Question

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 78 79 38 94 207 y km/100 14.3 19.2 5.6 11.3 35.9 (a) Verify that Σx = 496, Σy = 86.3, Σx2 = 65,454, Σy2 = 2020.99, Σxy = 11338.5, and r ≈ 0.94513. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0. Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. Correct: Your answer is correct. (c) Verify that Se ≈ 4.3483, a ≈ 0.3050, and b ≈ 0.1709. Se a b (d) Find the predicted distance (km/100) when a drift bottle has been floating for 70 days. (Use 2 decimal places.) km/100 (e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.) lower limit km/100 upper limit km/100 (f) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0. Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is sufficient evidence that β > 0. Correct: Your answer is correct. (g) Find a 95% confidence interval for β and interpret its meaning in terms of drift rate. (Use 2 decimal places.) lower limit upper limit

Answer 1