What is the optimal time for a scuba diver to be on the bottomof the ocean? That depends on the depth of the dive. The U.S. Navyhas done a lot of research on this topic. The Navy defines the\"optimal time\" to be the time at each depth for the best balancebetween length of work period and decompression time aftersurfacing. Let x = depth of dive in meters, and lety = optimal time in hours. A random sample of divers gavethe following data.
| x | 14.1 | 24.3 | 28.2 | 38.3 | 51.3 | 20.5 | 22.7 |
| y | 2.58 | 2.28 | 1.58 | 1.03 | 0.75 | 2.38 | 2.20 |
(a) Find Σx, Σy, Σx2,Σy2, Σxy, and r. (Roundr to three decimal places.)
| Σx = | |
| Σy = | |
| Σx2 = | |
| Σy2 = | |
| Σxy = | |
| r = | |
(c) Find a, and b. (Round your answers to fourdecimal places.)
(d) Find the predicted optimal time in hours for a dive depth ofx = 30 meters. (Round your answer to two decimalplaces.)
hr
(f) Use a 1% level of significance to test the claim thatβ < 0. (Round your answers to two decimal places.) Hint1: The standard error of b is 0.007058. Hint 2: Your answers to thet and critical t should have the same sign.
Conclusion
Fail to reject the null hypothesis. There is insufficientevidence that β < 0.
Reject the null hypothesis. There is insufficient evidence thatβ < 0.
Fail to reject the null hypothesis. There is sufficient evidencethat β < 0.
Reject the null hypothesis. There is sufficient evidence thatβ < 0.
