Sampling Worksheet: Rolling Down the River

Transcription

1 Sampling Worksheet: Rolling Down the River Name: Part I A farmer has just cleared a new field for corn. It is a unique plot of land in that a river runs along one side. The corn looks good in some areas of the field, but not in others. The farmer is not sure that it is worthwhile to harvest the corn, and wants to estimate the total corn that is in the field. To do this, he wants to harvest 10 plots of the 100 in the field, and use the average yield per plot to make his decision as to whether he will harvest or not. Method #1: Convenience Sample The farmer began by selecting 10 plots that would be the easiest to harvest. They are marked on the diagram of the field below: Comment on the farmer s selection:

2 Since selecting the plots, he has had second thoughts and has decided to come to you (knowing you are interested in data selection and this sort of thing) and allow you to determine the yield of the field. You will still be allowed to select 10 plots to harvest early. Your job is to determine which of the following methods to use and to determine if this is an improvement over the farmer s original plan. Method #2: Simple Random Sample (SRS) Use your calculator or a random number table to choose 10 plots to harvest. Mark them on the diagram below, and describe your method of selection: Describe the method of selection, and comment on the resulting selection:

3 Method #3: Stratified Sample Consider the field as grouped in vertical columns (called strata). Use your calculator or a random number table to choose one plot from each vertical column and mark them on the diagram below, and describe your method of selection: Describe the method of selection, and comment on the resulting selection:

4 Method #4: Stratified Sample Consider the field as grouped in horizontal rows (called strata). Use your calculator or a random number table to choose one plot from each horizontal row and mark them on the diagram below, and describe your method of selection: Describe the method of selection, and comment on the resulting selection: You have looked at four methods of choosing plots. Is there a reason, other than convenience, to choose one method over another? Explain

5 OK, the crop is now ready. Below is a diagram with the yield per plot. Estimate the average yield per plot based on each of the four sampling techniques you have used, and fill out the table below Sampling Method Convenience Sample Simple Random Sample Vertical Strata Horizontal Strata Average Yield per plot Estimate of total yield What was the actual yield of the farmer s land? How did your estimates vary according to the different sampling methods you used, and how do they compare to the actual yield of the land?

6 Which sampling method should the farmer use, and why do you think it is more precise? Sampling Worksheet: Rolling Down the River Name: Part II The farmer was impressed with the results of your study and seeks to improve the yield of the field the following year. Believing that irrigation is the answer, the farmer installs an irrigation system taking water from the river. The following year s yield is below: Redo your sampling using the same methods as before, and complete the table and comments as before. Method #1: Convenience Sample The farmer began by selecting 10 plots that would be the easiest to harvest. They are marked on the diagram of the field below:

7 Method #2: Simple Random Sample (SRS) Use your calculator or a random number table to choose 10 plots to harvest. Mark them on the diagram below: Method #3: Stratified Sample Consider the field as grouped in vertical columns (called strata). Use your calculator or a random number table to choose one plot from each vertical column and mark them on the diagram below:

8 Method #4: Stratified Sample Consider the field as grouped in horizontal rows (called strata). Use your calculator or a random number table to choose one plot from each horizontal row and mark them on the diagram below: Sampling Method Convenience Sample Simple Random Sample Vertical Strata Horizontal Strata Average Yield per plot Estimate of total yield

9 Considering the table above, comment on the effectiveness of the irrigation.