Over the last couple of days, for a sample size n=5 and n=50

• Took many, many, many samples of size n
• Computed the sample mean height \(\overline{x}\)
• Studied the variability/uncertainty of the 10,000 simulated \(\overline{x}\), as quantified by the standard error.

i.e. an expanded version of this

However, we know the true population mean height \(\mu\): the average of the 60K OkCupid user heights.

Why? Because we have access to the entire population:

mean(profiles$height)

## [1] 68.29528

• Question: If we know the true population mean height \(\mu = 68.30\), then why are we sampling?
• Answer: Only as a theoretical/rhetorical exercise to show the random behavior of \(\overline{x}\).
• In Practice: If you know the true value, then you don't need sampling.
• 

Now, let's suppose we didn't know the true value \(\mu\), so we needed to estimate it using

• A sample of size \(n\)
• A point estimate. For example the sample mean \(\overline{x}\)
• A confidence interval

• Question: Why did we take 10000 samples of size n=5 or n=50 and compute 10000 sample means \(\overline{x}\)?
• Answer: Only as a theoretical/rhetorical exercise to show the random behavior of \(\overline{x}\).
• In Practice: You only take one sample of size as large as you afford.

Tough concept to teach