1) A method that will produce a random sample of 10 plants from a total of 5,000 spinach plants is the systematic sampling method.
This is because the systematic sampling method allows for the selection of individual items at a regular interval from amongst the entire batch of plants.
Generally, if you need a sample size n from a population of size x, using the systematic sampling method, you should select every (x/n)th individual item for the sample.
Thus, to produce a random sample of 10 plants from a total of 5,000 spinach plants, the systematic sampling method lets us selects every (5000/10)th plant as part of the sample that we want.
Thus, we will select the 500th, 1000th, 1500th, 2000th, 2500th, 3000th..., 5000th plants to make up the random sample of 10 plants, from the total 5,000 spinach plants on the farm.
2) A random sample would be useful in this situation for majorly two reasons:
- It eliminates bias in the selection of plants to be tested
- it simplifies the task of selecting the plants t be tested