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 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.

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.

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.

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.

Example See Example 2.14, p. 88.

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.”

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

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.

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.

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.

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