Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles areused to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent thenumber of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery inkm/100. The following data are representative of one study using drift bottles to study ocean currents.203x daysy km/10072763214.79411.719.55.335.6(a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey2 = 2028.68, Exy = 11036.6, and r= 0.93853.ExEyEx?Ey2|Exy(b) Use a 1% level of significance to test the claim p 0. (Use 2 decimal places.)critical tConclusionReject the null hypothesis, there is sufficient evidence that p 0.Reject the null hypothesis, there is insufficient evidence that p 0.O Fail to reject the null hypothesis, there is insufficient evidence that p 0.O Fail to reject the null hypothesis, there is sufficient evidence that p 0.(c) Verify that S, 4.5528, a 1.4484, and b s 0.1668.Seab(d) Find the predicted distance (km/100) when a drift bottle has been floating for 90 days. (Use 2 decimal places.)|km/100(e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)lower limitkm/100upper limitkm/100(f) Use a 1% level of significance to test the claim that 6 0. (Use 2 decimal places.)critical tConclusionReject the null hypothesis, there is sufficient evidence that 8 0.O Reject the null hypothesis, there is insufficient evidence that ß 0.OFail to reject the null hypothesis, there is insufficient evidence that ß 0.OFail to reject the null hypothesis, there is sufficient evidence that ß 0.(g) Find a 95% confidence interval for ß and interpret its meaning in terms of drift rate. (Use 2 decimal places.)lower limitupper limitInterpretationO For every day of drift, the distance drifted decreases by an amount that falls within the confidence interval.O For every day of drift, the distance drifted decreases by an amount that falls outside the confidence interval.For every day of drift, the distance drifted increases by an amount that falls within the confidence interval.O For every day of drift, the distance drifted increases by an amount that falls outside the confidence interval.(h) Consider the following scenario. A sailboat had an accident and radioed a Mayday alert with a given latitude andlongitude just before it sank. The survivors are in a small (but well provisioned) life raft drifting in the part of the PacificOcean under study. After 50 days, how far from the accident site should a rescue plane expect to look? (Useplaces.)decimalkm/100

Question

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles areused to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent thenumber of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery inkm/100. The following data are representative of one study using drift bottles to study ocean currents.203x daysy km/10072763214.79411.719.55.335.6(a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey2 = 2028.68, Exy = 11036.6, and r= 0.93853.ExEyEx?Ey2|Exy(b) Use a 1% level of significance to test the claim p> 0. (Use 2 decimal places.)critical tConclusionReject the null hypothesis, there is sufficient evidence that p > 0.Reject the null hypothesis, there is insufficient evidence that p > 0.O Fail to reject the null hypothesis, there is insufficient evidence that p > 0.O Fail to reject the null hypothesis, there is sufficient evidence that p > 0.(c) Verify that S, 4.5528, a 1.4484, and b s 0.1668.Seab(d) Find the predicted distance (km/100) when a drift bottle has been floating for 90 days. (Use 2 decimal places.)|km/100(e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)lower limitkm/100upper limitkm/100(f) Use a 1% level of significance to test the claim that 6 > 0. (Use 2 decimal places.)critical tConclusionReject the null hypothesis, there is sufficient evidence that 8 > 0.O Reject the null hypothesis, there is insufficient evidence that ß > 0.OFail to reject the null hypothesis, there is insufficient evidence that ß > 0.OFail to reject the null hypothesis, there is sufficient evidence that ß > 0.(g) Find a 95% confidence interval for ß and interpret its meaning in terms of drift rate. (Use 2 decimal places.)lower limitupper limitInterpretationO For every day of drift, the distance drifted decreases by an amount that falls within the confidence interval.O For every day of drift, the distance drifted decreases by an amount that falls outside the confidence interval.For every day of drift, the distance drifted increases by an amount that falls within the confidence interval.O For every day of drift, the distance drifted increases by an amount that falls outside the confidence interval.(h) Consider the following scenario. A sailboat had an accident and radioed a Mayday alert with a given latitude andlongitude just before it sank. The survivors are in a small (but well provisioned) life raft drifting in the part of the PacificOcean under study. After 50 days, how far from the accident site should a rescue plane expect to look? (Useplaces.)decimalkm/100

Accepted Answer

a.
The provided information is

x days
y km/100
xy
x*x
y*y

72
14.7
1058.4
5184
216.09

76
19.5…

(a) Verify that Ex = 477, Ey = 86.8, Ex² = 62,029, Ey² = 2028.68, Exy = 11036.6, and r = 0.93853. Ex Ey Ex Ey2( Exy (b) Use a 1% level of significance to test the claimp > 0. (Use 2 decimal places.)