Question

I1. Gravetter/wallnau Eesentials- Chapter 12- End-od-chapter question 32 Aa One possible explanatisn for why some hirds migrate and others maintain yeer round residency in a single locatian intsligence. Speaficaly, birds with smal brains, relative to thelir body , are mply mot smart enough to fnd ood during the winter and must migrats to warmer dimates where food is eedly available (Sal, Letebure, & Rodnguez-Tej 2005% Birds with bigger brains, on the ather hand, are more creative and can find food ewan when the weather turs harsh. Follewing are hypothetical data similar to the actual ressarch resuts. The numbars represent relative brain siue for the indvidual birds in each sample Non Short-Distance Long Distance Migrating Migrants Migrants G 180 5 2X-2150 T-90 T- 55-48-34 use en ANOVA with ?-.05 to determine whether there are am sigrinant mian dfrentes among the three groups of birds. (use twa decimal plaoes) Distroubien O Reject the nul bypothesis; there are so signficant differences amang the three groups of birds O Tal to reject the null hypothess, there are no significant diflerences among the three proups of birds O Fal to reject the null hypothess; there are sigrificant differences among the three groups of birds O Reject the nul hypathesis; there are signfñicant ditferences ameng the three groups of birds Compube ni, the percentage of variance explained by the group differences, for these data (Use two dedmal Wrte a sentence demonstrating how a research report would present the resuits of the hypothesis test and the wous The rasuhs shaw signncare differences in the three proups of birds

Please answer all questions. Thank you!

Answer 1

(first part)

Total sum of square=sum(x²)-CF=sum(x²)-G²/n=2150-180*180/18=350

Within sum of square=sum(SS)=48+34+16=98

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	252	2	126	19.28571	7.14E-05	3.68232
Within Groups	98	15	6.533333
Total	350	17

(second part) right choice is fourth

Reject the null hypothesis , there is significant differences among the three group of birds

(third part) $\eta^2$ =SS(between)/SS(total)=252/350=0.72

(fourth part) there is large $\eta^2$ (>0.26)

(fifth part) q(0.05,3,15)=3.67

(sixth) HSD=(M_i-M_j)/sqrt(MS_w/n_h)

for non-migrating and short distance , HSD=(15-9)/sqrt(6.53*(1/6+1/6))=4.07 is more than q=3.67, so these pair is significant ( significant mean difference)

for non-migrating and long distance , HSD=(15-6)/sqrt(6.53*(1/6+1/6))=6.01 is more than q=3.67, so these pair is significant( significant mean difference)

for short-distance and long distance , HSD=(9-6)/sqrt(6.53*(1/6+1/6))=2.03 is less than q=3.67, so these pair is not significant ( non-significant mean difference)