Question

22. One possible explanation for why some bird’s migration and others maintain year-round residency in a single location is intelligence. Specifically, birds with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriguez- Teijeiro, 2015). Birds with bigger brain on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to the actual research results. The numbers represent relative brain size for the individual birds in each sample. LABEL EACH OF THE 4 HYPOTHESIS STEPS IN YOUR WORK PLEASE! FOR A 5 STAR RATING

Non-Migrating	Short Distance Migrates	Long Distance Migrates
18	6	4
13	11	9	N= 18
19	7	5	G= 180
12	9	6	x²= 2150
16	8	5
12	13	7
M= 15	M= 9	M= 6
T= 90	T= 54	T= 36
SS= 48	SS= 34	SS= 16

a) Use an ANOVA with = .05 to determine whether there are any significant mean differences among the three groups of birds.

c) Use the Tukey HSD post-test to determine which groups are significantly different.

LABEL EACH OF THE 4 HYPOTHESIS STEPS IN YOUR WORK PLEASE! FOR A 5 STAR RATING

Answer 1

From the given data,

Source	DF	Sum of Square	Mean Square	F Statistic	P-value
Groups (between groups)	2	252.000000	126.000000	19.285713	0.0000713979
Error (within groups)	15	98.000004	6.533334
Total	17	350.000004	20.588236

Hypothesis:

H0:1=2=3

There are no differences among three groups of birds.

H1:Atleast one of the treatement means is different.

Test statisctics:

F-statistics=19.2857

p-value:0.0001

Since p-value<0.05, we reject null hypothesis.

conclusion:Hence there is significant difference among three groups of birds.

Tukey HSD:

Pair	Difference	SE	Q	Lower CI	Upper CI	Critical Mean	p-value
x1-x2	6.000000	1.043498	5.749889	2.166836	9.833164	3.833164	0.00274119
x1-x3	9.000000	1.043498	8.624833	5.166836	12.833164	3.833164	0.0000572177
x2-x3	3.000000	1.043498	2.874944	-0.833164	6.833164	3.833164	0.138490

Group	x2	x3
x1	6.00	9.00
x2	0.0	3.00

The means of the following pairs are significantly different: x1-x2, x1-x3.