Understanding the Variability of a Point Estimate

Suppose the proportion of American adults who support the expansion of solar energy is p = 0.88, which is our parameter of interest.2 If we were to take a poll of 1000 American adults on this topic, the estimate would not be perfect, but how close might we expect the sample proportion in the poll would be to 88%? We want to understand, how does the sample proportion p̂ behave when the true population proportion is 0.88.3 Let’s find out! We can simulate responses we would get from a simple random sample of 1000 American adults, which is only possible because we know the actual support for expanding solar energy is 0.88. Here’s how we might go about constructing such a simulation:

1. There were about 250 million American adults in 2018. On 250 million pieces of paper, write “support” on 88% of them and “not” on the other 12%.

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2. Mix up the pieces of paper and pull out 1000 pieces to represent our sample of 1000 American adults.

3. Compute the fraction of the sample that say “support”.

Any volunteers to conduct this simulation? Probably not. Running this simulation with 250 million pieces of paper would be time-consuming and very costly, but we can simulate it using computer

1Not to be confused with phat, the slang term used for something cool, like this book. 2We haven’t actually conducted a census to measure this value perfectly. However, a very large sample has

suggested the actual level of support is about 88%. 388% written as a proportion would be 0.88. It is common to switch between proportion and percent. However,

formulas presented in this book always refer to the proportion, not the percent.

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