Question

Color	First Peck Frequency
Blue	16
Green	9
Yellow	6
Red	3

Birds use color to select and avoid certain types of food. The authors of a particular article studied the pecking behavior of 1-day-old bobwhites. In an area painted white, they inserted four pins with different colored heads. The color of the pin chosen on the bird's first peck was noted for each of 34 bobwhites, resulting in the accompanying table. Do these data provide evidence of a color preference (i.e. are the colors not all the same)? Test using α = 0.01. (Assume that the sample is representative of all 1-day-old bobwhites.) Let p₁, p₂, p₃, and p₄ be the proportions of bobwhites whose first peck is each of the four colors.

(a) State the appropriate null and alternative hypotheses.

(b) X2= _____

Critical Value=________

Fail to reject or reject

Answer 1

a) Ho:p1=p2=p3=p4

Ha :All four proportion are not equal or there is a color preference

b)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	1/4	16.000	8.500	2.57	6.618
2	1/4	9.000	8.500	0.17	0.029
3	1/4	6.000	8.500	-0.86	0.735
4	1/4	3.000	8.500	-1.89	3.559
total	1.000	34	34		10.941

test statistic X2 =

10.941

degree of freedom =categories-1=			3
for 0.01 level and 3 degree of freedom :rejection region =					11.345

as test statistic does not fall above critical value , we fail to reject Ho