The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient p (Greek letter rho)? We will build the formal structure of hypothesis tests of p in Section 11.4. 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 p ≠ 0. We do this by comparing the value | r | to an entry in Table 4-6. The value of α in the table gives us the probability of concluding that p ≠ 0 when, in fact, p = 0 and there is no population correlation. We have two choices for α: α = 0.05 and α = 0.01.
(a) Look at Problem 13 regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of | r | large enough to conclude that weight and age of Shetland ponies are correlated? Use α = 0.05.
(b) Look at Problem 15 regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of | r | large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use α = 0.01.