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	9
Yellow	7
Red	3

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 = 34
H_a: H₀ is not true.H₀: p₁ = p₂ = p₃ = p₄ = 9
H_a: H₀ is not true.    H₀: p₁ = p₂ = p₃ = p₄ = 0.25
H_a: H₀ is not true.H₀: p₁ = p₂ = p₃ = p₄ = 0.5
H_a: H₀ is not true.H₀: p₁ = p₂ = p₃ = p₄ = 0.01
H_a: 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.

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

.Fail to 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 cololor preference

Answer 1

Correct answer: H₀: p₁ = p₂ = p₃ = p₄ = 0.25
H_a: H₀ is not true.

From the given data

	Observed	Expected
	Freq (Oi)	Freq Ei	(Oi-Ei)^2 /Ei
Blue	15	8.5	4.970588235
Green	9	8.5	0.029411765
Yellow	7	8.5	0.264705882
Red	3	8.5	3.558823529
Total:	34	34	8.823529412

Test Statistic, X^2: 8.8235
Critical X^2: 11.34488

Degrees of freedom: 4-1 = 3

since Chi-square value < Chi-square critical value so we accept H0

Thus we conclude that p₁ = p₂ = p₃ = p₄ = 0.25

i.e. The proportion of 4 groups are same or equal