8 One hundred preying mantids were released into a greenhouse containing 400 ind

Question

8 One hundred preying mantids were released into a greenhouse containing 400 individual plants which are all the same size and age. The greenhouse was known to contain zero mantids prior to the release. After one weck, a census of all mantids on all 300 plants was done and the number of mantids on each plant determined. The resulting data are given in the table below number of mantids o number ofplants 245 0 A. Dothe mantids locate themselves randomly on the plants? Show work and give the p-value. B. Do the data agree with the idea that all the mantids survive the week and a locate themselves on a plant? Show work and give the p-value. C. Assume all mantids present in the greenhouse locate on a plant. What proportion of the released mantids survive 1 week?

Explanation / Answer

c) Assuming all mantids present in the greenhouse locate on a plant, based on given data only 68% survived - 245*0+43*1+11*2+1*3 = 68 out of 100

b) As per data, not all of them survived after a week since only 68 of them were observed over plant

a) With 68 mantinds and 300 plants, had mantids choosen plants randomly each plant would have had 0.23 chances of having mantids. Thus chances for a plant to get two mentids = 0.23*0.23=0.05. similarly 3 mentids = 0.01. Indicates 15 plants in 300 and 3 plants in 300 can have 2 and 3 mentids respectively. The obsereved data is close to theoretical value hinting near random

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