Ocean currents are important in studies of climate change, aswell as ecology studies of dispersal of plankton. Drift bottles areused to study ocean currents in the Pacific near Hawaii, theSolomon Islands, New Guinea, and other islands. Let xrepresent the number of days to recovery of a drift bottle afterrelease and y represent the distance from point of releaseto point of recovery in km/100. The following data arerepresentative of one study using drift bottles to study oceancurrents.

x days	72	76	32	93	207
ykm/100	14.8	19.1	5.3	11.8	35.7

(a) Verify that

?x = 480,

?y = 86.7,

?x² = 63,482,

?y² = 2025.67,

?xy = 11174.1,

and

r ? 0.94564.

?x
?y
?x2
?y2
?xy
r

(b) Use a 1% level of significance to test the claim

? > 0.

(Use 2 decimal places.)

t
critical t

Conclusion

(c) Verify that

S_e ? 4.2911,

a ? 1.6127,

and

b ? 0.1638.

Se
a
b

(d) Find the predicted distance (km/100) when a drift bottle hasbeen floating for 60 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

? > 0.

(Use 2 decimal places.)

t
critical t

(g) Find a 95% confidence interval for ? and interpret itsmeaning in terms of drift rate. (Use 2 decimal places.)

Lower limit=

Upper limit=

(h) Consider the following scenario. A sailboat had an accidentand radioed a Mayday alert with a given latitude and longitude justbefore 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 planeexpect to look? (Use 2 decimal places.)
= km/100