# Your research team has developed a new chemical to combat Japanese beetles that is not toxic to other living things. Your team wants to test the chemical in actual conditions and has selected a 100...

Your research team has developed a new chemical to combat Japanese beetles that is not toxic to other living things. Your team wants to test the chemical in actual conditions and has selected a 100 x 100 meter area where the chemical will be tested. Before the team can test the chemical, however, it needs to have a count of the number of Japanese beetles present before the chemical is applied. This number can then be compared to the count of Japanese beetles after the chemical has been used to see how effective it is in reducing the number of beetles.

It is your job as a member of the team to do the initial count of the beetles by taking a sample. In Self-Check Test 3, you performed a sampling activity. Use the data you collected in your sampling activity of pennies as the data for your sample of Japanese beetles to answer the following questions.

You have collected 20 Japanese beetles from the area, tagged them with a painted red dot, and then released in small numbers in various places in the hectare you are studying.

A. When you took a second random sample of 10 Japanese beetles, how many of the 10 were tagged?

B. How many groups of recaptured, tagged beetles are there in the 20 beetles you originally tagged?

C. Calculate approximately how many Japanese beetles are in the 100 x 100 meter area.

D. Is the data you collected on the beetles quantitative or qualitative data? Explain your answer.

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### 1 Answer

You need to estimate the Japanese beetles population in 100 x 100 meter area, hence, you may use the following mathematical model called mark-recapture method, such that:

`N = (M*n)/R`

N represents the estimated population

M represents the number of beetles in the first sample

n represents the number of beetles in the second sample

R represents the number of recaptured tagged beetles

Hence, since the number of beetles in the first sample is M = 20 and the number of beetles in the second sample is n = 10 and since all the beetles are tagged, then, the number of recaptures varies between 1 and 10, such that, R = 1,2,3,...,10.

Supposing that R = 1 yields:

`N = (20*10)/1 => N = 200 ` estimated population of beetles

Supposing that R = 2 yields:

`N = (20*10)/2 => N = 100` estimated population of beetles

Supposing that R = 3 yields:

`N = (20*10)/3 => N = 66 ` estimated population of beetles

Supposing that R = 4 yields:

`N = (20*10)/4 => N = 50 ` estimated population of beetles

Supposing that R = 5 yields:

`N = (20*10)/5 => N = 40` estimated population of beetles

Supposing that R = 6 yields:

`N = (20*10)/6 => N = 33` estimated population of beetles

Supposing that R = 7 yields:

`N = (20*10)/7 => N = 28` estimated population of beetles

Supposing that R = 8 yields:

`N = (20*10)/8 => N = 25` estimated population of beetles

Supposing that R = 9 yields:

`N = (20*10)/9 => N = 22` estimated population of beetles

Supposing that R = 10 yields:

`N = (20*10)/10 => N = 20` estimated population of beetles

Hence, the values of the estimated beetles population, under the given conditions, are the following {20,22,25,28,33,40,50,66,100,200}.

Since the data collected involve numerical values, hence, you may say that these data are quantitative and not qualitative.

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