4 Chapter 1 Basic Ideas and chooses the numbers 1, 2, 3, 4, 5, 6. Her friend George says that this isn’t a good choice, since it is very unlikely that a random sample will turn up the first six numbers. Is he right? Solution No. It is true that the combination 1, 2, 3, 4, 5, 6 is unlikely, but every other combination is equally unlikely. In a simple random sample of size 6, every collection of six numbers is equally likely (or equally unlikely) to come up. So Sally has the same chance as anyone to win the jackpot. EXAMPLE 1.5 Using technology to draw a simple random sample Use technology to draw a simple random sample of five employees from the following list. 1. Dan Aaron 11. Johnny Gaines 21. Jorge Ibarra 31. Edward Shingleton 2. Annie Bienh 12. Carlos Garcia 22. Maurice Jones 32. Michael Speciale 3. Oscar Bolivar 13. Julio Gonzalez 23. Jared Kerns 33. Andrew Steele 4. Dominique Bonnaud 14. Jacqueline Gordon 24. Kevin King 34. Neil Swain 5. Paul Campbell 15. James Graves 25. Frank Lipka 35. Sherry Thomas 6. Jeffrey Carnahan 16. Ronald Harrison 26. Carl Luther 36. Shequiea Thompson 7. Joel Chae 17. Andrew Huang 27. Laverne Mitchell 37. Barbara Tilford 8. Dustin Chen 18. Anthony Hunter 28. Zachary Quesada 38. Jermaine Tryon 9. Steven Coleman 19. Jonathan Jackson 29. Donnell Romaine 39. Lizbet Valdez 10. Richard Davis 20. Bruce Johnson 30. Gary Sanders 40. Katelyn Yu Solution We will use the TI-84 Plus graphing calculator. The step-by-step procedure is presented in the UsingTechnology section on page 9.We begin by choosing a seed, which is a number that the calculator uses to get the random number generator started. Display (a) shows the seed being set to 21. (The seed can be chosen in almost any way; this number was chosen by looking at the seconds display on a digital watch.) Display (b) presents the five numbers in the sample. (a) (b) The simple random sample consists of the employees with numbers 27, 39, 30, 35, and 17. These are Laverne Mitchell, Lizbet Valdez, Gary Sanders, Sherry Thomas, and Andrew Huang. Check Your Understanding 1. A pollster wants to estimate the proportion of voters in a certain town who are Democrats. He goes to a large shopping mall and approaches people to ask whether they are Democrats. Is this a simple random sample? Explain. 2. A telephone company wants to estimate the proportion of customers who are satisfied with their service. They use a computer to generate a list of random phone numbers, and call those people to ask them whether they are satisfied. Is this a simple random sample? Explain. Answers are on page 12. CAUTION If you use a different type of calculator, a different statistical package, or a different seed, you will get a different random sample. This is perfectly all right. So long as the sample is drawn by using a correct procedure, it is a valid random sample.
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