The correlation coefficientris a sample statistic. What does it tell us about the value of the population correlation coefficientp(Greek letter rho)? You do not know how to build the formal structure of hypothesis tests ofpyet. However, there is a quick way to determine if the sample evidence based onpis strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value ofrto determine ifp0. by comparing the value |r| to an entry in the correlation table. The value ofain the table gives us the probability of concluding thatp0 when, in fact,p= 0 and there is no population correlation. We have two choices fora:a= 0.05 ora= 0.01.

(a) Look at the data below regarding the variablesx= age of a Shetland pony andy= weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Usea= 0.05. (Round your answer forrto four decimal places.)x= 3, 6, 12, 19, 18 y= 60, 95, 140, 190, 190

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(b) Look at the data below regarding the variablesx= lowest barometric pressure as a cyclone approaches andy= 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? Usea= 0.01. (Round your answer forrto four decimal places.) x=1004, 975, 992, 935, 984, 934 y= 40, 100, 65, 145, 69, 145

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