Chapter 9.3, Problem 11P

In Problems 7–12, parts (a) and (b) relate to testing ρ. Part (c) requests the value of S_e. Parts (d) and (e) relate to confidence intervals for prediction. Parts (f) and (g) relate to testing β and finding confidence intervals for β.

Answers may vary due to rounding.

11. Oceanography: Drift Rates 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.

1. (a) Verify that ∑x = 492, ∑y = 86.7, ∑x² = 65,546, ∑y² = 2030.55, ∑xy = 11351.9, and r ≈ 0.93853.
2. (b) Use a 1% level of significance to test the claim ρ > 0.
3. (c) Verify that S_e ≈ 4.5759, a ≈ 1.1405, and b ≈ 0.1646
4. (d) Find the predicted distance (km/100) when a drift bottle has been floating for 90 days.
5. (e) Find a 90% confidence interval for your prediction of part (d).
6. (f) Use a 1% level of significance to test the claim that β > 0.
7. (g) Find a 95% confidence interval for β and interpret its meaning in terms of drift rate.
8. (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 (but 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?