AP Statistics Sampling Name Sampling Exercise (adapted from a document from the NCSSM Leadership Institute, July 2000). Problem: A farmer has just cleared a field for corn that can be divided into 100 smaller plots. The land has a river running down one side of it. The farmer isn t sure whether harvesting the entire field is worth the expense. So he decides to harvest 10 plots and use this information to estimate the total yield. Based on this information, he will decide whether to harvest the remaining plots. Method 1: Convenience The farmer begins by choosing 10 plots that are most convenient for him to harvest without any other considerations. Mark those on the grid below with an X. The farmer has second thoughts about the selection and has decided to come to you as an AP Statistics student to help him determine the approximate yield of the field. You are still using 10 plots to harvest early. Your job is to use one of the following methods and decide which method is the best to use. Method 2: Simple Random (SRS) Use your calculator or a random number table to choose 10 plots at random to harvest. Mark them on the grid below with an X and describe your method of selection. www.mastermathmentor.com - 1 - Stu Schwartz
Method 3: Column Think of the field as grouped in 10 vertical columns (the strata). Use your calculator or random number table, randomly choose one plot from each vertical strata and mark these plots on the grid with an X. Method 4: Row Think of the field as grouped in 10 horizontal rows (the strata). Use your calculator or random number table, randomly choose one plot from each horizontal strata and mark these plots on the grid with an X. www.mastermathmentor.com - 2 - Stu Schwartz
Method 5: Multistage 1 Think of the field as grouped as 10 sections as shown by the picture below. Use your calculator or random number table, randomly choose 5 sections. In sections 3, 4, 5, 6, 7 (if used), choose one plot from each row. In sections 1, 2, 8, and 9 (if used), choose two rows at random and then choose one plot from each row. In section 10 (if used) choose two plots. Mark the 10 plots you chose on the grid with an X. Method 6: Multistage 2 Think of the field as grouped as 10 sections as shown by the picture below. Use your calculator or random number table, randomly choose 5 sections. In sections 5 and (if used), choose one plot from each row. In sections 1, 2, 3, 4, 7, 8, 9, 10 (if used), choose two rows at random and then choose one plot from each row Mark the 10 plots you chose on the grid with an X. www.mastermathmentor.com - 3 - Stu Schwartz
AP Statistics Sampling Name Part 1: Tear this sheet off. A year has passed and the crop of corn is up. Below is a grid showing the yield per plot. REMEMBER, you would never have such information. You would only know this for the plots you planted. But for this exercise, this information is provided. Total yield: the sum the yield of your chosen plots Average yield per plot: Divide your total yield by 10 Estimate of field s yield: Multiply your average yield by 100 5 16 21 37 44 54 68 77 82 96 8 13 22 33 42 57 64 72 80 93 2 13 26 30 51 52 63 80 86 98 8 15 24 33 42 51 66 73 89 92 4 14 27 32 45 53 65 75 83 94 5 17 28 31 47 60 63 74 87 99 6 18 27 36 50 59 68 76 89 90 9 17 21 38 41 54 62 77 90 94 8 18 29 39 44 52 60 78 81 91 7 19 23 36 48 53 68 76 84 96 Sampling Method Convenience Simple Random Column Row Multistage 1 Total Yield Average yield per plot Estimate of field's yield Multistage 2 Answer the following questions: 1) Is there a good reason to choose one method over another (without having the benefit of the charts above)? Explain. 2) What was the actual yield of the farmer s field? Which method came closest to that figure? www.mastermathmentor.com - 4 - Stu Schwartz
Part 2: 3) Pool your results (estimated yield) from the entire class and then complete the chart below. Sampling Method Convenience SRS Column Row Multistage 1 Multistage 2 Mean Standard Deviation Minimum Q1 Median Q3 Maximum Outliers 4) Draw Boxplots for each of these on the same scale. 5) The goal for choosing a good sampling method is one that will best predict the mean of the population distribution with as small a variation as possible. By the analysis above, explain which method is the best at doing that, which is the worst (excluding convenience sample) and why. Best: Reason: Worst: Reason: www.mastermathmentor.com - 5 - Stu Schwartz