Chapter 11.4, Problem 10P

In Problems 7-12, parts (a) and (b) relate to testing $\rho$. Part (c) requests the value of $S_e$. Parts (d) and (c) relate to confidence intervals for prediction. Part (f) relates to testing $\beta$.

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

(Based on information taken from Textbook of Medical Physiology by A. C. Guyton, M.D.)

(a) Verify that $\begin{array}{l}{\displaystyle \sum x}=21.4,{\displaystyle \sum y}=132.8,{\displaystyle \sum x^2}=103.84,{\displaystyle \sum y^2}=4125.46,\hfill \\ {\displaystyle \sum xy}=652.6,\text{ and }r \approx \mathrm{0.984.}\hfill \end{array}$

(b) Use a 1% level of significance to test the claim that $\rho >0$.

(c) Verify that $S_e \approx 2.5319,a\approx -2.869,\text{ and }b\approx 6.876$.

(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 $\beta >0$.