ˆ = 54 7 =.75 nd p ˆ = 7 =.588, nd the stndrd error E = A 9% confidence intervl for p p ± = (.58,.3753). With 9% confidence, we estimte tht the percent of mice redy to breed in the good corn yers between 5.% lower nd 37.5% higher thn in the bd yers. hese methods cn be used becuse the popultions of mice re certinly more thn times s lrge s the smples, nd the counts of successes nd filures re t lest 5 in both smples. We must view the trpped mice s n R of ll mice in the two res () he smple proportion of women who felt vulnerble p ˆW =.48, nd the corresponding smple proportion for men p ˆ =.73. (b) A 95% confidence intervl for the difference p pw (.73.48) ±.96 + = (.773,.487). With 95% confidence, we estimte the percent of men who feel vulnerble in th re to be bout.8 to.4 bove the proportion of women who feel vulnerble. otice tht not included in our confidence intervl, so there significnt difference between these proportions t the 5% level.

7 8 hpter () A 95% confidence intervl for p ±.96 = (.435,.4486) With 95% confidence, we estimte the percent of crs tht go fster thn 65 mph when no rdr present between 43.5% nd 44.86%. (b) A 95% confidence intervl for p pr (.44.3) ±.96 + = (.,.38). With 95% confidence, we estimte the percent of crs going over 65 mph between.% nd 3.8% higher when no rdr present compred to when rdr present. (c) In cluster of crs, where one driver s behvior might ffect the others, we do not hve independence; one of the importnt properties of rndom smple A 95% confidence intervl for p ±.96 = (.693,.657). We re % confident tht between 6% nd 65% of ll dults use the internet. (b) A 95% confidence intervl for pu p (.79.38) ±.96 + = (.3693,.456). We re % confident tht the difference in the proportion of internet users nd nonusers who expect businesses to hve Web sites between.37 nd Let p = the proportion of students who use illegl drugs in schools with drug testing progrm nd p = the proportion of students who use illegl drugs in schools without drug testing progrm. We wnt to test H: p = p : p < p. he combined smple 7+ 7 proportion pˆ c =.3 nd the test stttic z = 3.53, with P-vlue =.. ince. <.,.3(.3)( ) we reject H. here extremely strong evidence tht drug use mong thletes lower in schools tht test for drugs. here should be some concern expressed bout the condition of two independent simple rndom smples, becuse these two smples my not be representtive of similr schools. 3.3 () he ptients were rndomly ssigned to two groups. he first group of 649 ptients received only spirin nd the second group of 65 ptients received spirin nd dipyridmole. (b) We wnt to test H: p = pversus H : p p. he combined smple proportion pˆ c =.nd the test stttic z =.73, with (.)( ) P-vlue =.64. ince.64 <., there very strong evidence tht there significnt difference in the proportion of strokes between spirin only nd spirin plus dipyridmole. (c) A 95% confidence intervl for p p

8 ompring wo Popultion Prmeters (.4.) ±.96 + = (.3,.97). We re 95% confident tht the difference in the proportion of deths for the two tretment groups between. nd.. otice tht in the confidence intervl, so we do not hve evidence of significnt difference in the proportion of deths for these two tretments t the 5% level. (d) A ype I error committed if the reserchers conclude tht there significnt difference in the proportions of strokes with these two tretments, when in fct there no difference. A ype II error committed if the reserchers conclude tht there no difference in the proportions of strokes with these two tretments, when in fct there difference. A ype II error more serious becuse no ptients would be hrmed with ype I error, but ptients suffer unnecessrily from strokes if the best tretment not recommended. 3.3 For computer ccess t home, we wnt to test H : p = pw : p pw. he combined smple proportion pˆ c =.65 nd the test stttic z =., with P-vlue =.34. he sme hypotheses re.65(.65)( 3+ 96) used for the proportions with computer ccess t work. he combined smple proportion pˆ c =.6 nd the test stttic z = 3.9, (.6)( 3+ 96) with P-vlue <.4. ince the P-vlue below ny resonble significnce level, sy %, we hve very strong evidence of difference in the proportion of blcks nd whites who hve computer ccess t work. 3.3 () Let p = the proportion of women got pregnnt fter in vitro fertiliztion nd intercessory pryer nd p = the proportion of women in the control group who got pregnnt fter in vitro fertiliztion. We wnt to test H: p = p : p p. he combined smple 44 + proportion pˆ c =.3846 nd the test stttic z = 3., with P-vlue =.4. ince.4 <., we.3846(.3846)( ) reject H. h very strong evidence tht the observed difference in the proportions of women who got pregnnt not due to chnce. (b) h study shows tht intercessory pryer my cuse n increse in pregnncy. However, it uncler if the women knew tht they were in tretment group. If they found out tht other people were prying for them, then their behviors my hve chnged nd there could be mny other fctors to explin the difference in the two proportions. (c) A ype I error would be committed if reserchers concluded tht the proportions of pregnncies re different, when in fct they re the sme. h my led mny couples to seek intercessory pryer. A ype II error would be committed if reserchers concluded tht the proportions re not different, when in fct they re different. ouples would fil to tke dvntge of helpful technique to improve their chnces of hving bby. For couples who re interested in hving bby, ype II error clerly more serious.

9 8 hpter () H should refer to popultion proportions p nd p, not smple proportions. (b) onfidence intervls ccount only for smpling error () Let p = the proportion of households where no messge ws left nd contct ws eventully mde nd p = the proportion of household where messge ws left nd contct ws eventully mde. We wnt to test H: p = p : p < p. he combined smple 58 + proportion pˆ c =.66 nd the test stttic z =.95, with P-vlue =.56. Yes, t the 5% level, there.66(.66)( + 9) good evidence tht leving messge increses the proportion of households tht re eventully contcted. (b) Let p = the proportion of households where no messge ws left but the survey ws completed nd p = the proportion of household where messge ws left nd the survey ws completed. We wnt to test H: p = p : p < p. he combined smple proportion pˆ c =.47 nd the test stttic z =.8, with P-vlue =.3. Yes, t the 5% level,.47(.47)( + 9) there good evidence tht leving messge increses the proportion of households who complete the survey. (c) A 95% confidence intervl for the difference p pwhen deling with eventul contct (.8,.3). A 95% confidence intervl for the difference p pwhen deling with completed surveys (.39,.). Although these effects do not pper to be lrge, when you re deling with hundreds (or thousnds) of surveys nything you cn do to improve nonresponse in the rndom smple useful () H: p = p : p > p where p the proportion of ll HIV ptients tking plcebo tht develop AID nd p the proportion of ll HIV ptients tking AZ tht develop AID. he popultions re much lrger thn the smples, nd npˆ, n( pˆ ), npˆ, n ( p) c c c 38 7 re ll t lest 5. (b) he smple proportions re p ˆ = =.874, p ˆ = =.39, nd p ˆc =.63. he test stttic z =.93, with P-vlue.63(.63)( ) of.7. here very strong evidence tht significntly smller proportion of ptients tking AZ develop AID thn if they took control. (c) either the subjects nor the reserchers who hd contct with them knew which subjects were getting which drug A ype I error would be committed if reserchers concluded tht the tretment more effective thn plcebo, when in fct it not. A consequence tht ptients would be tking AZ nd perhps suffering from side effects from the mediction tht not helpful. A ype II error would be committed if reserchers conclude tht there no difference in the success of ˆc

10 ompring wo Popultion Prmeters 83 AZ nd plcebo, when in fct there difference. he consequence tht ptients would not get the best possible tretment. A ype II error more serious in th sitution becuse we wnt ptients to get the best possible tretment () he number of orders completed in 5 dys or less before the chnges ws X =.6 = 3. With p ˆ =.6 nd Ep ˆ.59, the 95% confidence intervl for p (.9,.8). (b) After the chnges, X =.9 = 8. With p ˆ =.9 nd Ep ˆ., the 95% confidence intervl for p (.8584,.946). (c) he stndrd error of the difference in the proportions Ep ˆ nd the 95% confidence intervl for pˆ.335 p p (.6743,.857) or bout 67.4% to 8.6%. o, the confidence intervls re not directly relted. Ech intervl bsed on different smpling dtribution. Properties of the smpling dtribution of the difference cn be obtined from properties of the individul smpling dtributions in prts () nd (b), but the upper nd lower limits of the intervls re not directly relted () We must hve two simple rndom smples of high-school students from Illino; one for freshmn nd one for seniors. (b) he smple proportion of freshmn who hve used 34 nbolic steroids p ˆ F =.3. ince the number of successes (34) nd the number of 679 filures (645) re both t lest, the z confidence intervl cn be used. A 95% confidence intervl for p F.3±.96 = (.35,.7). We re 95% confident 679 tht between.35% nd.7% of high-school freshmn in Illinios hve used nbolic steroids. 4 (c) he smple proportion of seniors who hve used nbolic steroids p ˆ = otice tht.76 flls in the 95% confidence intervl for plusible vlues of pf from prt (b), so there no evidence of significnt difference in the two proportions. he test stttic for forml hypothes test z =.54 with P-vlue = We wnt to test H: p = p : p p. From the output, z = 3.45 with P- vlue =.6, showing significnt difference in the proportion of children in the two ge groups who sorted the products correctly. A 95% confidence intervl for p p (.5579, ). With 95% confidence we estimte tht between 5.4% nd 5.3% more 6- to 7- yer-olds cn sort new products into the correct ctegory thn 4- to 5-yer-olds () he two smple proportions re p ˆW =.3 nd p ˆ =.467. (b) We 53 8 wnt to test H : pw = p : pw p. he combined smple proportion pˆ c =.368 nd the test stttic z = 3.89, (.368)( ) with P-vlue <.. ince the P-vlue less thn ny resonble significnce level, sy

11 84 hpter 3 %, we reject H. We hve very strong evidence tht there significnt difference between the proportions of injured in-line skters who sustin wrt injuries with nd without wrt gurds. (hese re Rs of ll people injured while in-line skting with nd without wrt gurds, so we cn only mke our inference to these popultions.) (c) he proportion of nonresponse 45/6 =.84 or bout.84%. (d) Yes. uppose tht ll 45 people who were not interviewed were injured while wering wrt gurds. (h unlikely, but we re looking t the extreme cse to see if our nswer could chnge.) he proportion of injuries with wrt gurds now pˆ W =.54. he test stttic would become z =.49 with P vlue of.36, which not significnt. AE LOED! () ) We wnt to test H: = : >, where the men drive-thru service time for cdonld s (urger King) in nd the men percent drive-thru service time for cdonld s (urger King) in yer fter the incentive/rewrds progrms were implemented. () Using initb with df = 93, the 95% confidence intervl for ± = (6.574,.36). With 95% confidence we estimte tht the verge drive-thru service time decresed between 6.5 nd. seconds fter the incentive/rewrds progrm ws implemented t cdonld s. (3) We wnt to test H : = : >, where the men drive-thru service time for cdonld s in 4 nd the men percent drive-thru service time for co ell in he test stttic t = 4.6 with df = (the lrgest vlue below in ble ) or 6 (with initb) nd P-vlue <.5. Yes, these dt provide extremely strong evidence tht drive-thru service times t co ell were significntly fster thn those t cdonld s. (4) We wnt to test H: p = p : p < p where p the proportion of ll orders in tht were filled ccurtely nd correct chnge ws given nd p the proportion of orders in tht were filled ccurtely nd correct chnge ws given. he popultions re npˆ, n pˆ, npˆ, n p re ll t lest 5. (b) he much lrger thn the smples, nd c c c smple proportions re p ˆ =.8, p ˆ =.884, nd pˆ c = =.848. he test stttic z = 3.43, with P-vlue of.3. Yes, there.848(.848)( ) ws significnt improvement in ccurcy between nd. In short, the difference observed from these two independent smples (or something more extreme) would only occur bout 3 times in, trils. We hve very convincing evidence tht the observed difference not due to chnce, but to some other fctor, perhps better trining by the mngers! (5) Let p denote the proportion of inccurte for hick-fil-a in nd p denote the proportion inccurte orders t cdonld s in. A 95% confidence intervl for ±.96 + = (.95,.57). We re 95% ˆc p p

12 ompring wo Popultion Prmeters 85 confident tht the difference in the proportion of inccurte orders in for the two fst food resturnts between.9 nd.. otice tht not in the confidence intervl, so there significnt difference in the proportion of inccurte orders t the two resturnts. 3.4 () h two-smple t test. he two groups of women re (presumbly) independent. (b) df = 45 = 44. (c) he smple sizes re lrge enough, n = n = 45, tht the verges will be pproximtely orml, so the fct tht the individul responses do not follow orml dtribution hs little effect on the relibility of the t procedure. 3.4 () h n observtionl study becuse the reserchers simply observed the rndom smples of women; they did not impose ny tretments. (b) We wnt to test H : p = p versus H : p > p. he combined smple proportion pˆ c =.7448 nd the test stttic z = 5., with P-vlue <.. We hve very strong.7448(.7448)( + 7) evidence tht smller proportion of femle Hpnic drivers wer set belts in oston thn in ew York We wnt to test H : ph = pw : ph pw. he combined smple proportion pˆ c =.545 nd the test stttic z =.86, (.545)( ) with P-vlue = ince.3898 >.5, there not significnt difference between Hpnic nd white drivers. For the size of the difference, construct 95% (or other level) confidence intervl. A 95% confidence intervl for ph pw ( ) ±.96 + = (.8,.398). With 95% confidence we estimte the difference in the proportions for Hpnic nd white drivers who were set belts to be between. nd.4. otice tht in the 95% confidence intervl, so we would conclude tht there no difference t the 5% significnce level We wnt to test H : = : >, where the men difference (post pre) for the tretment group nd the men difference (post pre) for the control group. he boxplots (on the left below) show tht the dtributions re roughly symmetric with no outlier, nd the orml probbility plots (on the right below) show liner trends which indicte tht the orml dtribution resonble for these dt.

13 86 hpter diff Percent diff Differences (Post - Pre) Differences (Post - Pre) 5 he test stttic t = , with.5 < P-vlue <.5 nd df = 7 (initb gives P-vlue of.39 with df=3). he P-vlue less thn.5, so the dt give good evidence tht the positive subliminl messge brought bout greter improvement in mth scores thn the control. (b) A 9% confidence intervl for ± = (.3, 6.7) with df = 7; (.35, 6.65) using initb with df = 3. With 9% confidence, we estimte the men difference in gins to be.35 to 6.65 points better for the tretment group. (c) h ctully repeted mesures design, where two mesurements (repeted mesures) re tken on the sme individuls. ny students will probbly describe th design s completely rndomized design for two groups, with twt insted of mesuring one response vrible on ech individul, two mesurements re mde nd we compre the differences (improvements) () A 99% confidence intervl for p pw ( ) ± = (.465,.3359). Yes, becuse the 99% confidence intervl does not contin. (b) We wnt to test H : = W versus H : W. he test stttic t =.87, with P-vlue close to (initb reports P-vlue of.387 with df = 777.) ince.4 >., the difference between the men scores of men nd women not significnt t the % level () tched pirs t. (b) wo-smple t. (c) wo-smple t. (d) tched pirs t. (e) tched pirs t () A 99% confidence intervl for OP WI ± = (6.55, 69.45). (b) he fct tht the smple sizes re both so lrge (36 nd 395).

14 ompring wo Popultion Prmeters () We wnt to test H : P = : P >. he test stttic t =.7, with P-vlue close to.5. (initb reports P-vlue of with df = 44.) ince.5 >.5, we do not hve strong evidence tht pets hve higher men cholesterol thn clinic dogs. (b) A 95% confidence intervl for P ± = ( 4.579, 5.579). initb gives ( , ). With 95% confidence, we estimte the difference in the men cholesterol levels between pets nd clinic doges to be between 4 nd 53 mg/dl. (c) A 95% confidence intervl 68 for p 93±.6 = (65.58,.479). initb gives (65.534,.466). With 6 95% confidence, we estimte the men cholesterol level in pets to be between 65.5 nd.5 mg/dl. (d) We must hve two independent rndom smples to mke the inferences in prts () nd (b) nd rndom smple of pets for prt (c). It unlikely tht we hve rndom smples from either popultion () he two smple proportions re p ˆ = for residents of congested streets nd p ˆ = for residents of bypss streets. he difference pˆ ˆ p =.5 with stndrd error of E = (b) he hypotheses re H : p = p : p < p. he lterntive reflects the resonble expecttion tht reducing pollution might decrese wheezing. (c) he combined smple proportion pˆ c =.6 nd the test stttic z = 4.85, (.6)( ) with P-vlue <.. A sketch of the dtribution of the test stttic, ssuming H true, shown below orml density curve est stttic (z).5 5. otice tht reference line provided t 4.85 to illustrte how fr down in the lower til of the dtribution tht th vlue of the test stttic locted. he P-vlue tells us the chnce of observing test stttic of 4.85 or something smller if H true. As you cn see there lmost no chnce of th hppening, so we hve very convincing evidence tht the percent of residents reporting improvement from wheezing higher for residents of bypss streets. (d) he 95% confidence intervl, using the stndrd error from prt (b), hs mrgin of error =.68. hus, the 95% confidence intervl.5 ±.68 = (.,

15 88 hpter 3.838). he percentge reporting improvement ws between 8% nd % higher for bypss residents. (e) here my be geogrphic fctors (e.g., wether) or culturl fctors (e.g., diet) tht limit how much we cn generlize the conclusions. 3.5 () A 99% confidence intervl for ph p (.7.4) ± = (.99,.49). With 99% confidence, the percentge of blcks between 4.9% nd 9.9% higher for non-household providers. Yes, the difference significnt t the % level becuse the 99% confidence intervl does not contin. (b) A 99% confidence intervl for H.6. ± = (.7944,.456), using df =. (initb gives (.7948,.4588) with df =456.) With 99% confidence, the men number of yers of school for non-household workers between.4 nd.79 yers higher thn household providers. Yes, the difference significnt t the % level, becuse not included in the 99% confidence intervl.

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

STA 2023 Test #3 Practice Multiple Choice

STA 2023 Test #3 Practice Multiple Choice STA 223 Test #3 Prctice Multiple Choice 1. A newspper conducted sttewide survey concerning the 1998 rce for stte sentor. The newspper took rndom smple (ssume it is n SRS) of 12 registered voters nd found

More information

Chapter 8 - Practice Problems 1

Chapter 8 - Practice Problems 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.

More information

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

N Mean SD Mean SD Shelf # Shelf # Shelf #

N Mean SD Mean SD Shelf # Shelf # Shelf # NOV xercises smple of 0 different types of cerels ws tken from ech of three grocery store shelves (1,, nd, counting from the floor). summry of the sugr content (grms per serving) nd dietry fiber (grms

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

Tests for One Poisson Mean

Tests for One Poisson Mean Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution

More information

AP Statistics Testbank 7

AP Statistics Testbank 7 AP Sttistics Testbnk 7 Multiple-Choice Questions 1) In formulting hypotheses for sttisticl test of significnce, the null hypothesis is often ) sttement of "no effect" or "no difference." b) the probbility

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

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

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

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

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

Stat 301 Review (Test 2)

Stat 301 Review (Test 2) Stt 31 Review (Test 2) Below is tble of the tests tht we covered in chpters 6, 7, 12 nd 13. You will need to know the following for ech of the tests 1. Given problem, which test should be used? 2. How

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

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

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

1 Numerical Solution to Quadratic Equations

1 Numerical Solution to Quadratic Equations cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll

More information

Biostatistics 103: Qualitative Data Tests of Independence

Biostatistics 103: Qualitative Data Tests of Independence Singpore Med J 2003 Vol 44(10) : 498-503 B s i c S t t i s t i c s F o r D o c t o r s Biosttistics 103: Qulittive Dt Tests of Independence Y H Chn Prmetric & non-prmetric tests (1) re used when the outcome

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

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

On the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding

On the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl

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

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

C-crcs Cognitive - Counselling Research & Conference Services (eissn: 2301-2358)

C-crcs Cognitive - Counselling Research & Conference Services (eissn: 2301-2358) 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

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

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

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

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

Square Roots Teacher Notes

Square Roots Teacher Notes Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this

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

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

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

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

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

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

Quadratic Equations. Math 99 N1 Chapter 8

Quadratic Equations. Math 99 N1 Chapter 8 Qudrtic Equtions Mth 99 N1 Chpter 8 1 Introduction A qudrtic eqution is n eqution where the unknown ppers rised to the second power t most. In other words, it looks for the vlues of x such tht second degree

More information

Net Change and Displacement

Net Change and Displacement mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the

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

Biostatistics 102: Quantitative Data Parametric & Non-parametric Tests

Biostatistics 102: Quantitative Data Parametric & Non-parametric Tests Singpore Med J 2003 Vol 44(8) : 391-396 B s i c S t t i s t i c s F o r D o c t o r s Biosttistics 102: Quntittive Dt Prmetric & Non-prmetric Tests Y H Chn In this rticle, we re going to discuss on the

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

Section 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables

Section 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long

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

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

AP STATISTICS SUMMER MATH PACKET

AP STATISTICS SUMMER MATH PACKET AP STATISTICS SUMMER MATH PACKET This pcket is review of Algebr I, Algebr II, nd bsic probbility/counting. The problems re designed to help you review topics tht re importnt to your success in the clss.

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

Curve Sketching. 96 Chapter 5 Curve Sketching

Curve Sketching. 96 Chapter 5 Curve Sketching 96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of

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

Great Britain Tourism Survey. December 2015

Great Britain Tourism Survey. December 2015 Gret Britin Tourism Survey December 2015 December Results 2014 vs. 2015 In the period October to December 2014, dt collection issue resulted in the number of GBTS interviews conducted in ech of these three

More information

10.5 Graphing Quadratic Functions

10.5 Graphing Quadratic Functions 0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions

More information

11. Fourier series. sin mx cos nx dx = 0 for any m, n, sin 2 mx dx = π.

11. Fourier series. sin mx cos nx dx = 0 for any m, n, sin 2 mx dx = π. . Fourier series Summry of the bsic ides The following is quick summry of the introductory tretment of Fourier series in MATH. We consider function f with period π, tht is, stisfying f(x + π) = f(x) for

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

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

The Chain Rule. rf dx. t t lim " (x) dt " (0) dx. df dt = df. dt dt. f (r) = rf v (1) df dx

The Chain Rule. rf dx. t t lim  (x) dt  (0) dx. df dt = df. dt dt. f (r) = rf v (1) df dx The Chin Rule The Chin Rule In this section, we generlize the chin rule to functions of more thn one vrible. In prticulr, we will show tht the product in the single-vrible chin rule extends to n inner

More information

Ae2 Mathematics : Fourier Series

Ae2 Mathematics : Fourier Series Ae Mthemtics : Fourier Series J. D. Gibbon (Professor J. D Gibbon, Dept of Mthemtics j.d.gibbon@ic.c.uk http://www.imperil.c.uk/ jdg These notes re not identicl word-for-word with my lectures which will

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

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

Numerical integration

Numerical integration Chpter 4 Numericl integrtion Contents 4.1 Definite integrls.............................. 4. Closed Newton-Cotes formule..................... 4 4. Open Newton-Cotes formule...................... 8 4.4

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Theory of Forces. Forces and Motion

Theory of Forces. Forces and Motion his eek extbook -- Red Chpter 4, 5 Competent roblem Solver - Chpter 4 re-lb Computer Quiz ht s on the next Quiz? Check out smple quiz on web by hurs. ht you missed on first quiz Kinemtics - Everything

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

Research Notes. RatSWD. Research Note No. 11. Population Aging and Trends in the Provision of Continued Education

Research Notes. RatSWD. Research Note No. 11. Population Aging and Trends in the Provision of Continued Education 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

pork.org Pork Industry Productivity Analysis National Pork Board Research Grant Report Dr. Kenneth J. Stalder, Iowa State University

pork.org Pork Industry Productivity Analysis National Pork Board Research Grant Report Dr. Kenneth J. Stalder, Iowa State University pork.org 800-456-7675 Complete REPORT Pork Industry Productivity Anlysis Ntionl Pork Bord Reserch Grnt Report Dr. Kenneth J. Stlder, Iow Stte University Industry Summry The swine industry, like ny industry,

More information

Homework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.

Homework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule. Text questions, Chpter 5, problems 1-5: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed

More information

Let us recall some facts you have learnt in previous grades under the topic Area.

Let us recall some facts you have learnt in previous grades under the topic Area. 6 Are By studying this lesson you will be ble to find the res of sectors of circles, solve problems relted to the res of compound plne figures contining sectors of circles. Ares of plne figures Let us

More information

The Quadratic Formula and the Discriminant

The Quadratic Formula and the Discriminant 9-9 The Qudrtic Formul nd the Discriminnt Objectives Solve qudrtic equtions by using the Qudrtic Formul. Determine the number of solutions of qudrtic eqution by using the discriminnt. Vocbulry discriminnt

More information

4.0 5-Minute Review: Rational Functions

4.0 5-Minute Review: Rational Functions mth 130 dy 4: working with limits 1 40 5-Minute Review: Rtionl Functions DEFINITION A rtionl function 1 is function of the form y = r(x) = p(x) q(x), 1 Here the term rtionl mens rtio s in the rtio of two

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

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

NOTES AND CORRESPONDENCE. Uncertainties of Derived Dewpoint Temperature and Relative Humidity

NOTES AND CORRESPONDENCE. Uncertainties of Derived Dewpoint Temperature and Relative Humidity MAY 4 NOTES AND CORRESPONDENCE 81 NOTES AND CORRESPONDENCE Uncertinties of Derived Dewpoint Temperture nd Reltive Humidity X. LIN AND K. G. HUBBARD High Plins Regionl Climte Center, School of Nturl Resource

More information

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s R 2 s(t).

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s R 2 s(t). 4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The

More information

Chapter 1 : Genetics 101

Chapter 1 : Genetics 101 Chpter 1 : Genetics 101 Understnding the underlying concepts of humn genetics nd the role of genes, behvior, nd the environment will be importnt to ppropritely collecting nd pplying genetic informtion

More information

Introduction to Mathematical Reasoning, Saylor 111

Introduction to Mathematical Reasoning, Saylor 111 Frction versus rtionl number. Wht s the difference? It s not n esy question. In fct, the difference is somewht like the difference between set of words on one hnd nd sentence on the other. A symbol is

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

Rational Expressions

Rational Expressions C H A P T E R Rtionl Epressions nformtion is everywhere in the newsppers nd mgzines we red, the televisions we wtch, nd the computers we use. And I now people re tlking bout the Informtion Superhighwy,

More information

Network Configuration Independence Mechanism

Network Configuration Independence Mechanism 3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting

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

Quick Reference Guide: One-time Account Update

Quick Reference Guide: One-time Account Update Quick Reference Guide: One-time Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)

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

The Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center

The Math Learning Center PO Box 12929, Salem, Oregon 97309 0929  Math Learning Center Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,

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

PRACTICE 7: DETERMINATION BY VOLUMETRIC TECHNICS OF ALKALINITY IN WATER SAMPLES

PRACTICE 7: DETERMINATION BY VOLUMETRIC TECHNICS OF ALKALINITY IN WATER SAMPLES Áre de Toxicologí PRACTICE 7: DETERMINATION BY VOLUMETRIC TECHNICS OF ALKALINITY IN WATER SAMPLES OVERVIEW Prcticl ctivity of the Áre of Toxicologí Universidd Miguel Hernández de Elche Environmentl Anlytic

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

Well say we were dealing with a weak acid K a = 1x10, and had a formal concentration of.1m. What is the % dissociation of the acid?

Well say we were dealing with a weak acid K a = 1x10, and had a formal concentration of.1m. What is the % dissociation of the acid? Chpter 9 Buffers Problems 2, 5, 7, 8, 9, 12, 15, 17,19 A Buffer is solution tht resists chnges in ph when cids or bses re dded or when the solution is diluted. Buffers re importnt in Biochemistry becuse

More information

5.2 The Definite Integral

5.2 The Definite Integral 5.2 THE DEFINITE INTEGRAL 5.2 The Definite Integrl In the previous section, we sw how to pproximte totl chnge given the rte of chnge. In this section we see how to mke the pproximtion more ccurte. Suppose

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

Name: Lab Partner: Section:

Name: Lab Partner: Section: Chpter 4 Newton s 2 nd Lw Nme: Lb Prtner: Section: 4.1 Purpose In this experiment, Newton s 2 nd lw will be investigted. 4.2 Introduction How does n object chnge its motion when force is pplied? A force

More information

Basic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, }

Basic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, } ƒ Bsic Mth Review Numers NATURAL NUMBERS {1,, 3, 4, 5, } WHOLE NUMBERS {0, 1,, 3, 4, } INTEGERS {, 3,, 1, 0, 1,, } The Numer Line 5 4 3 1 0 1 3 4 5 Negtive integers Positive integers RATIONAL NUMBERS All

More information

Chapter 6 Solving equations

Chapter 6 Solving equations Chpter 6 Solving equtions Defining n eqution 6.1 Up to now we hve looked minly t epressions. An epression is n incomplete sttement nd hs no equl sign. Now we wnt to look t equtions. An eqution hs n = sign

More information

Data replication in mobile computing

Data replication in mobile computing Technicl Report, My 2010 Dt repliction in mobile computing Bchelor s Thesis in Electricl Engineering Rodrigo Christovm Pmplon HALMSTAD UNIVERSITY, IDE SCHOOL OF INFORMATION SCIENCE, COMPUTER AND ELECTRICAL

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

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks

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

ON THE FRAME-STEWART ALGORITHM FOR THE TOWER OF HANOI

ON THE FRAME-STEWART ALGORITHM FOR THE TOWER OF HANOI ON THE FRAME-STEWART ALGORITHM FOR THE TOWER OF HANOI MICHAEL RAND 1. Introduction The Tower of Hnoi puzzle ws creted over century go by the number theorist Edourd Lucs [, 4], nd it nd its vrints hve chllenged

More information

FDIC Study of Bank Overdraft Programs

FDIC Study of Bank Overdraft Programs FDIC Study of Bnk Overdrft Progrms Federl Deposit Insurnce Corportion November 2008 Executive Summry In 2006, the Federl Deposit Insurnce Corportion (FDIC) initited two-prt study to gther empiricl dt on

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

14.2. The Mean Value and the Root-Mean-Square Value. Introduction. Prerequisites. Learning Outcomes

14.2. The Mean Value and the Root-Mean-Square Value. Introduction. Prerequisites. Learning Outcomes he Men Vlue nd the Root-Men-Squre Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men

More information

The Effects of Adding Crisco Puritan Canola Oil with Omega-3 DHA to Sugar Cookies

The Effects of Adding Crisco Puritan Canola Oil with Omega-3 DHA to Sugar Cookies The Effects of Adding Crisco Puritn Cnol Oil with Omeg-3 DHA to Sugr Cookies Kitlin Kolember Kylene Kroemer ABSTRACT: Trns fts in foods hve been linked to obesity nd helth issues in Americ s popultion.

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