Question

Do lizards play a role in spreading plant seeds? Some research carried out in South Africa would suggest so. Researchers on a study collected 400 seeds of a particular type of fig, 100 of which were from each treatment: lizard dung, bird dung, rock hyrax dung, and uneaten figs. They planted these seeds in batches of 5, and for each group of 5 they recorded how many of the seeds germinated. This resulted in 20 observations for each treatment. The treatment means and standard deviations are given in the accompanying table.

Treatment	n	x	s
Uneaten figs	20	2.40	0.30
Lizard dung	20	2.30	0.33
Bird dung	20	1.70	0.35
Hyrax dung	20	1.45	0.27

(a)

Construct the appropriate ANOVA table. (Use technology. Round your answers to three decimal places.)

Source of variation	Degrees of freedom	Sum of squares	Mean squares	F Ratio	F Prob
Between Groups
Within Group
Total	79

Test the hypothesis that there is no difference between mean number of seeds germinating for the four treatments. (Use a significance level of 0.05.)

State the appropriate null and alternative hypotheses. (Let μ₁, μ₂, μ₃, and μ₄ be the true means for the four different treatments.)

H₀ : μ₁ = μ₂ = μ₃ = μ₄
H_a : at least three of the four μ_i's are differentH₀ : at least two of the four μ_i's are different

H_a : μ₁ = μ₂ = μ₃ = μ₄    H₀ : μ₁ = μ₂ = μ₃ = μ₄
H_a : at least two of the four μ_i's are differentH₀ : μ₁ = μ₂ = μ₃ = μ₄

H_a : all four of the μ_i's are differentH₀ : all four of the μ_i's are different
H_a : μ₁ = μ₂ = μ₃ = μ₄

State the test statistic and P-value. (Use technology. Round your answers to three decimal places.)

F=

P-value=

State the conclusion in the problem context.

We reject H₀. The data do not provide convincing evidence that the mean number of seeds germinating for the four populations is not the same.We fail to reject H₀. The data do not provide convincing evidence that the mean number of seeds germinating for the four populations is not the same.    We fail to reject H₀. The data provide convincing evidence that the mean number of seeds germinating for the four populations is not the same.We reject H₀. The data provide convincing evidence that the mean number of seeds germinating for the four populations is not the same.

(b)

Is there evidence that seeds eaten and then excreted by lizards germinate at a higher rate than those eaten and then excreted by birds? Give statistical evidence to support your answer. (Use a table. Use μ_lizard − μ_bird. Round your answers to three decimal places.)

Assume the value of q is 3.72. There  ---is, is not--- is not is evidence that seeds eaten and then excreted by lizards germinate at a higher rate than those eaten and then excreted by birds. The 95% T-K confidence interval is (____,_____) which  ---does, does not--- does does not contain zero. This  ---indicates, does not indicate--- indicates does not indicate a significant difference between the germination rate between those two population.

Answer 1