Question

It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff (so that the direction X should be uniformly distributed on the interval from 0° to 360°). To test this, 120 pigeons are disoriented, let loose, and the direction of flight of each is recorded; the resulting data follows. Use the chi-squared test at level 0.10 to see whether the data supports the hypothesis.

Direction	0−<45°	45−<90°	90−<135°	135−<180°
Frequency	11	17	17	15

Direction	180−<225°	225−<270°	270−<315°	315−<360°
Frequency	13	20	17	10

State the appropriate hypotheses.

a. H₀: p₁ ≠ p₂ ≠ ... ≠ p₈ ≠ 0.125
b. H_a: all p_i's = 0.125H₀: p₁ ≠ p₂ ≠ ... ≠ p₈ ≠ 0.125
c. H_a: at least one p_i = 0.125     H₀: p₁ = p₂ = ... = p₈ = 0.125
d. H_a: no p_i = 0.125H₀: p₁ = p₂ = ... = p₈ = 0.125
e .H_a: at least one p_i ≠ 0.125

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =  

What can be said about the P-value for the test?

a. P-value < 0.005

b. 0.005 < P-value < 0.01

c. 0.01 < P-value < 0.025

d. 0.025 < P-value < 0.05

e. 0.05 < P-value < 0.10

f. P-value > 0.10

State the conclusion in the problem context.

a. Reject H₀. There is not enough evidence to disprove the claim.

b. Fail to reject H₀. There is not enough evidence to disprove the claim.     

c. Reject H₀. There is enough evidence to disprove the claim.Fail to reject H₀.

d. There is enough evidence to disprove the claim.

Answer 1

The statistical software output for this problem is :

H₀: p₁ = p₂ = ... = p₈ = 0.125
e .H_a: at least one p_i ≠ 0.125

Test statistics = 5.47

f. P-value > 0.10

b. Fail to reject H₀. There is not enough evidence to disprove the claim.