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).
x 7.5 4.8 4.2 3.3 2.1 (units: mm Hg/10)
y 44.8 31.5 26.2 16.2 13.9 (units: mm Hg/10)
(a) Verify that Σx = 21.9, Σy = 132.6, Σx2 = 112.23, Σy2 = 4141.38, Σxy = 679.89, and r ≈ 0.982.
(b) Use a 1% level of significance to test the claim that ρ > 0. (Use 2 decimal places.)
c) Verify that Se ≈ 2.7444, a ≈ -0.097, and b ≈ 6.077.
(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 4.1. (Use 2 decimal places.)
(e) Find a 99% confidence interval for y when x = 4.1. (Use 1 decimal place.)
(f) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.)
(g) Find a 99% confidence interval for β and interpret its meaning. (Use 2 decimal places.)