STAT 110 - Section 5 Lecture 4 Professor Hao Wang University of South Carolina Spring 2012 Last time Bad sample: Convenience and voluntary sample Good sample: Simple random sample (SRS) This time • How to get a simple random sample (SRS) Random Digits table of random digits – a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with the following two properties: 1. Each entry in the table is equally likely to be any of the 10 digits 0 through 9. 2. The entries are independent of each other. That is, knowledge of one part of the table gives no information about any other part. Random Digits • Table A on pages 550-551 • The digits appear in groups of 5 to make the table easier to read. • The groups and rows have no meaning. • So, how do you use the table? • Digits can be read across a row, down a column, or in any other order. • Standard practice is to read across the row. Random Digits Example A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. Use Table A at line 102 to choose 6 minority managers to be interviewed. 01-Agarwal 02-Alfonseca 03-Baxter 04-Bowman 05-Cortez 06-Cross 07-Dewald 08-Fleming 09-Gates 10-Goel 11-Gomez 12-Hernandez 13-Huang 14-Kim 15-Liao 16-Mourning 17-Peters 18-Puri 19-Rodriguez 20-Shen 21-Vega Random Digits • Step 1: Label Assign a numerical label to every individual in the population (sampling frame). All labels must have the same number of digits. • Step 2: Table Use the random number table to select labels at random. Random Digits Example Let the class be the population. Let’s take an SRS of size n=2. There are N=200 on the roll. Everyone numbers off. Since all labels must have the same number of digits, the numbers should be 001 to 200. Start with line 116 of Table A. How do we read it? Who is chosen as our sample? Problem 3 You are reporting on apartments in Columbia. You decide to select 3 complexes at random for in-depth interviews with residents. Use Table A at line 116 (read across the row) to select your sample. 01-Abbott Arms 02-Asbury Arms 03-Ashland 04-Bent Tree 05-Briargate 06-Brook Pines 07-Cedarwood 08-Claire Tower 09-Colony East 10-Cornell Arms 11-Fairways 12-Fox Run 13-Green Oaks 14-Hunter’s Green 15-Keswick 16-Landmark 17-Paces Run 18-Ravenwood 19-Riverview 20-Stone Ridge 21-Whaley’s Mill Problem 3 The third complex chosen is: A - 03 B - 10 C - 14 D - 45 E - 92 Comparing sampling methods You will be given a sheet of 100 rectangular shapes. Leave it face down until told to look. When told to, flip it over for 5 seconds and make a guess at the average size of the rectangles on the sheet. Then flip it back over. Write your guess down. Choosing a non-random sample Now, look at the sheet and pick five rectangles that you think are most representative. Take their average by adding up the total number of squares and dividing by 5. Write that value down. Randomly choosing a convenience sample This time we need to use the random number table. Use the row corresponding to the day your birthday falls on (if the 26th – 30th, wrap back around to the top of the page). So if your birthday is the 1st use row 101, if it’s the 24th use row 124, and if it’s the 26th you wrap back around and use 101 too. Start a number of digits in equal to the month you were born in. Randomly choosing a convenience sample (pt. 2) Now choose the first number from 00 to 99 and take that rectangle (remember 00=100) and the four closest to it. Add up their sizes and divide by 5. Using a simple random sample Take the next five numbers from 00 to 99 as your simple random sample of size five. Add up their sizes and divide by 5. What range was your guess in? A – 3.9 or less B – 4.0 to 5.6 C – 5.7 to 9.1 D – 9.2 to 10.9 E – 11.0 or higher Choose 5 you think are representative: A – 3.9 or less B – 4.0 to 5.6 C – 5.7 to 9.1 D – 9.2 to 10.9 E – 11.0 or higher Take a convenience sample: A – 3.9 or less B – 4.0 to 5.6 C – 5.7 to 9.1 D – 9.2 to 10.9 E – 11.0 or higher Take a SRS: A – 3.9 or less B – 4.0 to 5.6 C – 5.7 to 9.1 D – 9.2 to 10.9 E – 11.0 or higher True or False In a table of random digits: Each pair of digits has chance 1/100 of being 33 A.True B. False True or False In a table of random digits: There are exactly four 4s in each row of 40 digits. A.True B. False True or False In a table of random digits: The digits 99999 can never appear as a group, because this pattern is not random. A.True B. False True or False In a table of random digits: The digits 34965 are more random than 24242. A. True B. False