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8. [-/0.39 Points] DETAILS BBUNDERSTAT12 9.1.021.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The correlation coefficient ris 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 rto determine if p # 0. We do this by comparing the value In to an entry in the correlation table. The value of o 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 of: ox = 0.05 or ox = 0.01. Critical Values for Correlation Coefficient r n & = 0.05 = 0.01 n a = 0.05 a = 0.01 n ex = 0.05 a = 0.01 1.00 1.00 13 0.53 0.68 0.41 0.53 0.95 0.99 14 0.53 0.66 0.4 0.52 0.88 0.96 15 0.51 0.64 0.40 0.51 0.81 0.92 16 0.50 0.61 0.30 0.50 7 0,75 0.87 17 0.48 0.61 0.31 0.49 8 0.7 0.83 18 0.47 0.59 28 0.37 0.48 9 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 0.73 21 0.43 0.55 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 Il large enough to conclude that weight and age of Shetland ponies are correlated? Use ox = 0.05. (Round your answer for / to four decimal places.) 3 6 12 20 20 60 95 140 182 188 LA USE SALT critical r Conclusion O 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. 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 In large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use ox = 0.01. (Round your answer for /to four decimal places.) X 1004 975 992 935 986 930 40 100 65 145 68 155 critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. 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 Need Help? Read It Watch It
