Question

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. Color First Peck Frequency Blue 15 Green 8 Yellow 7 Red 4 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. State the appropriate null and alternative hypotheses. H0: p1 = p2 = p3 = p4 = 0.5 Ha: H0 is not true. H0: p1 = p2 = p3 = p4 = 0.01 Ha: H0 is not true. H0: p1 = p2 = p3 = p4 = 0.25 Ha: H0 is not true. H0: p1 = p2 = p3 = p4 = 34 Ha: H0 is not true. H0: p1 = p2 = p3 = p4 = 9 Ha: H0 is not true. Find the test statistic and critical value. Round your test statistic to three decimal places and your critical value to two decimal places.) X2 = critical value = State the conclusion in the problem context. Fail to reject H0. There is convincing evidence that there is a color preference. Reject H0. There is convincing evidence that there is a color preference. Reject H0. There is not convincing evidence that there is a color preference. Fail to reject H0. There is not convincing evidence that there is a color preference.

Answer 1

H0: p1 = p2 = p3 = p4 = 0.25

Ha: H0 is not true.

Applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Blue	0.250	15	8.50	2.23	4.971
Green	0.500	8	17.00	-2.18	4.765
Yellow	0.250	7	8.50	-0.51	0.265
Red	0.250	4	8.50	-1.54	2.382
total	1.250	34	42.5		12.382

test statistic X² =12.382

critical value =11.34

Reject H0. There is convincing evidence that there is a color preference.