Concept explainers
Pollution monitoring Suppose that the presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wants to estimate the area of algae growth. Group members measure across the algae growth (see Figure 13.35) and obtain the data (in feet) in the table.
x | Width w | x | Width w |
0 | 0 | 50 | 27 |
10 | 15 | 60 | 24 |
20 | 18 | 70 | 23 |
30 | 18 | 80 | 0 |
40 | 30 |
(a) Can either the Trapezoidal Rule or Simpson's Rule be used to calculate the area of the algae growth?
(b) When either the Trapezoidal Rule or Simpsons Rule can he used, which is usually more accurate?
(c) Use Simpsons Rule to approximate the area of the algae growth.
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Chapter 13 Solutions
WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term
- Using your graphing calculator, make a scatter plot of the data from the table. Then graph your model from Question 2 along with the data. How well does your model fit the data? What could you do to try to improve your model?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_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 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…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 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 >…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 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_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 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_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, Ex = 61,451, Ey = 2033.69, Exy = 10995.7, and r 0.93868. %3D %3D %3D %3D Σχ 1 473 ΣΥ| 86.7 Ex2 61451 Ey2 2033.69 Exy 10995.7 r0.93868 (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) t 4.72 critical t 4.54 Conclusion 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…arrow_forwardThe following table shows the mass of an object recorded over time. Time (min) Mass (g) 15 44 20 36 23 22 42 19 47 18 (a) Make a scatter plot of the data in the grid below.arrow_forward
- A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia = 63.3 yr. 1 X,=65.2 yr. 2 o, = 9.1 yr. = 7.3 yr. n1 = 120 = 150arrow_forwardPls show work so I can understandarrow_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. Σx = 476, Σy = 87.1, Σx2 = 62,290, Σy2 = 2046.87, Σxy = 11121.3,and r ≈ 0.94367. x days 72 76 32 91 205y km/100 14.7 19.6 5.3 11.7 35.8 a) Use a 1% level of significance to test the claim ? > 0.(Use 2 decimal places.)t =critical t= b) Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2 decimal places.)________ km/100 c) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)lower limit = _____…arrow_forward
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