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# Download Introduction to Chance Models (Section 1.1) Introduction A key step

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```Now consider a different sampling method: What if you were to close your eyes and point blindly
at the page with a pencil 10 times, taking for your sample the 10 words that your pencil lands
on.
12. Do you think this sampling method is likely to be biased? If so, in which direction?
Explain.
A sample is only useful to us if the data we collect on our sample is similar to the results we
would find in the entire population. In this sense, we say the sample is representative of the
population.
13. Suggest another technique for selecting 10 words from this population in order for the
sample to be representative of the population with regard to word length and e-words.
Taking a simple random sample
Key idea: A simple random sample ensures that every sample of size n is equally likely to be
the sample selected from the population. In particular, each observational unit has the same
change of being selected as every other observational unit.
The key to obtaining a representative sample is using some type of random mechanism to
select the observational units from the population, rather than relying on convenience samples
or any type of human judgment. Instead of having you choose ârandomâ words using your own
judgment, we will now ask you to take a simple random sample of words and evaluate your
results. The first step is to obtain a sampling frame - a complete list of every member of the
population where each member of the population can be assigned a number. Below is a copy of
the Gettysburg address that includes numbers in front of every word. For example, the 43rd word
is nation.
14. Go to the Random Numbers generator at http://www.random.org
Generate 10 Numbers in the range from 1 to 268. What should you do if you get a
duplicate number generated?
Enter the random numbers in the table below:
Randomly generated ten ID values from 1-268
Using your randomly generated values, look up the corresponding word from the
sampling frame. Fill in the data table below.
June 27, 2014
MAA PREP workshop
51
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