Homework Data (A) An ichthyologist is interested in the effect of herbivory on a

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Homework Data (A) An ichthyologist is interested in the effect of herbivory on algal growth in a stream ecosystem. To answer this question, she set up a series of artificial streams in which algae was allowed to grow for three weeks. After the acclimation period, he added a population of algivorous fish, Campostoma anomalum (Central Stoneroller Minnow) to half of the streams (n=12), and allowed the other streams (n=12) to be herbivore free. After four more weeks, she measured and calculated the mean length of the algal lawn in each stream. Two of the streams which had the fish treatment were unfortunately contaminated with a powerful agricultural herbicide when a grounds-keeper sprayed too close to the experimental streams. Those two data points were eliminated from the final analysis. 1. Develop null and alternative hypothesis. (include all subalternatives) 2. Run and report the Student's T-test. 3. Report df (n + n - 2) 4. Convert the T value into a P value and report the P value. 5. Fail to reject and reject the appropriate hypothesis. Mean algal length (cm) Herbivore absent streams Herbivore present streams 13 10 12 4 3 7 9 7 11 5 14 6 8 4 16 9 12 16 10 5 12 13 Homework Data (A) An ichthyologist is interested in the effect of herbivory on algal growth in a stream ecosystem. To answer this question, she set up a series of artificial streams in which algae was allowed to grow for three weeks. After the acclimation period, he added a population of algivorous fish, Campostoma anomalum (Central Stoneroller Minnow) to half of the streams (n=12), and allowed the other streams (n=12) to be herbivore free. After four more weeks, she measured and calculated the mean length of the algal lawn in each stream. Two of the streams which had the fish treatment were unfortunately contaminated with a powerful agricultural herbicide when a grounds-keeper sprayed too close to the experimental streams. Those two data points were eliminated from the final analysis. 1. Develop null and alternative hypothesis. (include all subalternatives) 2. Run and report the Student's T-test. 3. Report df (n + n - 2) 4. Convert the T value into a P value and report the P value. 5. Fail to reject and reject the appropriate hypothesis. Mean algal length (cm) Herbivore absent streams Herbivore present streams 13 10 12 4 3 7 9 7 11 5 14 6 8 4 16 9 12 16 10 5 12 13

Explanation / Answer

1)

ho: there Is no significant difference in the mean length of the algal lawn in each stream when Herbivore was absent and present. U1 = u2

h1: there Is significant difference in the mean length of the algal lawn in each stream when Herbivore was absent and present. U1 =/= u2

2)

t=(X1bar-X2bar)/sqrt(s1^2/n1+s2^2/n2)

t = (11.08-7.3)/SQRT(3.34^2/12+3.65^2/10)

2.513371578

3)

df=

12+10-2

20

4)

p-value

2*(1-P(T<|t|)

2*(1-P(T<|2.513372|)

=T.DIST.2T(2.513372,20)

0.020635317

5)

since p-value < 0.05, I reject ho at 5% level of significance

herbivore absent herbivore present mean 11.08 7.30 sd 3.34 3.65 n 12 10

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