1st year business stats

[kinslayer]

(source data in attachment)

Question 7 of Lab 3: "Calculate some descriptive statistics to help you determine which of the following statements best describes the situation with respect to the coconut price received in Dili compared to outside of Dili."

The average price outside Dili is lower and also there are three farmers outside Dili who got higher prices than the max in Dili so my answer was: "on average prices received outside of Dili are lower, but a few farmers who sold their crops outside of Dili received prices higher than any of those who sold in Dili."

However the correct answer was: "You are more likely to sell your crops outside of Dili, but on average the price received is smaller."

Can someone explain this to me? There are more farmers in the data who sold outside Dili than in but how does that tell us that you're more likely to sell outside Dili than in? Also how is a correct statement the wrong answer? 

[bobbyz0r]

That question was asking which statement best describes the situation, not which statement is correct.

As a result, you have to decide which statement is more important in the grand scheme of things. Knowing that "on average prices received outside of Dili are lower, but a few farmers who sold their crops outside of Dili received prices higher than any of those who sold in Dili." will not give you as much representative information as knowing that "You are more likely to sell your crops outside of Dili, but on average the price received is smaller.".

[kinslayer]

I get that, but how does the data tell you that you're more likely to sell your crops outside of Dili? All I see is that a bunch more farmers from outside Dili were surveyed than inside it.

[Reckoner]

Think of the data as being in two groups, those who sell outside and and those who don't. The number of observations for outside is greater than those that aren't outside. So there is a greater than 50% chance that an individual sells outside. So of I randomly choose a farmer, I'll have a greater than 50% chance that they sell outside the city according to out sample. Don't use "greater than 50% chance", use whatever the actual proportion is.

So you're basically looking at Pr(that a farmer sells outside) vs Pr(not selling outside).   

[kinslayer]

So you're basically looking at Pr(that a farmer sells outside) vs Pr(not selling outside).   

The way I see it, this is not the right probability -- what we want is the conditional probability Pr(farmer sells | farmer is in Dili) vs Pr(farmer sells | farmer is outside Dili).

So we need to find Pr(farmer sells | farmer is in Dili) = Pr (farmer sells & farmer is in Dili) / Pr(farmer is in Dili) and same for outside.

The denominator we can estimate via the sample proportion but how do we get the numerator?

[Reckoner]

You're exactly right, but are over-complicating the question. Think of "selling" as setting up a stall, or simply being a farmer that wishes to sell. "What is the probability that a farmer is outside Dili and sells" has to be interpreted the same as "what is the probability that a farmer is outside Dili". We have to assume that all farmers sell. That is, only look at their location as a variable.   

When it says "more likely to sell outside of Dili", it's not referring to the success rate of the farmers in selling their produce, merely the fact that they try to sell.

What you're saying is more "useful" in that it tells us more information, but as you said we can't find the numerator as we have no data to obtain it unfortunately.

It can be very easy to read too much into some of the stuff you'll come across in this unit. Interpretation of the explanations and the assumptions that you have to make/are being made are very important. 

[kinslayer]

Thanks, that all makes sense, I guess I just needed to make sure I wasn't going crazy.

If the answer text included "farmers are more likely to sell" then everything makes much more sense, to me at least. "You're more likely to sell" makes it sound like it's talking about what your success rate would be if you sold inside vs. outside Dili which is a completely different idea.