Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000-foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet).

Based on information taken from Textbook of Medical Physiology by A. C. Guyton, M.D.)
Parts (a) and (b) relate to testing p. Part (c) requests the value of Se. Part (e) relates to confidence intervals for prediction. Part (f) relates to testing β.
Answers may vary due to rounding.
(a) Verify that ˆ‘x = 21.4, ˆ‘y = 132.8, ˆ‘x2 = 103.84, ˆ‘y2 = 4125.46, ˆ‘xy = 652.6, and r ‰ˆ 0.984.
(b) Use a 1% level of significance to test the claim that p > 0.
(c) Verify that Se ‰ˆ 2.5319, a ‰ˆ ˆ’2.869, and b ‰ˆ 6.876.
(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 4.0.
(e) Find a 90% confidence interval for y when x = 4.0.
(f) Use a 1% level of significance to test the claim that β > 0.

Transcribed Image Text:

2.1 (units: mm Hg/10) 13.9 (units: mm Hg/10) 6.7 5.1 4.2 3.3 43.6 32.9 26.2 16.2