Testing the mean of one sample

An illustrative and fairly common statistical hypothesis test is the one sample t-test. You use it when you have one sample and you want to test whether that sample likely came from a population by comparing the mean against the known population mean. For this test to work, you have to know the population mean.

In this example, we'll be using R's built-in precip dataset that contains precipitation data from 70 US cities, using the code given below:

   > head(precip) 
       Mobile      Juneau     Phoenix Little Rock Los Angeles  
         67.0        54.7         7.0        48.5        14.0  
      Sacramento  
         17.2 

Don't be fooled by the fact that there are city names in there—this is a regular old vector—it's just that the elements are labeled. We can directly take the mean of this vector, just like a normal one:

  > is.vector(precip) 
  [1] TRUE 
  > mean(precip) 
  [1] 34.88571

Let's pretend that we, somehow, know the mean precipitation of...