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Applying Random Sampling Methods And Random Number Generators

Applying Random Sampling Methods and Random Number Generators

The last four sampling methods discussed all use random selections at some point in the process of selecting a sample. The simplest way to introduce this random chance is to use either a table of randomly generated numbers (found in most textbooks) or an online random number generator. The following examples will illustrate this procedure. This problem will involve a small population for illustration purposes, but the process would be the same for a large population.
Suppose a quality control inspector needs to make sure that the watches produced on the afternoon shift are free of defect. The population is all the watches produced on that day’s afternoon shift. The inspector will label them watches A through W. The inspector will choose a sample of 8 watches to inspect.  The sample will be chosen using simple random sampling, systematic sampling, and stratified sampling.  Because they do not apply to this example, quota and cluster sampling will not be performed.

First, suppose the inspector chooses a simple random sample. The population members are listed in any order: A, B, C, D, E, F, G, H, I, J ,K L, M, N, O, P , Q, R, S, T, U, V, W. Next, eight random numbers from 1 to 23 are needed. There are many random number generators available on the internet. For this example, Research Randomizer was used. This generator was used to create a list of eight random numbers: 13, 4, 20, 9, 16, 23, 15, 3. The watches selected for the sample are the ones whose position in the population list matches a random number. Therefore, watches C, D, I, M, O, P, T, and W are chosen to be inspected.

Next, suppose the inspector uses systematic sampling. In systematic sampling, the randomness comes from the list ordering, so the numbers from 1 to 23 need to be randomized to create an ordering for the population list. Another random number generator is Doug’s Random Sampling Applet. This was used to generate the needed list of random numbers: 3, 5, 19, 7, 21, 22, 12, 10, 6, 2, 18, 23, 13, 4, 15, 1, 9, 14, 11, 16, 8, 17, 20. This is the random ordering that will be used for the population list of watches: C, E, S, G, U, V, L, J, F, B, R, W, D, O, A, I, N, K, P, H, Q, T. Next, the inspector would select every 2nd watch in the list until 8 are selected, since 23/8 = 2.875. Therefore, the watches selected for the sample are C, S, U, L, F, R, D, and A.

Finally, suppose the inspector chooses a sample using stratified sampling. This requires more information about the population so it can be divided into appropriate strata. In this example, suppose the inspector knows that watches A – L were made on production line 1 and watches M – W were made on production line 2. These would be appropriate strata because both productions lines should be checked for quality. Since both lines made approximately the same number of watches, the sample could include 4 from each. Thus, two sets of four randomly generated numbers are needed. For the first set, the numbers should be from 1 to 12; for the second, from 1 to 11. For this example, an online random number generator, called Lotto, was used. This generator was used to create the two lists. List 1: 7, 4, 3, 8. List 2: 7, 11, 10, 6. The watches chosen in the stratified sampling process are G, D, C, H, S, W, V, and R.

 

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