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All of our estimates thus far have been based on a sample size of 10 randomly selected sub-regions out of 100. In this part, we will examine the effects of changing the sample size to 20 sub-regions.
Here is a sequence of 20 random numbers selected by sampling without replacement:
81 48 66 94 87 60 51 30 92 97 00 41 27 12 38 64 93 79 50 59
Here is the corresponding sample of 20 sub-regions:
As before, we estimate the total number of penguins in the region by finding the mean of our samples, and then multiplying by 100 (the number of regions):
100 x [(5 + 6 + 5 + 6 + 3 + 7 + 4 + 5 + 5 + 7 + 5 + 5 + 4 + 4 + 5 + 6 + 7 + 4 + 5 + 4)/20] = 510
This estimate is very accurate (it is within 10 of the actual number of penguins). Let's now investigate the effect that increasing the sample size has on the accuracy of our estimation procedure.
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