Stat 301 Review (Test 2)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Stat 301 Review (Test 2)"

Transcription

1 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 to write the hypotheses for the problem. 3. How to clculte nd/or red the test sttistic from the printout. 4. How to clculte nd/or red the P-vlue from the printout. 5. Wht conclusions should be drwn? Type of test 1-smple z-test 1-smple t-test Mtchedpirs When is it used? Confidence intervl Hypothesis test procedure One set of dt σ is known Quntittive dt One set of dt σ is unknown Quntittive dt Vlues re mtched. Either both mesurements re recorded on the sme unit or before fter study is conducted. Quntittive dt x z* To find the z* vlue, look t the lst row of the t-tble. Find the confidence intervl from SPSS printout (be sure to dd in the test vlue) OR x t* To find the t* vlue, look t the n-1 degrees of freedom row on the t-tble. Find the confidence intervl from SPSS printout OR x diff s n n sdiff t* n To find the t* vlue, look t the n-1 degrees of freedom row on the t-tble. Hypotheses H versus H, Test Sttistic x z H or H n P-vlue H, use P( Z z ), H, use P( Z z ), or H, use 2 P( Z z ) Look up P-vlues on TABLE A Hypotheses H versus H, H or H Test Sttistic t x s OR red SPSS printout n P-vlue H, use P( T t ), H, use P( T t ) or H, use 2 P( T t ) Look up P-vlues on the t-tble (df=n-1) OR red SPSS printout Hypotheses H diff versus H, H or H diff Test Sttistic t xdiff sdiff OR red SPSS printout n P-vlue H, use P( T t ), diff diff H, use P( T t ) or diff H, use 2 P( T t ) diff Look up P-vlues on the t-tble (df=n-1) OR red SPSS printout diff 1

2 2-smple t-test Dt comes from two independent smples selected from two independent popultions or completely rndomized experiment with two fctor levels or tretments. Quntittive dt Find the confidence intervl from the SPSS printout OR x x t * s s 1 2 n n 1 2 To find the t* vlue, look t the smller of n 1 1 nd n 2 1 degrees of freedom row on the t-tble. Hypotheses H versus 1 2 H 1 2, 1 2 Test Sttistic x1 x2 t 2 2 s1 s2 n n 1 2 H or H 1 2 OR red SPSS printout P-vlue H, use P( T t ), 1 2 H, use P( T t ) or 1 2 H, use 2 P( T t ) 1 2 Look up P-vlues on the t-tble OR red SPSS printout One-wy ANOVA Dt comes from more thn two independent smples or from n experiment with one fctor with multiple levels of tht fctor. Quntittive dt None Hypotheses H I ' H not ll the I s re the sme Test sttistic Red F from the SPSS printout. P-vlue Red P-vlue from the SPSS printout. Further nlysis If you reject the null hypothesis, further nlysis is necessry to determine which mens re different. Bonferroni s procedure is one possibility. Approprite if 2 (smllest s) > lrgest s Two-wy ANOVA Compres the mens of popultions tht re clssified two wys or the men response in two-fctor experiment. Quntittive dt None Hypotheses H min effect of A is zero H min effect of A is not zero H min effect of B is zero H min effect of B is not zero H interction between A nd B is zero H interction between A nd B is not zero Test sttistics Red F from the SPSS printout. P-vlue Red P-vlue from the SPSS printout. 2

3 There re some dditionl concepts tht you will need to understnd. They re listed below 1. Assumptions tht need to be met in order to perform the following tests or clculte the confidence intervls. 2. How robust the tests bove re to the ssumption of normlity with respect to the smple size. 3. Whether the test you re performing is resonble considering the distribution of your dt nd your smple size. 4. The reltionship between confidence intervls nd two-sided tests nd when confidence intervl cn be used to drw conclusions regrding hypothesis test. 5. How lrge smple is needed to gin certin mrgin of error in one-smple Z-test? 6. Know how to test the stndrd devitions to see if it is OK to pool the vrinces in both the one nd two-wy ANOVAs Clculte R nd the estimte for. 8. When it is better to clculte confidence intervl versus conduct hypothesis test. 9. Determine which mens re different in ANOVA given the SPSS printout in Bonferroni s procedure. 1. Be ble to describe nd interpret side-by-side boxplots nd plots of mens for the onewy nd two-wy ANOVAs. 11. Know how the two-wy ANOVA is different from the one-wy ANOVA nd two-smple comprison of mens. 12. Know how to recognize the response vrible, fctors, number of levels for ech fctor nd the totl number of observtions. 13. Be ble to interpret the pproprite grphs for both one-wy nd two-wy ANOVAs. The following problems hve been tken from old tests. 3

4 Problems 1-4 re multiple choice. There my be more thn one correct nswer for ech question. Circle ALL nswers which re correct. 1. Circle the letter of the following methods tht would decrese the width of confidence intervl for men, if ll else stys the sme.. Increse the smple size. b. Decrese the smple size. c. Increse the level of confidence. d. Decrese the level of confidence. e. None of the bove. 2. A 95% confidence intervl indictes tht. 95% of the intervls constructed using this process bsed on sme-sized smples from this popultion will include the popultion men. b. 95% of the time the intervl will include the smple men c. 95% of the possible popultion mens will be included by the intervl d. 95% of the possible smple mens (sme-size smples) will be included by the intervl e. None of the bove. 3. Which of the following is true if your P-vlue is.1 nd your is.5?. You reject H. b. You do not reject H. c. Your results re significnt. d. Your results re not significnt. e. None of the bove. 4. John took simple rndom smple of 25 lemon drop pcks from box tht ws shipped to him, nd he counted how mny lemon drops were in ech pck. From the smple, he clculted 99% confidence intervl of (25.99, 34.2). The compny clims tht their pcks of lemon drops ech contin n verge of 36 lemon drops. John wnted to use his confidence intervl to determine if the compny ws correct. Conclusion?. The compny is correct. b. John would fil to reject his null hypothesis t the 1% level of significnce becuse 36 flls outside the rnge of the confidence intervl. c. John would reject his null hypothesis t the 1% significnce level becuse 36 flls outside the rnge of the confidence intervl. d. John would reject his null hypothesis t the 5% since the 95% confidence intervl is more nrrow thn the 99% confidence intervl, so it would lso not contin 36. e. Both c nd d re correct. 4

5 MATCHING (3 points ech) For problems 5-14, in ech of the three boxes, specify which type of problem it is. For the type of story, it cn be ny of the following (specify by the letter) A. 1-smple men B. One-wy ANOVA C. 2-smple comprison of mens D. Two-wy ANOVA E. Mtched pirs 5. Is there difference in the popultion verge number of green M&Ms for plin, penut nd lmond M&M pcks? Type of Story Distribution ( Z, t, or F ) Test or CI? 6. Estimte the popultion men number of green M&Ms in fun pck if the popultion stndrd devition is.4? 7. Do the colors (red, ornge, yellow, green, blue, nd brown) nd type of M&M (plin, penut nd lmond) hve n effect on the cost of producing the M&M on verge in the popultion? 8. A report from the M&M/Mrs cndy compny clims tht there is n verge of 5 brown M&Ms in ech fun pck. If we smple of 5 fun pcks, do we gree tht 5 is the popultion men number of brown M&Ms per pck? 9. On verge, re there lrger number of brown plin M&Ms thn brown penut M&Ms in their respective fun pcks in the popultion? 1. Estimte the popultion verge difference between the number of blue nd brown M&Ms in ech fun pck by checking 1 different bgs. 11. Do the type of M&M (plin, penut nd lmond) nd ge of tste tester (kid, teen, dult, senior citizen) hve n effect on the popultion men tste rting (on 1-1 scle)? 12. Estimte the popultion men difference in tste rtings (on 1-1 scle) kids give plin M&Ms nd dults give plin M&Ms. 13. Estimte the popultion verge weight of 1 M&Ms if the stndrd devition for the smple is Is the popultion verge number of green M&Ms in fmily-size pck more thn 5 if we know.3? 5

6 15. A drug compny hs developed new sttin type drug tht reduces totl cholesterol levels (HDL + LDL), mesured in mg/dl, in mle ptients with high risk of hert ttcks. The drug compny wnts to determine the effectiveness of its new drug; s strt, compny reserchers mesured the cholesterol level of rndom smple of 16 high risk mle ptients. The results of stemplot re shown below long with the SPSS output from the dt One-Smple Sttistics N Men Std. Devition Std. Error Men Cholesterol level cholesterol levels Stem-nd-Lef Plot Frequency Stem & Lef The compny compred the high risk group s verge cholesterol level to the trget for ll men, 2mg/dl. They wnted to be sure their high risk group did hve higher cholesterol levels on verge. The SPSS output is shown below One-Smple Test Test Vlue = 2 95% Confidence Intervl of the Difference t df Sig. (2-tiled) Men Difference Lower Upper Cholesterol level

7 . Is t-test procedure pproprite for this dt? Why? b. Stte the hypotheses for this test. c. Give the test sttistic, degrees of freedom, the P-vlue. d. Stte your conclusions in terms of the reserchers problem. e. Wht is the 95% confidence intervl for the groups cholesterol level? f. Wht is the 99% confidence intervl for the groups cholesterol level? 7

8 16. The drug compny reserchers now investigte the effectiveness of the new drug to reduce cholesterol level. Ech member of the smple group of high risk ptients is given the new drug dily for period of 3 months. After the tretment, ech of the 16 members cholesterol level is mesured nd the differences in cholesterol were computed (before fter). The SPSS nlysis of their test is shown below. Pired Smples Sttistics Men N Std. Devition Std. Error Men Pir 1 Cholesterol before Cholesterol fter Pired Smples Test Pir 1 Cholesterol before - Cholesterol fter Men Std. Devition Pired Differences Std. Error Men 95% Confidence Intervl of the Difference Lower Upper t df Sig. (2-tiled) Wht is the 95% confidence intervl for the men difference of cholesterol (before fter)? b. The reserchers wnt to do hypothesis test to determine if the new drug reduces cholesterol level on verge, with significnce level of =.5. Stte the hypotheses, the test sttistic, P-vlue, nd your conclusions in terms of the story. c. Would it be pproprite to use the confidence intervl in prt to test whether the new drug reduces cholesterol (your test in prt b)? Why or why not? 8

9 17. An experiment ws conducted to determine whether there ws difference in the verge weights of the combs of roosters fed two different vitmin-supplement diets. Twenty-eight helthy roosters were rndomly divided into two groups, with one group receiving diet I nd the other receiving diet II. After the study period, the comb weight (in milligrms) ws recorded for ech rooster. The output is given here Independent Smples Test weight Equl vrinces ssumed Equl vrinces not ssumed Levene's Test for Equlity of Vrinces F Sig. t df Sig. (2-tiled) t-test for Equlity of Mens Men Difference 99% Confidence Intervl of the Std. Error Difference Difference Lower Upper Answer the following questions bsed on the output bove. Stte the null nd lterntive hypotheses for this problem. b. Wht is the test sttistic? P-vlue? c. Stte your conclusion in terms of the problem using significnce of.1. d. Bsed on the output, wht is 99% confidence intervl for the difference in comb weights between the two groups? 9

10 18. A food compny is developing new brekfst drink, nd their mrket nlysts re currently working on preliminry tste-testing studies. However, their SPSS output pges got dropped on the floor nd the pges from two different reserch projects got mixed up. Unfortuntely the reserchers just lbeled the vribles x nd y, so the vrible nmes won t be of ny help. Answer the questions below nd on the next pge using the pproprite output for the sitution. (Some output won t be used t ll.) Group St tistics rting group x y Std. Error N Men Std. Devition Men Inde pende nt Smples Test rting Equl vrinces ssumed Equl vrinces not ssumed Levene's Test for Equlity of Vrinces F Sig. t df Sig. (2-tiled) t-test for Equlity of Mens Men Difference 95% Confidence Intervl of the Std. Error Difference Difference Lower Upper

11 For one reserch project, the mrket nlysts were interested in whether customers preferred their new brekfst drink to their current brekfst drink. They sked smple of 2 people to try ech drink in rndom order nd rte the flvor of both on scle of 1 to 1, 1 being very unplesnt nd 1 being very plesnt. (Note old = x nd new = y). Wht type of sitution is this mtched pirs or two-smple comprison of mens? b. Stte the null nd lterntive hypotheses. c. Wht is the test sttistic reported in the pproprite output on the previous pge? d. If the test sttistic hd been missing from the output, show how you would clculte it by hnd. Give the generl formul nd plug in the correct numbers for the formul. You do not need to use your clcultor to compute the ctul test sttistic. e. Using the pproprite output, wht is the correct P-vlue for the test in prt b? f. Wht is your conclusion in terms of the resercher s question? Use.5 significnce level. 11

12 19. A chemicl compny recently introduced new fertilizer for corn, which they reported significntly incresed the yield bove the men of 1.6 bushels per cre tht ws estblished five yers go. To test the compny s clim t α =.1, scientist rndomly selected ten fields of corn nd pplied the new fertilizer t the rte recommended by the compny. At hrvest, smple men of 12.2 bushels per cre ws obtined. Assume the yields per cre re normlly distributed with known popultion stndrd devition σ = 2.53 bushels per cre.. Stte the pproprite set of hypotheses. b. Clculte the test sttistic. c. Find the P-vlue for the test. d. Stte your conclusions in terms of the originl problem. e. Drw picture showing the norml curve. Lbel the, smple men nd P-vlue on the curve. 12

13 2. You mesure the weights of 24 mle runners. These runners re not rndom smple from popultion, but you re willing to ssume tht their weights represent the weights of similr runners. The verge weight of your smple is kg, with stndrd devition is 4.5 kg.. Give 99% confidence intervl for the verge weight of mle runner. b. Wht is your mrgin of error? c. You suspected tht the verge weight for the popultion of mle runners is not the 61.3 you red bout in the running mgzine rticle. How could you use your confidence intervl from prt to do test t the.1 significnce level? Stte your hypotheses nd report nd explin your conclusions of this test in wy the generl public could understnd. 13

14 Distnce Men of distnce 21. A historicl debte is occurring in golf on the impct technology is hving on the gme. A golfer wnts to study the difference three types of drivers hve on the distnce the golf bll flies when hit with those drivers. The types of drivers re (1) steel shfted PowerBuilt persimmon, circ 1965; (2) steel shfted TylorMde metlwood, circ 1985; nd (3) grphite shfted titnium heded Ping, circ 25. This golfer hits dozen blls with ech of the different drivers. An ssistnt mesures nd records the totl distnce for ech drive; the dt nd SPSS results re s follows Persimmon 1985 Steel 25 Titnium Driver Type 1965 Persimmon 1985 Steel 25 Titnium Driver Type N Men Std. Devition 1965 Persimmon Steel Titnium Totl ANOVA Distnce Between Groups Within Groups Totl Sum of Squres df Men Squre F Sig

15 Multiple Comprisons Dependent Vrible Distnce Bonferroni (I) Driver Type 1965 Persimmon 1985 Steel 25 Titnium (J) Driver Type 1985 Steel 25 Titnium 1965 Persimmon 25 Titnium 1965 Persimmon 1985 Steel *. The men difference is significnt t the.5 level. Men Difference 95% Confidence Intervl (I-J) Std. Error Sig. Lower Bound Upper Bound * * * * Looking t the side-by-side boxplot nd the mens plot, describe the comprison of distnce of the three driver types. b. For this nlysis, ws it resonble to pool the stndrd devitions (vrinces) nd why? Show your work. c. Wht is the pooled stndrd devition? d. Wht is 2 R? e. The golfer is interested in compring the men distnce mong the three types of drivers. Stte the null nd lterntive hypotheses, stte the test sttistic, the P-vlue, nd your conclusion in terms of the problem. f. Does your conclusion to prt c tell the golfer everything he needs to know? If so, explin why. If not, give the golfer dditionl informtion bout the three types of drivers nd stte where you found your informtion. 15

16 Estimted Mrginl Mens 22. In ddition to studying the effect of the driver type, the golfer wnts to study the effect of the golf bll type on distnce. Three types of blls were used nd they re (1) wound bll with round dimples, circ 1965; (2) wound bll with hexgonl dimples, circ 1985; nd (3) solid bll with icoshedr dimple pttern, circ 25. This golfer hits three drives with ech of the different blls nd with ech of the different drivers. Agin, his ssistnt mesures nd records the totl distnce for ech drive; the dt nd SPSS results re s follows Driver Bll Estimted Mrginl Mens of Distnce 24 Bll type 1965 round 1985 hexgonl 25 icoshedrl Persimmon 1985 Steel 25 Titnium Driver Type 16

17 . Bsed on the grph on the previous pge, wht ffects distnce? The driver type? The bll type? The interction between bll nd driver? Why? ANOVA output Dependent Vrible Distnce Source Corrected Model Intercept driver bll driver * bll Error Totl Corrected Totl Tests of Be tween-subjects Effe cts Type III Sum of Squres df Men Squre F Sig R Squred =.859 (Adjusted R Squred =.796) b. Bsed on the ANOVA output, summrize your conclusions in terms of the problem. 17

18 23. Three dt sets re represented below using side-by-side Boxplots. If we rn the one-wy ANOVA on the three dt sets, which dt set would produce the highest F-sttistic? Dt set A Dt set B Dt set C Test_1 Test_2 Test_3 Test_1 Test_2 Test_3 Test_1 Test_2 Test_3 Answer choice D It is impossible to even estimte this without first running ANOVA. The mth deprtment wnted to test the effectiveness of three teching methods in prepring students for the finl exm in clculus. The instructor rndomly ssigned students to ech of the teching methods. Answer questions bsed on the output bellow. Test_scores Totl Descriptive s 95% Confidence Intervl for Men N Men Std. Devition Std. Error Lower Bound Upper Bound Minimum Mximum ANOVA Tes t_scores Between Groups Within Groups Totl Sum of Squres df Men Squre F Sig

19 Multiple Comprisons Dependent Vrible Test_scores Bonferroni (I) Teching_method (J) Teching_method *. The men difference is significnt t the.5 level. Men Difference 95% Confidence Intervl (I-J) Std. Error Sig. Lower Bound Upper Bound * * Which sttement below is correct?. One-wy ANOVA is pproprite becuse two times the smllest stndrd devition is no lrger thn the lrgest stndrd devition. b. One-wy ANOVA is pproprite becuse two times smllest stndrd devition is lrger thn the lrgest stndrd devition. c. One-wy ANOVA is not pproprite becuse two times the smllest stndrd devition is no lrger thn the lrgest stndrd devition. d. One-wy ANOVA is not pproprite becuse two times smllest stndrd devition is lrger thn the lrgest stndrd devition. e. The ppropriteness of the ANOVA hs nothing to do with the stndrd devitions. 25. Bsed on the ANOVA printout t the 5% level of significnce,. we reject H, nd conclude tht there is enough evidence to show tht the men test scores from the three teching methods re ll the sme. b. we reject H, nd conclude tht there is not enough evidence to show tht the men test scores from the three teching methods re ll the sme. c. we fil to reject H, nd conclude tht there is not enough evidence to show tht the men test score from the three teching methods re ll the sme. d. we reject H, nd conclude tht there is enough evidence to show tht the men test scores from the three teching methods re not ll the sme. e. we reject H, nd conclude tht there is not enough evidence to show tht the men test scores from the three teching methods re not ll the sme. f. we reject H, nd conclude tht there is not enough evidence to show tht the men test scores from the three teching methods re ll different. 26. Wht is the estimte of the pooled stndrd devition? b c d e. cnnot be determined 19

20 Estimted Mrginl Mens Estimted Mrginl Mens Estimted Mrginl Mens 27. Which of the following is true?. Bonferroni s procedure is pproprite for this problem nd shows us tht teching method 3 yields significntly different test results thn methods 1 nd 2, however there is no significnt difference between the other methods. b. Bonferroni s procedure is pproprite for this problem nd shows us tht teching method 3 yields significntly different test results thn method 2, however there re no other significnt differences. c. Bonferroni s procedure is pproprite for this problem nd shows tht method 3 is the best nd method 2 is the worst. d. Bonferroni s procedure is not pproprite. The output below shows the effect tht color nd rom hve on the number of insects trpped on sticky bords. Two colors re tested (yellow= nd white=1) nd two scents (no scent= or scent=1). Dependent Vrible number Source Corrected Model Intercept scent color scent * color Error Totl Corrected Totl Tests of Be tween-subjects Effe cts Type III Sum of Squres df Men Squre F Sig R Squred =.959 (Adjusted R Squred =.943) 28. Choose the grph tht best illustrtes the output bove. Grph A Grph B Grph C Estimted Mrginl Mens of number Estimted Mrginl Mens of number Estimted Mrginl Mens of number 22.5 color 1 25 color color scent scent 1 scent 1 2

21 29. Bsed on the ANOVA output, which of the conclusions below is correct.. Both the min effects for scent nd color re significnt, but their interction is not. b. The min effects for scent nd color nd their interction re ll significnt. c. Only the min effect of scent is significnt. d. Only the min effect of color is significnt. e. Nothing is significnt. 3. A resercher wished to compre the effect of different rtes of stepping on hert rte in step-erobics workout. A collection of 3 dult volunteers 15 women nd 15 men were selected from locl gym. The men were rndomly divided into three groups of five subjects ech. Ech group did stndrd step-erobics workout with group 1 t low rte of stepping, group 2 t medium rte of stepping, nd group 3 t rpid rte. The women were lso rndomly divided into three groups of five subjects ech. As with the men, ech group did stndrd step-erobics workout with group 1 t low rte of stepping, group 2 t medium rte of stepping, nd group 3 t rpid rte. The men hert rte t the end of the workout for ll subjects ws determined in bets per minute.. Wht re the fctors in this experiment? (1) Rte of stepping nd hert rte. (2) Rte of stepping nd gender. (3) Hert rte nd gender. (4) Gym membership nd gender. b. Wht re the dvntges of studying the two fctors simultneously in the sme experiment? (1) It is more efficient to study two fctors simultneously rther thn seprtely. (2) We cn reduce the residul vrition in model by including second fctor thought to influence the response. (3) We cn investigte interction between fctors. (4) All of the bove. c. The mens plot nd the P-vlue for the test for interction show little evidence of interction. Wht cn we conclude? (1) There is little difference in the hert rtes of men nd women. (2) The chnge in hert rte due to different stepping rtes is similr for men nd women. (3) Chnges in stepping rte re positively ssocited with hert rte. (4) Step exercise is eqully beneficil to men nd women. 21

22 Frequency Use the following output to nswer questions 32 through 38 Sugr intke needs to be minimized during pregnncy for women who re dignosed with gesttionl dibetes. Does this men they should void brekfst cerels which cn be high in sugr. A study on sugr content of brekfst cerel ws conducted. A simple rndom smple of brekfst cerels ws tken nd the one smple t-test ws pplied to the dt. Answer questions 31 through 37 bsed on the output below. One -Smple Sttistics SUGARg Std. Error N Men Std. Devition Men One -Smple Test SUGARg Test Vlue = 5 95% Confidence Intervl of the Men Difference t df Sig. (2-tiled) Difference Lower Upper Number of Grms of Sugr in Cerel Men =8.2 Std. Dev. =4.567 N =2. SUGARg SUGARg 31. Which of the sttements below is correct?. It is pproprite to use the one smple t-procedure becuse strtified rndom smple ws selected. b. It is not pproprite to use the one smple t-procedure becuse bsed on the br grph the IQR is too lrge. c. It is pproprite to use the one smple t-procedure becuse the smple size is 2 nd there is no strong skewness or outliers. d. The one smple t-procedure is not pproprite becuse the smple size is not t lest 4. 22

23 32. If you wnted to determine if the verge sugr content of brekfst cerel differs from 5g your P-vlue would be. 3.2 b c..5 d..25 e For the hypothesis test in #32, grph nd lbel the test sttistic, the P-vlue, nd on the curve below. 34. If you wnted to determine if the verge sugr content of brekfst cerel is greter thn 5g, your P-vlue would be. 3.2 b c..5 d..25 e If you wnted to determine if the verge sugr content of brekfst cerel is less thn 5g, your P-would be. 3.2 b c..5 d..25 e For the hypothesis test in #35, grph nd lbel the test sttistic, the P-vlue, nd on the curve below. 37. A 95% confidence intervl for the verge sugr content of cerel is. (1.66, 5.334) b. (6.66, 1.334) c. (9.266, ) d. (4.24, 8.472) e. None of the bove. 23

24 Select the correct type of test from the choices below. In the mrgin, write brief explntion of why you picked tht type of test. (For exmple, 3 independent groups with 1 quntittive vrible. ) A. One smple z-test B. One smple t-test C. Mtched pirs t-test D. Two-smple comprison of mens t test E. One-wy ANOVA F. Two-wy ANOVA 38. An eductor believes tht new directed reding ctivities in the clssroom will help elementry school pupils improve some spects of their reding bility. She rrnges for third grde clss of 21 students to tke prt in these ctivities for n 8-week period. A control clssroom of 23 pupils follows the curriculum without the ctivities. At the end of 8 weeks, ll students re given degree of reding power test. 39. An eductor believes tht new directed reding ctivities in the clssroom will help elementry school pupils improve some spects of their reding bility. She tests group of 21 students before they tke prt in the ctivities nd fter they tke prt in the ctivities. She then compres the two scores. 4. An gronomist wnts to determine whether the verge cellulose content of vriety of lflf is bove 14 mg/g. The smple men is mg/g, nd the popultion stndrd devition is 5 mg/g. 41. An gronomist wnts to determine whether the verge cellulose content of vriety of lflf is bove 14 mg/g. The smple men is mg/g, nd the smple stndrd devition is 5 mg/g. 42. Is there difference in the popultion verge weight of bbies born to women of different rces (white, Africn Americn, Hispnic, etc)? 43. How do rce, weight gin of the pregnnt womn (less thn verge, verge, more thn verge), nd the interction of rce nd weight gin of the womn ffect the weight of the womn s bby? 24

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2013 Flax Weed Control Trial

2013 Flax Weed Control Trial 2013 Flx Weed Control Tril Dr. Hether Drby, UVM Extension Agronomist Susn Monhn, Conner Burke, Eric Cummings, nd Hnnh Hrwood UVM Extension Crops nd Soils Technicins 802-524-6501 Visit us on the web: http://www.uvm.edu/extension/cropsoil

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

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

Plotting and Graphing

Plotting and Graphing Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured

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

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

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 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

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

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

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

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

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

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

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

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

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

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

Mathematics Higher Level

Mathematics Higher Level Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:

More information

Rational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and

Rational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions

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

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

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

TECHNICAL REPORT Lloyd M. Dunn, PhD & Douglas M. Dunn, PhD Overview Revisions in the New Edition

TECHNICAL REPORT Lloyd M. Dunn, PhD & Douglas M. Dunn, PhD Overview Revisions in the New Edition TECHNICAL REPORT Lloyd M. Dunn, PhD & Dougls M. Dunn, PhD Overview... 1 Revisions in the New Edition... 1 Content Coverge... 2 Scores Reported... 2 Stndrdiztion of PPVT 4... 2 Evidence Bsed on Relibility...

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

4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A

4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter

More information

MATLAB Workshop 13 - Linear Systems of Equations

MATLAB Workshop 13 - Linear Systems of Equations MATLAB: Workshop - Liner Systems of Equtions pge MATLAB Workshop - Liner Systems of Equtions Objectives: Crete script to solve commonly occurring problem in engineering: liner systems of equtions. MATLAB

More information

1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam

1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam 1./1.1 Introduction to Computers nd Engineering Problem Solving Fll 211 - Finl Exm Nme: MIT Emil: TA: Section: You hve 3 hours to complete this exm. In ll questions, you should ssume tht ll necessry pckges

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

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

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

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

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

Formal Languages and Automata Exam

Formal Languages and Automata Exam Forml Lnguges nd Automt Exm Fculty of Computers & Informtion Deprtment: Computer Science Grde: Third Course code: CSC 34 Totl Mrk: 8 Dte: 23//2 Time: 3 hours Answer the following questions: ) Consider

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

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

QUANTITATIVE METHODS IN PSYCHOLOGY A Power Primer

QUANTITATIVE METHODS IN PSYCHOLOGY A Power Primer QUANTITATIE METHODS IN PSYCHOLOGY A Power Primer Jcob Cohen New \brk University One possible reson for the continued neglect of sttisticl power nlysis in reserch in the behviorl sciences is the inccessibility

More information

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,

More information

Mechanics Cycle 1 Chapter 5. Chapter 5

Mechanics Cycle 1 Chapter 5. Chapter 5 Chpter 5 Contct orces: ree Body Digrms nd Idel Ropes Pushes nd Pulls in 1D, nd Newton s Second Lw Neglecting riction ree Body Digrms Tension Along Idel Ropes (i.e., Mssless Ropes) Newton s Third Lw Bodies

More information

and thus, they are similar. If k = 3 then the Jordan form of both matrices is

and thus, they are similar. If k = 3 then the Jordan form of both matrices is Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If

More information

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University

More information

Math Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.

Math Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function. Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while

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

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

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

Variable Dry Run (for Python)

Variable Dry Run (for Python) Vrile Dr Run (for Pthon) Age group: Ailities ssumed: Time: Size of group: Focus Vriles Assignment Sequencing Progrmming 7 dult Ver simple progrmming, sic understnding of ssignment nd vriles 20-50 minutes

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

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

AREA OF A SURFACE OF REVOLUTION

AREA OF A SURFACE OF REVOLUTION AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.

More information

THE RATIONAL NUMBERS CHAPTER

THE RATIONAL NUMBERS CHAPTER CHAPTER THE RATIONAL NUMBERS When divided by b is not n integer, the quotient is frction.the Bbylonins, who used number system bsed on 60, epressed the quotients: 0 8 s 0 60 insted of 8 s 7 60,600 0 insted

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

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

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

Probability m odels on horse-race outcomes

Probability m odels on horse-race outcomes Jour nl of Applied Sttistics, Vol. 25, No. 2, 1998, 221± 229 Probbility m odels on horse-rce outcomes M UKHTAR M. ALI, Deprtment of Economics, University of Kentucy, USA SUMMARY A number of models hve

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

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

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

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

Derivatives and Rates of Change

Derivatives and Rates of Change Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te

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

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

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

Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh

Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is

More information

Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;

Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C; B-26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndom-numer genertor supplied s stndrd with ll computer systems Stn Kelly-Bootle,

More information

The Definite Integral

The Definite Integral Chpter 4 The Definite Integrl 4. Determining distnce trveled from velocity Motivting Questions In this section, we strive to understnd the ides generted by the following importnt questions: If we know

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

Thinking out of the Box... Problem It s a richer problem than we ever imagined

Thinking out of the Box... Problem It s a richer problem than we ever imagined From the Mthemtics Techer, Vol. 95, No. 8, pges 568-574 Wlter Dodge (not pictured) nd Steve Viktor Thinking out of the Bo... Problem It s richer problem thn we ever imgined The bo problem hs been stndrd

More information

Threshold Population Levels for Rural Retail Businesses in North Dakota, 2000

Threshold Population Levels for Rural Retail Businesses in North Dakota, 2000 Agribusiness & Applied Economics Miscellneous Report No. 191 July 2002 Threshold Popultion Levels for Rurl Retil Businesses in North Dkot, 2000 Rndl C. Coon nd F. Lrry Leistritz Deprtment of Agribusiness

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

Version 001 Summer Review #03 tubman (IBII20142015) 1

Version 001 Summer Review #03 tubman (IBII20142015) 1 Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This print-out should he 35 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03

More information