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)? You do not know how to build the formal structure of hypothesis tests of p yet. However, there is a quick way to determine if the sample evidence based on p 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 pe 0. We do this by comparing the value Iri to an entry in the correlation table. The value of a in the table gives us the probability of concluding that p0 when, in fact, p= 0 and there is no population correlation. We have two choices for a: a = 0.05 or a = 0.01. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Critkal Values for Correlation Coelidentr n 0.05 001 a 0.05 ea-0.05 0.01 001 1.00 1.00 13 0.53 068 23 041 095 0.99 0.53 14 0.53 0,66 0.88 0.96 24 0.40 0.52 15 as1 0.64 25 0.40 6 081 092 051 16 a50 0.61 26 0.39 0.50 0.75 0.87 17 0.48 0.61 27 071 0.83 18 0.47 0.49 9 0.59 28 0.57 0.48 0.67 0.80 19 0.46 0.58 29 0.37 0.47 10 0.63 0.76 20 0.44 0.56 30 0.36 0.46 11 0.60 075 21 043 0.55 12 0.58 0.71 22 0.42 0.54 (a) Look at the data below regarding the variables x age of a Shetland pony and y= weight of that pony. Is the value of Irl large enough to conclude that weight and age of Shetland ponies are correlated? Use a = 0.05. (Round your answer for r to four decimal places.) 12 24 16 Y 60 95 140 182 172 n USE SALT critical r Conclusion • Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. O Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. (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 Irl large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use a = 0.01. (Round your answer for r to four decimal places.) X 1004 930 149 975 992 935 145 982 75 y 40 100 65 critical r Conclusion • Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.