Question

In: Statistics and Probability

Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial...

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 =

Solutions

Expert Solution

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


Related Solutions

Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial...
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...
Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial...
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...
A person living at high altitude, where the partial pressure of oxygen is very low, would...
A person living at high altitude, where the partial pressure of oxygen is very low, would likely have high levels of __________ in their plasma which __________ the affinity of hemoglobin for oxygen. 2,3-DPG; increases                                          b. myoglobin; decreases                        c.    myoglobin; increases                                                         d. 2,3 DPG; decrease Increased calcium entry into vascular circular smooth muscle cells could be caused by increased ________ near the afferent arterioles supplying the glomerulus thus ________ the glomerular filtration rate....
Problem 7.1. Let f (x, y) = x4 − 3xy + 2y2. (a) Compute the partial...
Problem 7.1. Let f (x, y) = x4 − 3xy + 2y2. (a) Compute the partial derivatives of f as well as its discriminant. Then use solve to find the critical points and to classify each one as a local maximum, local minimum, or saddle point. (b) Check your answer to (a) by showing that fminsearch correctly locates the same local minima when you start at (0.5, 0.5) or at (−0.5, 0.5). (c) What happens when you apply fminsearch with...
Let z=e^(x) tan y. a. Compute the first-order partial derivatives of z. b. Compute the second-order...
Let z=e^(x) tan y. a. Compute the first-order partial derivatives of z. b. Compute the second-order partial derivatives of z. c.∗ Convert z = f(x,y) into polar coordinates and then compute the first- order partial derivatives fr and fθ by directly differentiating the com- posite function, and then using the Chain Rule.
Annual high temperatures in a certain location have been tracked for several years. Let X represent...
Annual high temperatures in a certain location have been tracked for several years. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places). x y 2 34.82 3 33.28 4 34.84 5 35.1 6 33.26 7 35.42 8 34.18 9 34.54 10 34.4 11 35.86 12 35.12 13 37.88 The equation is? Interpret the slope For each...
Annual high temperatures in a certain location have been tracked for several years. Let X represent...
Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. At the 0.01 significance level, does the data below show significant (linear) correlation between X and Y? x y 5 36.63 6 35.9 7 35.77 8 38.64 9 30.51 10 29.68 11 30.35 12 21.42 13 19.99 14 18.26 15 12.03 16 15.8 Yes, significant correlation No
Annual high temperatures in a certain location have been tracked for several years. Let X represent...
Annual high temperatures in a certain location have been tracked for several years. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places). x y 3 35.01 4 35.38 5 37.75 6 36.12 7 36.49 8 40.16 9 38.93 10 39.7 11 42.77 12 43.24 13 42.11 14 44.08 The equation is ˆ y = x +...
1)Annual high temperatures in a certain location have been tracked for several years. Let X represent...
1)Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = _____________ x + ________________ x y 3 10.42 4 10.96 5 13.8 6 17.14 7 16.98 8 21.22 9 23.96 10 23.9 11 27.14 12 30.28 13 30.22 14 34.06 15 37.1 16 36.74 17 41.08 18 41.62 2)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT