(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 that 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 < 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ < 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ < 0. (c) Find Se, a, and b. (Round your answers to four decimal places.) Se = a = b =
(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 that 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 < 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ < 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ < 0. (c) Find Se, a, and b. (Round your answers to four decimal places.) Se = a = b =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
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.
| x | 13.1 | 23.3 | 31.2 | 38.3 | 51.3 | 20.5 | 22.7 |
| y | 2.78 | 2.18 | 1.48 | 1.03 | 0.75 | 2.38 | 2.20 |
(a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.)
(b) Use a 1% level of significance to test the claim that ρ < 0. (Round your answers to two decimal places.)
Conclusion
(c) Find Se, a, and b. (Round your answers to four decimal places.)
(d) Find the predicted optimal time in hours for a dive depth of x = 24 meters. (Round your answer to two decimal places.)
hr
(e) Find an 80% confidence interval for y when x = 24 meters. (Round your answers to two decimal places.)
(f) Use a 1% level of significance to test the claim that β < 0. (Round your answers to two decimal places.)
Conclusion
| Σx = | |
| Σy = | |
| Σx2 = | |
| Σy2 = | |
| Σxy = | |
| r = |
(b) Use a 1% level of significance to test the claim that 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 < 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ < 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ < 0.
(c) Find Se, a, and b. (Round your answers to four decimal places.)
| Se = | |
| a = | |
| b = |
(d) Find the predicted optimal time in hours for a dive depth of x = 24 meters. (Round your answer to two decimal places.)
hr
(e) Find an 80% confidence interval for y when x = 24 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 β < 0. (Round your answers to two decimal places.)
| t = | |
| critical t = |
Conclusion
Reject the null hypothesis. There is insufficient evidence that β < 0.Fail to reject the null hypothesis. There is insufficient evidence that β < 0. Reject the null hypothesis. There is sufficient evidence that β < 0.Fail to reject the null hypothesis. There is sufficient evidence that β < 0.
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