In: Statistics and Probability
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 | 6.9 | 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) |
(a) Find ?x, ?y, ?x2, ?y2, ?xy, and r. (Round r to three decimal places.)
?x = | |
?y = | |
?x2 = | |
?y2 = | |
?xy = | |
r = |
(b) Use a 1% level of significance to test the claim that
? > 0. (Round your answers to two decimal places.)
t = | |
critical t = |
(c) Find Se, a, and b. (Round
your answers to four decimal places.)
Se = | |
a = | |
b = |
(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.)
lower limit | mm Hg/10 |
upper limit | mm Hg/10 |
(f) Use a 1% level of significance to test the claim that
? > 0. (Round your answers to two decimal places.)
t = | |
critical t = |
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 |
(a) Find ?x, ?y, ?x2, ?y2, ?xy, and r. (Round r to three decimal places.)
x | y | x^2 | y^2 | xy |
6.9 | 43.6 | 47.61 | 1900.96 | 300.84 |
5.1 | 32.9 | 26.01 | 1082.41 | 167.79 |
4.2 | 26.2 | 17.64 | 686.44 | 110.04 |
3.3 | 16.2 | 10.89 | 262.44 | 53.46 |
2.1 | 13.9 | 4.41 | 193.21 | 29.19 |
21.6 | 132.8 | 106.56 | 4125.46 | 661.32 |
?x = 21.6 | |
?y = 132.8 | |
?x2 = 106.56 | |
?y2 = 4125.46 | |
?xy =661.32 | |
r = 0.9842 |
(b) Use a 1% level of significance to test the claim that ? > 0.
(Round your answers to two decimal places.)
t = 9.63 | |
critical t = | =T.INV(0.99,3) |
4.540702859 |
(c) Find Se, a, and b. (Round your answers to four decimal
places.)
Se = | |
a = -2.01304 | |
b = 6.61413 |
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