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. Letxrepresent the number of days to recovery of a drift bottle after release andyrepresent 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. xdays= 72, 74, 32, 97, 206 ykm/100=14.2, 19.5, 5.1, 11.2, 35.8

x=481,

y=85.8,

x²=63,529,

y²=2014.98,

xy=11089.8,

andr0.92670.

S_e5.0542,

a1.3513,

andb0.1643.

Find the predicted distance (km/100) when a drift bottle has been floating for60days. (Use 2 decimal places.)

=11.21km/100

(a) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)

lower limit=

upper limit=

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

(Use 2 decimal places.)

t=

criticalt=

(c) Find a 95% confidence interval forand interpret its meaning in terms of drift rate. (Use 2 decimal places.)

lower limit=

upper limit=

(d) 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. After20days,how far from the accident site should a rescue plane expect to look? (Use 2 decimal places.)