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Simple Random Sampling

Simple Random Sampling. Lecture 7 Section 2.5 Tue, Jan 27, 2004. Simple Random Sample. Simple Random Sample of size n – A sample of size n chosen in such a way that all possible samples of size n have the same chance of being selected. Selecting a Simple Random Sample.

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Simple Random Sampling

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  1. Simple Random Sampling Lecture 7 Section 2.5 Tue, Jan 27, 2004

  2. Simple Random Sample • Simple Random Sample of size n – A sample of size n chosen in such a way that all possible samples of size n have the same chance of being selected.

  3. Selecting a Simple Random Sample • Given a population of size N, number the members from 1 to N. • Then use a random number generator (such as on a calculator) to generate n random integers from 1 to N. • If the sampling is done without replacement, then repetitions should be discarded.

  4. Using a Random Number Table • See the Random Number Table on page 85. • Use it to select a random sample of size n = 10 from a population of size N = 100. • Use it to select a random sample of size n = 10 from a population of size N = 133.

  5. Using the TI-83 • Press MATH. • Use arrow keys to highlight PRB menu. • Press 5 to select randInt (item #5). • Enter randInt(1, 100) and press ENTER. • A random number appears. • Press ENTER repeatedly for more random numbers.

  6. Setting the Seed • A random number generator uses a "seed" value to get the next random number. (See p. 87.) • Enter the desired seed, say, 33. • Press STO. • Press MATH, hightlight PRB, select rand (item #1). • Press ENTER. The seed is set to 33.

  7. Example • See Example 2.14, p. 88.

  8. Let's Do It! • Let's do it! 2.4 – A Simple Random Sample of Companies. • Let's do it! 2.5 – Simple Random Sampling. • Divide the class into two groups. • Change “proportion of women” to “proportion of freshmen.”

  9. Using Excel • Click in Cell A1. • Type =rand(). • Press ENTER. A random number appears. • Click in Cell B1. • Type =100*A1. • Press ENTER.

  10. Using Excel • Click in Cell C1. • Type =ceiling(B1,1). • Press ENTER. An random integer from 1 to 100 appears. • The functions rand() and ceiling() may be found under “Function…” in the Insert menu.

  11. Using Excel • Select the rectangle of cells A1 – C1 through A20 – C20. • Press CTRL-D to “fill down.” • Column C now contains 20 random numbers from 1 to 100.

  12. Using Excel • This could all be accomplished in one column by typing =ceiling(100*rand(), 1) in Cell A1 and filling down through Cell A20. • Excel does not give you access to the seed.

  13. Assignment • Page 112: Exercises 16 – 21, 23 – 24.

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