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What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y optimal time in hours. A random sample of divers gave the following data. 51.3 20.5 22.7 2.20 26.3 32.2 12.1 2.48 38.3 1.98 1.68 1.03 0.75 2.38 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Round r to three decimal places.) Ex = 203.4 Ey = 12.5 Ex2- 6909.06 Ey2 = 25.021 Syy = 312.832

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y optimal time in hours. A random sample of divers gave the following data. 51.3 20.5 22.7 2.20 26.3 32.2 12.1 2.48 38.3 1.98 1.68 1.03 0.75 2.38 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Round r to three decimal places.) Ex = 203.4 Ey = 12.5 Ex2- 6909.06 Ey2 = 25.021 Syy = 312.832

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 20.5 22.7 12.1 26.3 32.2 38.3 51.3 y 2.48 1.98 1.68 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex2, Ey2, Exy, and r. (Round r to three decimal places.) Ex = 203.4 Ey = 12.5 Ex2 = 6909.06 Ey2 = 25.021 Exy = 312.832 r= -0.970 (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t= -8.92 critical t= -3.37 Conclusion O Reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient 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) Find S, a, and b. (Round your answers to five decimal places.) S. 0.17790 a = 3.25138 -0.05044 (d) Find the predicted optimal time in hours for a dive depth of x = 27 meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval for y when x = 27 meters. (Round your answers to two decimal places.) lower limit hr upper limit hr (f) Use a 1% level of significance to test the claim that < 0. (Round your answers to two decimal places.) t= critical t Conclusion O Reject the null hypothesis. There is sufficient evidence that B < 0. O Reject the null hypothesis. There is insufficient evidence that ß < 0. O Fail to reject the null hypothesis. There is sufficient evidence that 6 < 0. O Fail to reject the null hypothesis. There is insufficient evidence that ß < 0. (g) Find a 90% confidence interval for ß and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation O For a 1 meter increase in depth, the optimal time increases by an amount that falls within the confidence interval. O For a 1 meter increase in depth, the optimal time decreases by an amount that falls outside the confidence interval. For a 1 meter increase in depth, the optimal time decreases by an amount that falls within the confidence interval. For a 1 meter increase in depth, the optimal time increases by an amount that falls outside the confidence interval.
Transcribed Image Text:What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 20.5 22.7 12.1 26.3 32.2 38.3 51.3 y 2.48 1.98 1.68 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex2, Ey2, Exy, and r. (Round r to three decimal places.) Ex = 203.4 Ey = 12.5 Ex2 = 6909.06 Ey2 = 25.021 Exy = 312.832 r= -0.970 (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t= -8.92 critical t= -3.37 Conclusion O Reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient 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) Find S, a, and b. (Round your answers to five decimal places.) S. 0.17790 a = 3.25138 -0.05044 (d) Find the predicted optimal time in hours for a dive depth of x = 27 meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval for y when x = 27 meters. (Round your answers to two decimal places.) lower limit hr upper limit hr (f) Use a 1% level of significance to test the claim that < 0. (Round your answers to two decimal places.) t= critical t Conclusion O Reject the null hypothesis. There is sufficient evidence that B < 0. O Reject the null hypothesis. There is insufficient evidence that ß < 0. O Fail to reject the null hypothesis. There is sufficient evidence that 6 < 0. O Fail to reject the null hypothesis. There is insufficient evidence that ß < 0. (g) Find a 90% confidence interval for ß and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation O For a 1 meter increase in depth, the optimal time increases by an amount that falls within the confidence interval. O For a 1 meter increase in depth, the optimal time decreases by an amount that falls outside the confidence interval. For a 1 meter increase in depth, the optimal time decreases by an amount that falls within the confidence interval. For a 1 meter increase in depth, the optimal time increases by an amount that falls outside the confidence interval.
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