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 taken from the reference by Professor E.A. Kay, University of Hawaii.

Reference: A Natural History of the Hawaiian Islands. edited by E. A. Kay. University of Hawaii Press.

(a) Verify that Σx = 492. Σy = 86.7. Σx² = 65.546. Σy² = 2030.55.

Σxy = 11351.9, and r = 0.93853.

(b) Use a 1% level of significance to test the claim ρ > 0.

(c) Verify that S_e ≈ 4.5759, a ≈ 1.1405 and b ≈ 0.1646

(d) Find the predicted distance (km/100) when a drift bottle has been floating for 90 days.

(e) Find a 90% confidence interval for your prediction of part (d).

(f) Use a I % level of significance to test the claim that β > 0.

(g) Find a 95% confidence interval for (3 and interpret its meaning in terms of drift rate.

(h) Consider the following scenario. A sailboat had an accident and radioed a Mayday alert with a given latitude and longitude just before it sank. The survivors are in a small (hut well provisioned) life raft drifting in the part of the Pacific Ocean under study. After 30 days, how far from the accident site should a rescue plane expect to look?

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x days y km/100 79 19.5 74 34 97 208 14.6 5.3 11.6 35.7