Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Textbook Question
Chapter 8.2, Problem 32E
Refer to Procedure 8.1.
- a. Explain in detail the assumptions required for using the z-interval procedure.
- b. How important is the normality assumption? Explain your answer.
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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 representative of one study using drift bottles to study ocean currents.
x days
76
79
36
95
207
y km/100
14.2
19.6
5.4
11.2
35.9
(a) Verify that
Σx = 493,
Σy = 86.3,
Σx2 = 65,187,
Σy2 = 2029.21,
Σxy = 11317.3,
and
r ≈ 0.93885.
Σx
Σy
Σx2
Σy2
Σxy
r
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Use 2 decimal places.)
t
critical t
(c) Verify that
Se ≈ 4.6183,
a ≈ 0.5575,
and
b ≈ 0.1694.
Se
a
b
Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2…
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 representative of one study using drift bottles to study ocean currents.
x days
74
77
34
96
208
y km/100
14.9
19.1
5.8
11.9
35.7
(a) Find
Σx,
Σy,
Σx2,
Σy2,
Σxy,
and
r.
(Round r to three decimal places.)
Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Round your answers to two decimal places.)
t =
critical t =
Conclusion
Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ >…
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 representative of one study using drift bottles to study ocean currents.
x days
75
79
35
91
203
y km/100
14.2
19.1
5.8
11.2
35.4
(a) Verify that
Σx = 483,
Σy = 85.7,
Σx2 = 62,581,
Σy2 = 1978.69,
Σxy = 10982.3,
and
r ≈ 0.94895.
Σx
Σy
Σx2
Σy2
Σxy
r
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Use 2 decimal places.)
t
critical t
(c) Verify that
Se ≈ 4.1118,
a ≈ 0.7378,
and
b ≈ 0.1698.
Se
a
b
Chapter 8 Solutions
Introductory Statistics (10th Edition)
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Ch. 8.1 - In each of Exercises 8.118.16, we provide a sample...Ch. 8.1 - Prob. 12ECh. 8.1 - In each of Exercises 8.118.16, we provide a sample...Ch. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Wedding Costs. According to Brides Magazine,...Ch. 8.1 - Cottonmouth Litter Size. In the article The...Ch. 8.1 - Wedding Costs. Refer to Exercise 8.17. Assume that...Ch. 8.1 - Cottonmouth Litter Size. Refer to Exercise 8.18....Ch. 8.1 - Fuel Tank Capacity. Consumer Reports provides...Ch. 8.1 - Home Improvements. The American Express Retail...Ch. 8.1 - Giant Tarantulas. A tarantula has two body parts....Ch. 8.1 - Serum Cholesterol Levels. In formation on serum...Ch. 8.1 - Prob. 25ECh. 8.1 - New Mobile Homes. Refer to Examples 8.1 and 8.2....Ch. 8.2 - Find the confidence level and for a. a 90%...Ch. 8.2 - Find the confidence level and for a. an 85%...Ch. 8.2 - What is meant by saying that a 1 confidence...Ch. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Refer to Procedure 8.1. a. 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- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardOcean 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 representative of one study using drift bottles to study ocean currents. x days 75 79 35 91 203 y km/100 14.2 19.1 5.8 11.2 35.4 (d) Find the predicted distance (km/100) when a drift bottle has been floating for 80 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 β > 0. (Use 2 decimal places.) t critical t (g) Find a 95% confidence interval for β and interpret…arrow_forward
- 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 representative of one study using drift bottles to study ocean currents. 203 x days y km/100 72 76 32 14.7 94 11.7 19.5 5.3 35.6 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 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 claim p> 0. (Use 2 decimal places.) critical t Conclusion Reject 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…arrow_forwardQ22arrow_forwardWhich of the following is not one of the uses of a scatter plot and regression line a. to estimate the average y at a specific value of x. b. All three are uses of the scatterplot and regression line c. to determine if a change in x causes a change in y d. to predict y at a specific value of x.arrow_forward
- 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 representative of one study using drift bottles to study ocean currents. x days y km/100 74 75 34 92 203 14.9 19.5 5.4 11.9 35.8 (a) Verify that Ex = 478, Ey = 87.5, Ex2 - 61,930, Ey? = 2054.67, Exy = 11110.9, and r- 0.94201. Ex £y Ex? Ey²[ Exy (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject the null hypothesis, there is insufficient evidence that p > 0.…arrow_forwardOcean 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 representative of one study using drift bottles to study ocean currents. x days y km/100 71 76 31 92 203 14.2 19.6 5.8 11.2 35.9 (a) Verify that Ex = 473, Ey = 86.7, Ex² = 61,451, Ey? 2033.69, Exy = 10995.7, and r 0.93868. %3D %3D %3D %3D %3D Σχ Ey Ex? Ey2 Σχy (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) critical t Conclusion Reject 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…arrow_forwardOcean 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 representative of one study using drift bottles to study ocean currents. x days y km/100 72 14.7 203 35.6 76 32 5.3 94 19.5 11.7 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey? = 2028.68, Exy = 11036.6, and r= 0.93853. Ex 477 Ey 86.8 Ex2 62029 Ey2 2028.68 Exy 11036.6 r 0.93853 (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) t 8.15 critical t 4.54 Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p> 0. O Fail to reject the null…arrow_forward
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