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 bestbalance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and lety = optimal time in hours. A random sample of divers gave the following data.20.52.3812.126.3xLY 2.4832.21.6838.351.322.71.981.030.752.20(a) Find Ex, Ey, Ex2, Ey2, Exy, and r. (Round r to three decimal places.)Ex = 203.4Ey = 12.5Ex2 = 312.382Ey2 = 6909.06Exy = 25.021(b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.)t =critical tConclusionO Reject the null hypothesis. There is insufficient evidence that p < 0.O Reject the null hypothesis. There is sufficient evidence that p < 0.OFail 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 Se a, and b. (Round your answers to five decimal places.)S = 0.177903.25138ab= 0.05044(d) Find the predicted optimal time in hours for a dive depth of x = 27 meters. (Round your answer to two decimalplaces.)hr(e) Find an 80% confidence interval for y when x = 27 meters. (Round your answers to two decimal places.)lower limithrupper limithr(f) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.)t=critical tConclusionReject the null hypothesis. There is sufficient evidence that p < 0.O Reject the null hypothesis. There is insufficient evidence that ß < 0.Fail to reject the null hypothesis. There is sufficient evidence that ß < 0.O Fail to reject the nll hypothesis. There is insufficient evidence that ß < 0.O(g) Find a 90% confidence interval for ß and interpret its meaning. (Round your answers to three decimal places.)lower limitupper limitInterpretationO For a 1 meter increase in depth, the optimal time increases by an amount that falls within the confidenceinterval.O For a 1 meter increase in depth, the optimal time decreases by an amount that falls outside the confidenceinterval.O For a 1 meter increase in depth, the optimal time decreases by an amount that falls within the confidenceinterval.O For a 1 meter increase in depth, the optimal time increases by an amount that falls outside the confidenceinterval.

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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