Expand Your Knowledge: Using a Table to Test r The

Chapter , Problem 19

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Expand Your Knowledge: Using a Table to Test \(\rho\) The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient \(\rho\) (Greek letter rho)? We will build the formal structure of hypothesis tests of r in Section 10.3. However, there is a quick way to determine if the sample evidence based on r is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if \(\rho\ \neq\  0\). We do this by comparing the value |r| to an entry in Table 10-6. The value of \(\alpha\) in the table gives us the probability of concluding that \(\rho\ \neq\  0\) when, in fact, \(\rho = 0\) and there is no population correlation. We have two choices for \(\alpha\): \(\alpha = 0.05\) or \(\alpha =  0.01\).