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).

x	7.5	5.2	4.2	3.3	2.1	(units: mm Hg/10)
y	43.6	33.3	26.2	16.2	13.9	(units: mm Hg/10)

a) Use a 1% level of significance to test the claim that ρ > 0. (Use 2 decimal places.)

t-

critical t-

b) Find a 90% confidence interval for y when x = 2.7. (Use 1 decimal place.)

lower limit
upper limit

c) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.)

t
critical t

d) Find a 90% confidence interval for β and interpret its meaning. (Use 2 decimal places.)

lower limit
upper limit

Answer 1

EXCEL output:

Regression Analysis 0.964 r 0.982 Std. Error 2.692 Dep. Var.y ANOVA table Source df 1581.7489 80.27 MS value 0029 Regression 581.7489 Residual 21.7431 7.2477 Total 603.4920 4 confidence interval Regression out coefficients df 3-p-value-90%lower 8 9137 7.0858 8.959 0029 4.3424 90%upperstd. coeff. 7.8318 0.000 7.43650.982 vanables Intercept std. error t 0.3730 3.1694 0.11 5.8895 0.6574 Predicted values for: 90% onfidenceinterval .90% red ctionInterval x Predicted lower upper 2.7 lower upper Leverage 0.385 16.2746 12.3450 20.2041 8.8193 23.7298 The value of correlation coefficient is 0.982

0.982/5-2 v1-0.9822 1.7009 0.1889 = 9.00 The value oftest statistic is t = 9.00 The critical value oft is 4.54. The 90% confidence interval for y when x = 2.7 is Lower limit = 12.3 Upper limit 20.2 The value oftest statistic is t = 8.96

The critical value oft is 4.54. The 90% confidence interval for ß is Lower linmít = 4.34 Upper limit 7.44.