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. Letx represent the number of days to recovery of a drift bottle after release andy 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.
(a) Find
Σx,
Σy,
Σx2,
Σy2,
Σxy,
and
r.
(Round
r to three decimal places.)
Σx = |
|
Σy = |
|
Σx
2 = |
|
Σy
2 = |
|
Σxy = |
|
r = |
|
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Round your answers to two decimal places.)
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.
(c) Find
Se,
a,
and
b.
(Round your answers to four decimal places.)
(d) Find the predicted distance (km/100) when a drift bottle has been floating for 80 days. (Round your answer to two decimal places.)
km/100
(e) Find a 90% confidence interval for your prediction of part (d). (Round your answers to two decimal places.)
lower limit |
km/100 |
upper limit |
km/100 |
(f) Use a 1% level of significance to test the claim that
β > 0.
(Round your answers to two decimal places.)
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.