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2 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 per serving) of the cerels is given below. Sugr iber N Men SD Men SD Shelf # Shelf # Shelf # Test for significnt differences in sugr content mong the three shelves.. ssess whether or not the dt meet the ssumptions necessry for n NOV. b. Construct n NOV summry tble nd find the observed men squre rtio. c. Compre the observed men squre rtio to its pproprite test sttistic d. Stte your conclusion (explin wht reecting or retining the null hypothesis mens) e. ccording to your results, which shelf displys the cerels with the highest sugr content? f. Clculte the effect size (η / T) nd explin wht it represents.. Test for significnt differences in fiber content mong the three shelves.. ssess whether or not the dt meet the ssumptions necessry for n NOV. b. Construct n NOV summry tble nd find the observed men squre rtio. c. Compre the observed men squre rtio to its pproprite test sttistic d. Stte your conclusion (explin wht reecting or retining the null hypothesis mens) e. ccording to your results, which shelf displys the cerels with the highest fiber content? f. Clculte the effect size (η / T) nd explin wht it represents.. fctory hs three production lines producing glss sheets tht re ll supposed to be of the sme thickness. qulity inspector tkes rndom smple of n 0 sheets from ech production line nd mesures their thickness. The glss sheets from the first production line hve smple men of.015 mm with smple stndrd devition of mm. The smple men nd stndrd devition of the second production line re.018 mm nd mm. The third production line produced glss with men of.996 mm nd stndrd devition of 0.1 mm. Wht conclusions should the qulity inspector drw? Clculte the effect size (η / T) nd explin wht it represents. 4. The presence of hrmful insects in frm fields is detected by erecting bords covered with sticky mteril nd then exmining the insects trpped on the bords. To investigte which colors re most ttrctive to cerel lef beetles, reserchers plced six bords of ech of four colors in field of ots in July. Using the dt in the following tble, wht conclusions cn you drw? Clculte the effect size (η / T) nd explin wht it represents. Number of Insects Trpped Men Std. Dev. Yellow White Green Blue Complete the following NOV summry tbles. Conduct the significnce test nd clculte the effect size (η / T) for ech tble. Source R Groups rror 6.81 Totl Source R Groups rror.6 Totl 9 6. The effect of cffeine levels on performing simple finger-tpping tsk ws investigted. 0 mle college students were trined in finger tpping nd rndomly ssigned to receive either 0, 100, or 0 of cffeine. Two hours lter, the students were sked to finger tp nd the number of tps per minute ws counted. Wht conclusions cn you drw from this dt (using SP s clss). If the differences mong groups re sttisticlly significnt, re they lso of prcticl significnce? Cffeine Tps per minute Men Std. Dev

3 Solutions to NOV exercises NOT: You cn use n online NOV clcultor t (google NOV clcultor ) 1) Decide whether or not n NOV is pproprite. ) re we compring two or more group (tretment) mens? b) Does our dt meet the ssumptions necessry to run n NOV?. re the groups independent? b. re the observtions within ech group normlly distributed? (Grph, p-p plot, or use Kolmogorov-Smirnov test) c. Homogeneity of vrince ssumption: re the group/tretment vrinces equl? i. Use the test to check for equl vrinces: Compute: l rgest smllest nd compre to from the tble, where # of groups nd n observtions per group. n 1 If your clculted < the vlue from the tble, you cn procede. If your clculted > the vlue from the tble, we cnnot conduct n ordinry NOV. c) Stte the null nd lternte hypotheses: H 0 : µ 1 µ... µ or vs. H : Not H 0 H : α 0 vs. H : α 0 d) Clculte the smple mens nd stndrd devitions for ech tretment: X xi n e) Clculte the overll men: f) Clculte sums of squres: M X " n N X ( ) n X! M 1 nd s ( x X ) i n 1 "(n!1)s T + g) Clculte degrees of freedom: 1 N T N 1 h) ill-in the NOV summry tble with your clculted nd vlues: Source Sums of Squres Degrees of freedom Men Squre Men Squre Rtio Between Groups (Tretment ffect) Within Groups (rror vrince) Totl i) Clculte the men squres: ) Clculte the men squre rtio: R nd compre it to 1 N from the -tbles. If R > 1 N we reect the null hypothesis. If < 1 N we retin the null hypothesis. k) Clculte the effect size: η (the proportion of totl vrince ccounted for by the tretments) T l) Write your conclusion nd perform pproprite follow-up tests.

4 xercise #1: Sugr N Men SD H : α 0 (the three shelves hve equl popultion mens; no tretment effect) (0)(4.8) + (0)(9.85) + (0)(6.10) M X H : α 0 (the tretment mens re not ll equl; tretment effect exists) Shelf # Shelf # Shelf # l rgest smllest compred to. 95 (OK to move on) 19 ( 0)( ) + ( 0)( ) + ( 0)( ) ( 0 1)(.18) + ( 0 1)( 1.985) + ( 0 1)( 1.865) Source R Shelf ffect rror Totl Since our clculted (observed) rtio is bigger thn the criticl - vlue, we reect the null hypothesis η % of the vrince in sugr is ccounted for by shelf loction. xercise #: iber N Men SD Shelf # Shelf # Shelf # H : α 0 (the three shelves hve equl popultion mens; no tretment effect) H : α 0 (the tretment mens re not ll equl; tretment effect exists) l rgest 1.77 smllest compred to. 95 (OK to move on) 19 (0)(1.68) + (0)(0.95) + (0)(.17) M X ( 0)( ) + ( 0)( ) + ( 0)( ) ( 0 1)( 1.166) + ( 0 1)( 1.16) + ( 0 1)( 1.77) Source R Shelf ffect rror Totl Since our clculted (observed) rtio is bigger thn the criticl - vlue, we reect the null hypothesis η % of the vrince in fiber is ccounted for by shelf loction. Is this of prcticl significnce?

5 xercise #: Thickness N Men SD Group Group Group H : α 0 (the three production lines produce glss of the sme thickness) H : α 0 (the production line effects the thickness of glss) l rgest smllest compred to. 07 (We shouldn t continue) 9 (0)(.015) + (0)(.018) + (0)(.996) M X ( 0)( ) + ( 0)( ) + ( 0)( ) ( 0 1)(.107) + ( 0 1)(.155) + ( 0 1)(.1) Source R Line rror Totl Since our clculted (observed) rtio is smller thn the criticl - vlue, we retin the null hypothesis η % of the vrince in glss thickness is due to production line differences. You cn see why there is no significnt group effect. xercise #4: Insects N Men SD Yellow White Green Blue H : α 0 (the colors mke no difference) H : α 0 (the tretment mens re not ll equl; tretment effect exists) compred to 1. 7 (OK to move on) M X [ ] " # ( ! 7.9 ) ! 7.9 4!1 ( ) + ( 1.5! 7.9) + ( 14.8! 7.9) $ % ( 0 1)[ ] Source R Color rror Totl Since our clculted (observed) rtio is bigger thn the criticl - vlue, we reect the null hypothesis. η % of the vrince in insects cptured is ccounted for by color.

6 xercise #5: Source R Groups rror Totl Source R Groups rror Totl η 0.19 η xercise #6: Cffeine Tps per minute Men Std. Dev Test of Homogeneity of Vrinces TPS Levene Sttistic 1 Sig NOV TPS Between Groups Within Groups Totl Dependent Vrible: TPS Sum of Squres Men Squre Sig Multiple Comprisons! Tukey HSD Bonferroni (I) CN 0 0 (J) CN *. The men difference is significnt t the.05 level. Men Difference 95% Confidence Intervl (I-J) Std. rror Sig. Lower Bound Upper Bound * * * * !

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