Alright! Let's imagine the farmer's land as a huge pizza, with the western fields being on one half, and the eastern fields being on the other half. Imagine the crops are like the toppings scattered across this pizza.
Now, when the farmer takes a random sample of 12 crops from the western fields, it's like picking 12 toppings from the left half of the pizza. Similarly, taking a sample of 12 crops from the eastern fields is like picking 12 toppings from the right half of the pizza.
Now, let's talk about the term "independent". When we say that two samples are independent, we mean that picking items from one sample doesn't affect what might be picked in the other sample. Imagine if you had a bag of red marbles and a bag of blue marbles. If you pick some red marbles, it doesn’t change what's in the bag of blue marbles. They're independent.
Back to the pizza analogy: since the western and eastern fields are two separate halves of the land (like two halves of the pizza), picking crops from the western fields doesn't affect the crops in the eastern fields, and vice versa. They are like two separate bags of marbles.
This is why we can say that the samples the farmer takes from the western and eastern fields are independent. It’s because the health or the state of the crops in the western fields doesn’t change what’s going on with the crops in the eastern fields, and picking 12 crops from one side doesn't change what you could pick from the other side. The two groups of crops are doing their own thing, like dancers in two separate dance studios.
In summary, when the farmer takes 12 crops from the western fields and 12 crops from the eastern fields, these samples are considered independent because what happens in one field doesn’t mess with what happens in the other field. They are like two separate pizzas with their own toppings, or like two bags of marbles minding their own business.