Random Sampling Question

Probability theory and statistics

Random Sampling Question

Postby Guest » Thu Feb 25, 2021 7:13 pm

okay guys this is the question:

A zoo has 80 cotton-top tamarins. Describe in detail how the random- number table given below could be used to select a sample of 5 of them, for a study of tail lengths.
8330 3992 1840 0330 1290 3237 9165 4815 0766
(5marks)

So im not really sure where to go with this one, i can't see it being any type of systematic so it must be simple random sampling, but the issue is, there are nine groups of four numbers and I can't see a way to get these 36 numbers to relate back to the 80 tamarins.
Any help appreciated.
Guest
 

Re: Random Sampling Question

Postby Guest » Sat Feb 27, 2021 12:07 pm

Guest wrote:okay guys this is the question:

A zoo has 80 cotton-top tamarins. Describe in detail how the random- number table given below could be used to select a sample of 5 of them, for a study of tail lengths.
8330 3992 1840 0330 1290 3237 9165 4815 0766
(5marks)

So im not really sure where to go with this one, i can't see it being any type of systematic so it must be simple random sampling, but the issue is, there are nine groups of four numbers and I can't see a way to get these 36 numbers to relate back to the 80 tamarins.
Any help appreciated.

First number the tamarins 1 to 80.
You have nine 4 digit numbers
8330 3992 1840 0330 1290 3237 9165 4815 0766

I would separate them into
83 30 39 92 18 40 03 30 12 90 32 37 91 65 48 15 07 66
eighteen two digit numbers. Now drop all those that are larger than 80
30 39 18 40 03 30 12 32 37 65 48 15 07 66

Pick 5 or those is a way that preserves the randomness.

For example, choose the first 5 numbers and pick tamarins 30, 39, 18, 40, and 03.
or choose the last 5 numbers and pick tamarins 65, 48, 15, 07, 66.
Guest
 

Re: Random Sampling Question

Postby romsek » Sat Feb 27, 2021 2:24 pm

The problem with the method detailed above is that the digits 8 and 9 have distinctly lower probabilities of occurrence than digits 0-7 after processing.

So the resulting indices aren't as random as they could be since the underlying distribution for choosing them isn't uniform.

What I would do is note that [tex]\dfrac{10000}{80} = 125[/tex] and do the following.

Treat each 4 tuple as a decimal number [0, 9999]

Mod each 4 tuple with 80 to obtain an index [tex]k[/tex] that lies in [0, 79]

Use [tex]k+1[/tex] as an index to choose a tamarin with.

This results in a uniform distribution on the indices.

romsek
 
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