Hypothesis testing
In the previous chapter, we introduced hypothesis testing as a means to quantify the probability that a given hypothesis (such as that the two samples were from a single population) is true. We will use the same process to quantify the probability that a correlation exists in the wider population based on our sample.
First, we must formulate two hypotheses, a null hypothesis and an alternate hypothesis:
H0 is the hypothesis that the population correlation is zero. In other words, our conservative view is that the measured correlation is purely due to chance sampling error.
H1 is the alternative possibility that the population correlation is not zero. Notice that we don't specify the direction of the correlation, only that there is one. This means we are performing a two-tailed test.
The standard error of the sample r is given by:
This formula is only accurate when 
is close to zero (recall that the magnitude of r influences our confidence), but fortunately, this is exactly...
