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 4.9 4.2 3.3 2.1 (units: mm Hg/10) Y42.2 31.7 26.2 16.2 13.9 (units: mm Hg/10) (a) Verify that Ex = 21.2, Ey = 130.2, Ex? = 101.84, Ey² = 3927.82, Exy = 630.76, and r= 0.982. Ex Ey Ly2 Exy (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is sufficient evidence that p > 0. (c) Verify that S, = 2.5193, a = -1.883, and b = 6.586. a b.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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).
(units: mm Hg/10)
(units: mm Hg/10)
х 6.7
4.9
4.2
3.3
2.1
42.2
31.7
26.2
16.2
13.9
(a) Verify that Ex = 21.2, Ey = 130.2, Ex? = 101.84, Ey? = 3927.82, Exy = 630.76, and r= 0.982.
Ex
Ey
Ex?
Ey2
Exy
(b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.)
critical t
Conclusion
O Reject the null hypothesis, there is sufficient evidence that p > 0.
O Reject the null hypothesis, there is insufficient evidence that p > 0.
Fail to reject the null hypothesis, there is insufficient evidence that p > 0.
O Fail to reject the null hypothesis, there is sufficient evidence that p > 0.
(c) Verify that S, 2.5193, a = -1.883, and b= 6.586.
S.
a
b
(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 4.7. (Use 2
decimal places.)
(e) Find a 99% confidence interval for y when x = 4.7. (Use 1 decimal place.)
lower limit
upper limit
(f) Use a 10% level of significance to test the claim that B> 0. (Use 2 decimal places.)
t
critical t
Conclusion
O Reject the null hypothesis, there is sufficient evidence that > 0.
O Reject the null hypothesis, there is insufficient evidence that B > 0.
O Fail to reject the null hypothesis, there is insufficient evidence that 6 > 0.
Fail to reject the null hypothesis, there is sufficient evidence that B > 0.
(g) Find a 99% confidence interval for ß and interpret its meaning. (Use 2 decimal places.)
lower limit
upper limit
Interpretation
O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure
oxygen increases by an amount that falls outside the confidence interval.
O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure
oxygen increases by an amount that falls within the confidence interval.
O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure
oxygen decreases by an amount that falls outside the confidence interval.
O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure
oxygen decreases by an amount that falls within the confidence interval.
Transcribed Image Text: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). (units: mm Hg/10) (units: mm Hg/10) х 6.7 4.9 4.2 3.3 2.1 42.2 31.7 26.2 16.2 13.9 (a) Verify that Ex = 21.2, Ey = 130.2, Ex? = 101.84, Ey? = 3927.82, Exy = 630.76, and r= 0.982. Ex Ey Ex? Ey2 Exy (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is sufficient evidence that p > 0. (c) Verify that S, 2.5193, a = -1.883, and b= 6.586. S. a b (d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 4.7. (Use 2 decimal places.) (e) Find a 99% confidence interval for y when x = 4.7. (Use 1 decimal place.) lower limit upper limit (f) Use a 10% level of significance to test the claim that B> 0. (Use 2 decimal places.) t critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that > 0. O Reject the null hypothesis, there is insufficient evidence that B > 0. O Fail to reject the null hypothesis, there is insufficient evidence that 6 > 0. Fail to reject the null hypothesis, there is sufficient evidence that B > 0. (g) Find a 99% confidence interval for ß and interpret its meaning. (Use 2 decimal places.) lower limit upper limit Interpretation O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen increases by an amount that falls outside the confidence interval. O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen increases by an amount that falls within the confidence interval. O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen decreases by an amount that falls outside the confidence interval. O For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen decreases by an amount that falls within the confidence interval.
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