So, we have estimated that the true population mean is about 65.2; we know the population mean isn't exactly 65.19704—but by just how much might our estimate be off?
To answer this question, let's take repeated samples from the population again. This time, we're going to take samples of size 40 from the population 10,000 times and plot a frequency distribution of the means:
> means.of.our.samples <- numeric(10000)
> for(i in 1:10000){
+ a.sample <- sample(all.us.women, 40)
+ means.of.our.samples[i] <- mean(a.sample)
+ } We get the distribution as follows:
Figure 5.3: The sampling distribution of sample means
This frequency distribution is called a sampling distribution. In particular, as we used sample means as the value of interest, this is called the sampling distribution of the sample means (whew!). You can create a sampling distribution of any statistic (median, variance, and so on), but when we refer to sampling distributions throughout...