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 2.50 0.30 Lizard dung 20 2.30 0.33 Bird dung 20 1.70 0.34 Hyrax dung 20 1.45 0.28 (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 ?1, ?2, ?3, and ?4 be the true means for the four different treatments.) H0 : all four of the ?i's are different Ha : ?1 = ?2 = ?3 = ?4H0 : ?1 = ?2 = ?3 = ?4 Ha : all four of the ?i's are different H0 : at least two of the four ?i's are different Ha : ?1 = ?2 = ?3 = ?4H0 : ?1 = ?2 = ?3 = ?4 Ha : at least three of the four ?i's are differentH0 : ?1 = ?2 = ?3 = ?4 Ha : at least two of the four ?i's are different 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 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. 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 reject H0. The data do not 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 ?lizard − ?bird. Round your answers to three decimal places.) Assume the value of q is 3.72. There 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

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 2.50 0.30 Lizard dung 20 2.30 0.33 Bird dung 20 1.70 0.34 Hyrax dung 20 1.45 0.28 (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 ?1, ?2, ?3, and ?4 be the true means for the four different treatments.) H0 : all four of the ?i's are different Ha : ?1 = ?2 = ?3 = ?4H0 : ?1 = ?2 = ?3 = ?4 Ha : all four of the ?i's are different H0 : at least two of the four ?i's are different Ha : ?1 = ?2 = ?3 = ?4H0 : ?1 = ?2 = ?3 = ?4 Ha : at least three of the four ?i's are differentH0 : ?1 = ?2 = ?3 = ?4 Ha : at least two of the four ?i's are different 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 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. 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 reject H0. The data do not 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 ?lizard − ?bird. Round your answers to three decimal places.) Assume the value of q is 3.72. There 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Treatment	n	x	s
Uneaten figs	20	2.50	0.30
Lizard dung	20	2.30	0.33
Bird dung	20	1.70	0.34
Hyrax dung	20	1.45	0.28

(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 ?₁, ?₂, ?₃, and ?₄ be the true means for the four different treatments.)

H₀ : all four of the ?_i's are different
H_a : ?₁ = ?₂ = ?₃ = ?₄H₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : all four of the ?_i's are different H₀ : at least two of the four ?_i's are different
H_a : ?₁ = ?₂ = ?₃ = ?₄H₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : at least three of the four ?_i's are differentH₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : at least two of the four ?_i's are different

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 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. 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 reject H₀. The data do not 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

?_lizard − ?_bird.

Round your answers to three decimal places.)

Assume the value of q is 3.72. There 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 contain zero. This a significant difference between the germination rate between those two populations.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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