Stat 301 Review (Test 2)


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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 Pvlue from the printout. 5. Wht conclusions should be drwn? Type of test 1smple ztest 1smple ttest 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 ttble. 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 n1 degrees of freedom row on the ttble. Find the confidence intervl from SPSS printout OR x diff s n n sdiff t* n To find the t* vlue, look t the n1 degrees of freedom row on the ttble. Hypotheses H versus H, Test Sttistic x z H or H n Pvlue H, use P( Z z ), H, use P( Z z ), or H, use 2 P( Z z ) Look up Pvlues on TABLE A Hypotheses H versus H, H or H Test Sttistic t x s OR red SPSS printout n Pvlue H, use P( T t ), H, use P( T t ) or H, use 2 P( T t ) Look up Pvlues on the ttble (df=n1) OR red SPSS printout Hypotheses H diff versus H, H or H diff Test Sttistic t xdiff sdiff OR red SPSS printout n Pvlue H, use P( T t ), diff diff H, use P( T t ) or diff H, use 2 P( T t ) diff Look up Pvlues on the ttble (df=n1) OR red SPSS printout diff 1
2 2smple ttest 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 ttble. 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 Pvlue 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 Pvlues on the ttble OR red SPSS printout Onewy 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. Pvlue Red Pvlue 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 Twowy ANOVA Compres the mens of popultions tht re clssified two wys or the men response in twofctor 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. Pvlue Red Pvlue 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 twosided 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 onesmple Ztest? 6. Know how to test the stndrd devitions to see if it is OK to pool the vrinces in both the one nd twowy 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 sidebyside boxplots nd plots of mens for the onewy nd twowy ANOVAs. 11. Know how the twowy ANOVA is different from the onewy ANOVA nd twosmple 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 onewy nd twowy ANOVAs. The following problems hve been tken from old tests. 3
4 Problems 14 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 smesized 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 (smesize smples) will be included by the intervl e. None of the bove. 3. Which of the following is true if your Pvlue 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 514, 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. 1smple men B. Onewy ANOVA C. 2smple comprison of mens D. Twowy 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 11 scle)? 12. Estimte the popultion men difference in tste rtings (on 11 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 fmilysize 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 OneSmple Sttistics N Men Std. Devition Std. Error Men Cholesterol level cholesterol levels StemndLef 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 OneSmple Test Test Vlue = 2 95% Confidence Intervl of the Difference t df Sig. (2tiled) Men Difference Lower Upper Cholesterol level
7 . Is ttest procedure pproprite for this dt? Why? b. Stte the hypotheses for this test. c. Give the test sttistic, degrees of freedom, the Pvlue. 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. (2tiled) 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, Pvlue, 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 vitminsupplement diets. Twentyeight 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. (2tiled) ttest 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? Pvlue? 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 tstetesting 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. (2tiled) ttest 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 twosmple 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 Pvlue 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 Pvlue 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 Pvlue 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 (IJ) Std. Error Sig. Lower Bound Upper Bound * * * * Looking t the sidebyside 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 Pvlue, 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 tweensubjects 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 sidebyside Boxplots. If we rn the onewy ANOVA on the three dt sets, which dt set would produce the highest Fsttistic? 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 (IJ) Std. Error Sig. Lower Bound Upper Bound * * Which sttement below is correct?. Onewy ANOVA is pproprite becuse two times the smllest stndrd devition is no lrger thn the lrgest stndrd devition. b. Onewy ANOVA is pproprite becuse two times smllest stndrd devition is lrger thn the lrgest stndrd devition. c. Onewy ANOVA is not pproprite becuse two times the smllest stndrd devition is no lrger thn the lrgest stndrd devition. d. Onewy 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 tweensubjects 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 steperobics 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 steperobics 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 steperobics 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 Pvlue 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 ttest 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. (2tiled) 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 tprocedure becuse strtified rndom smple ws selected. b. It is not pproprite to use the one smple tprocedure becuse bsed on the br grph the IQR is too lrge. c. It is pproprite to use the one smple tprocedure becuse the smple size is 2 nd there is no strong skewness or outliers. d. The one smple tprocedure 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 Pvlue would be. 3.2 b c..5 d..25 e For the hypothesis test in #32, grph nd lbel the test sttistic, the Pvlue, nd on the curve below. 34. If you wnted to determine if the verge sugr content of brekfst cerel is greter thn 5g, your Pvlue 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 Pwould be. 3.2 b c..5 d..25 e For the hypothesis test in #35, grph nd lbel the test sttistic, the Pvlue, 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 ztest B. One smple ttest C. Mtched pirs ttest D. Twosmple comprison of mens t test E. Onewy ANOVA F. Twowy 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 8week 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.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
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