The correlation coefficient r is a sample statistic.What does it tell us about the value of the population correlationcoefficient ρ (Greek letter rho)? You do not know how tobuild the formal structure of hypothesis tests of ρ yet.However, there is a quick way to determine if the sample evidencebased on ρ is strong enough to conclude that there is somepopulation correlation between the variables. In other words, wecan use the value of r to determine if ρ ≠ 0. Wedo this by comparing the value |r| to an entry in thecorrelation table. The value of α in the table gives usthe probability of concluding that ρ ≠ 0 when, in fact,ρ = 0 and there is no population correlation. We have twochoices for α: α = 0.05 or α = 0.01.

(a) Look at the data below regarding the variables x =age of a Shetland pony and y = weight of that pony. Is thevalue of |r| large enough to conclude that weight and ageof Shetland ponies are correlated? Use α = 0.05. (Use 3decimal places.)

x	3	6	12	19	23
y	60	95	140	184	184

r
critical r

(b) Look at the data below 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 windspeed of a cyclone are correlated? Use α = 0.01. (Use 3decimal places.)

x	1004	975	992	935	978	940
y	40	100	65	145	75	155

r
critical r