Aviation and high-altitude physiology is a specialty in the study of medicine. L

Question

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).

(a) Find ?x, ?y, ?x2, ?y2, ?xy, and r. (Round r to three decimal places.)

(b) Use a 1% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

(c) Find Se, a, and b. (Round your answers to four decimal places.)

(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 5.0. (Round your answer to two decimal places.)
mm Hg/10

(e) Find a 90% confidence interval for y when x = 5.0. (Round your answers to one decimal place.)

(f) Use a 1% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

x 6.9 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)

Explanation / Answer

(a) Find ?x, ?y, ?x2, ?y2, ?xy, and r. (Round r to three decimal places.)

(b) Use a 1% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

(c) Find Se, a, and b. (Round your answers to four decimal places.)

2.49902

(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 5.0. (Round your answer to two decimal places.)
mm Hg/10

y^= -2.01304 + 6.61413 *x

= -2.01304 + 6.61413 *5

=  31.05761

SUMMARY OUTPUT Regression Statistics Multiple R 0.984218031 R Square 0.968685132 Adjusted R Square 0.958246843 Standard Error 2.499028797 Observations 5 ANOVA df SS MS F Significance F Regression 1 579.5565652 579.5565652 92.80113944 0.002374351 Residual 3 18.73543478 6.245144928 Total 4 598.292 Coefficients Standard Error t Stat P-value Lower 95% Intercept -2.013043478 3.169627343 -0.63510415 0.570489035 -12.1002123 x 6.614130435 0.68658783 9.633334803 0.002374351 4.429101533

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