A biologist wants to estimate the number of fox dens in a large area Suppose tha
ID: 3305993 • Letter: A
Question
A biologist wants to estimate the number of fox dens in a large area Suppose that the actual location of these dens are as depicted in the picture below 0 0 ol o The biologist divides the area into a grid and selects a simple random sample of 9 patches from the 96 patches. To do this she assigns the numbers 1 through 96 to the patches. The patch a1 is 1, the patch a2 is 2, and so on. To select a simple random sample she uses the following R code set seed(2582) patches-seq(from=1, to-96) sample(patches, size-9) (a) Complete the table below In the first row enter the numbers of the selected patches in the same order as provided to you by R. In the second row enter the number of dens for each patch
Explanation / Answer
Following the R-codes given, the the outputs generated are as follows [to be used for (a) to (c)]:
> set.seed(2582)
> patches=seq(from=1,to=96)
> sample(patches, size=9)
[1] 85 82 25 51 14 62 33 35 16
Counting the corresponding numbers of dens in the patches randomly obtained by R (with seed 2582), we can answer all the questions:
(a) 33 35 16
2 2 2
(b) 0+2+2+3+3+2+2+2+2 = 18 dens
(c) Estimate based on the simple random sampling = 96 X (18/9) = 192 dens (because 18 dens in 9 sample, and there are 96 patches in total)
Following the R-codes given, the the outputs generated are as follows [to be used for (d) to (f)]:
> set.seed(2582)
> zone1=seq(from=1,to=32)
> zone2=seq(from=33,to=64)
> zone3=seq(from=65,to=96)
> sample(zone1, size=3)
[1] 29 27 8
> sample(zone2, size=3)
[1] 50 37 53
> sample(zone3, size=3)
[1] 76 77 70
Similar to previous section, on counting the dens for the patches obtained by R, we can answer the rest of the questions:
(d) 76 77 70
3 2 1
(e) 0+1+1+4+3+5+3+2+1= 20 dens
(f) Estimate based on the stratified random sampling = 96 X (20/9) = 213.3 dens (i.e. about 213 dens) (because 20 dens in 9 sample, and there are 96 patches in total).
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