AP Statistics Sec 5.1: An Exercise in Sampling: The Corn Field
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1 AP Statistics Sec.: An Exercise in Sampling: The Corn Field Name: A farmer has planted a new field for corn. It is a rectangular plot of land with a river that runs along the right side of the field. The corn looks good in some areas of the field but not others and the farmer is not sure that harvesting the field is worth the expense. The farmer decided to subdivide the entire rectangular field into smaller plots as shown in the grid below. He then decided to harvest of these plots, find the mean yield for these plots and use this information to estimate the mean yield per plot for the entire field. Based on this estimate, he will decide whether to harvest the entire field. Part I. A. Method Number One: Convenience Sample The farmer began by choosing plots that would be easy to harvest because they were closest to where his farm equipment was located. These plots are marked with X on the grid below: X X X X X X X X X X But before actually harvesting the corn from these plots, the farmer has had second thoughts about his selection and has decided to come to you (knowing that you are an AP statistics student, somewhat knowledgeable, but far cheaper than a professional statistician) to determine the approximate yield of the field. You will still be allowed to pick plots to harvest. Your job is to determine which of the following methods is the best one to use and to decide if this is an improvement over the farmer s original plan. AP Statistics Section.: An exercise in Sampling: The Corn Field Page of
2 AP Statistics Sec.: An Exercise in Sampling: The Corn Field B. Method Number Two: Simple Random Sample Use your calculator or a random number table to choose plots to harvest. Describe your method of selection, perform the selection, and mark the plots selected on the grid below with an X. Description of your method: C. Method Number Three: Stratified Sample (Vertical Strata) Consider the field as grouped in vertical columns (called strata). Using your calculator or a random number table, randomly choose one plot from each vertical column and mark these plots with an X on the grid below. AP Statistics Section.: An exercise in Sampling: The Corn Field Page of
3 AP Statistics Sec.: An Exercise in Sampling: The Corn Field D. Method Number Four: Stratified Sample (Horizontal Strata) Consider the field as grouped in horizontal rows (also called strata). Using your calculator or a random number table, randomly choose one plot from each horizontal row and mark these plots with an X on the grid below. E. Method Number Five: Cluster Sampling (Vertical Clusters) In this method you will randomly select an entire vertical column of data as a cluster. Discuss your method for selecting this column and mark each plot in the column with an X in the grid below. AP Statistics Section.: An exercise in Sampling: The Corn Field Page of
4 AP Statistics Sec.: An Exercise in Sampling: The Corn Field F. Method Number Six: Cluster Sampling (Horizontal Clusters) In this method you will randomly select an entire horizontal row of data as a cluster. Discuss your method for selecting this row and mark each plot in the column with an X in the grid below. G. Method Number Seven: Systematic Sampling In this method you will randomly select the first plot in the grid and then select every th plot after that until you have selected a total of plots. Discuss your method for selecting the starting plot and the direction you moved for selecting the subsequent plots. Mark each plot with an X in the grid below. AP Statistics Section.: An exercise in Sampling: The Corn Field Page of
5 AP Statistics Sec.: An Exercise in Sampling: The Corn Field The crop is ready and its time to harvest. Below is a grid with the yield in bushels of corn per plot. Estimate the average yield per plot based on each of the seven sampling techniques and enter these values in the table below. Sampling Method Sample Mean Yield A. Convenience B. SRS C. Vertical Strata D. Horizontal Strata E. Vertical Clusters F. Horizontal Clusters G. Systematic. You have looked at seven different methods of choosing plots. Discuss with your group reasons, other than convenience, to choose one method over another.. Compare your results with those of your group. Were your results similar? AP Statistics Section.: An exercise in Sampling: The Corn Field Page of
6 AP Statistics Sec.: An Exercise in Sampling: The Corn Field. Compare your estimates of the population yield according to the different sampling methods you used. Decide which sampling method you believe would best represent the average yield per plot for the entire field. Discuss your reasoning with your group.. Pool the results for all the students in your class. Use Fathom to construct dot plots, calculate the mean, and the standard deviation for each sampling method and compare these results. Complete the table below and comment on which sampling method or methods you believe is the best choice to use under these conditions. Discuss your reasoning for your selection. Sampling Method A. Convenience B. SRS C. Vertical Strata D. Horizontal Strata E. Vertical Clusters F. Horizontal Clusters G. Systematic Mean of The Sample Means of Class Data Standard Deviation of The Sample Means of Class Data. The actual average yield per plot of the farmer s field was. bushels of corn. How do the plots and values of the pooled results from question relate to this actual value? Which sampling method(s) had a mean for its distribution that was close to this actual value? From those distributions which sampling method would you choose and why? AP Statistics Section.: An exercise in Sampling: The Corn Field Page of
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