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. 26.3 x 15.1 38.3 51.3 20.5 22.7 y 2.48 2.38 1.68 1.03 0.75 2.38 2.20 32.2 (a) Find Ex, Ey, Ex², zy2, Exy, and r. (Round r to three decimal places.) Ex-206.4 y = 12.9 Ex2=6990.66 22-26.765 Exy= 300.792 r= -0.9528 (b) Use a 1% level of significance to test the claim that < 0. (Round your answers to two decimal places.) = -7.0141 critical t= Conclusion Fail to reject the null hypothesis. There is sufficient evidence that < 0. Reject the null hypothesis. There is insufficient evidence that < 0. Fail to reject the null hypothesis. There is insufficient evidence that < 0. o Reject the null hypothesis. There is sufficient evidence that < 0. (c) Find Sea, and b. (Round your answers to five decimal places.) Se- 0.23496 x b= (d) Find the predicted optimal time in hours for a dive depth of x = 34 meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval for y when x 34 meters. (Round your answers to two decimal places.) lower limit hr hr upper limit (f) Use a 1% level of significance to test the claim that < 0. (Round your answers to two decimal places.) critical t= Conclusion o Reject the null hypothesis. There is sufficient evidence that < 0. Fail to reject the null hypothesis. There is insufficient evidence that < 0. Fail to reject the null hypothesis. There is sufficient evidence that < 0. Reject the null hypothesis. There is insufficient evidence that < 0. (9) Find a 90% confidence interval for 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 decreases by an amount that falls within the confidence interval. 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 increases 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. Need Help? Wach

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. 26.3 x 15.1 38.3 51.3 20.5 22.7 y 2.48 2.38 1.68 1.03 0.75 2.38 2.20 32.2 (a) Find Ex, Ey, Ex², zy2, Exy, and r. (Round r to three decimal places.) Ex-206.4 y = 12.9 Ex2=6990.66 22-26.765 Exy= 300.792 r= -0.9528 (b) Use a 1% level of significance to test the claim that < 0. (Round your answers to two decimal places.) = -7.0141 critical t= Conclusion Fail to reject the null hypothesis. There is sufficient evidence that < 0. Reject the null hypothesis. There is insufficient evidence that < 0. Fail to reject the null hypothesis. There is insufficient evidence that < 0. o Reject the null hypothesis. There is sufficient evidence that < 0. (c) Find Sea, and b. (Round your answers to five decimal places.) Se- 0.23496 x b= (d) Find the predicted optimal time in hours for a dive depth of x = 34 meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval for y when x 34 meters. (Round your answers to two decimal places.) lower limit hr hr upper limit (f) Use a 1% level of significance to test the claim that < 0. (Round your answers to two decimal places.) critical t= Conclusion o Reject the null hypothesis. There is sufficient evidence that < 0. Fail to reject the null hypothesis. There is insufficient evidence that < 0. Fail to reject the null hypothesis. There is sufficient evidence that < 0. Reject the null hypothesis. There is insufficient evidence that < 0. (9) Find a 90% confidence interval for 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 decreases by an amount that falls within the confidence interval. 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 increases 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. Need Help? Wach

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks