PART A - highlight answers.

The correlation coefcient r is a sample statistic. What does it tell us about the value of the population correlation coefcient .9 (Greek letter rho]? You do not know how to build the formal structure of hypothesis tests of .0 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 i 0. We do this by comparing the value Irl to an entryr in the correlation table. The value of c: in the table gives us the probabilityr of concluding that p t 0 when, in fact, .0 = O and there is no population correlation. We have two choices form: a = 0.05 or a = 0.01. Cllhl lm {or Cnelditl (Initial: Jr n II = 0.05 II' = 0.01 n a = 9.05 or = 0.01 5 LOO LOCI 25 0.41 0.5 3 4 0.95 0.99 24 0.40 0.52 S 0.85 0.95 25 0.40 0.5 I E 0.81 0.92 26 0.39 0.50 3" 0.?5 0.8? 27 0.53 0.49 3 0.71 0.53 25 0.57 0.45- 9 0.6? 0.50 29 0.37 0.4? 10 0.6 3 0.76 3') 0.35 0.46 l l 0.60 0.?5 ru 0.53 0.?I (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 yalue of |r| large enough to conclude that lowest barometric pressure and wind speed ofa cyclone are correlated? Use a = 0.01. [Round your answer for rto four decimal places.) x 1994 91-3 992 935 992 939 n 40 mo 55 145 so 154 r: critical r|:| Conclusion C- RejeC' the null hypothesis, there is sufcient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. C- RejeC' the null hypothesis, there is insufcient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. C- Fail to reject the null hypothesis, there is insufcient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. C- Fail to reject the null hypothesis, there is sufcient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.