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Aerobic fitness, measured by the ability to consume oxygen, relates to the heart

ID: 3367208 • Letter: A

Question

Aerobic fitness, measured by the ability to consume oxygen, relates to the heart, blood vessels, and lungs working together to deliver oxygen-rich blood to the muscles during exercise. A high level of aerobic fitness is associated with lower risks of several diseases, including high blood pressure and coronary heart disease. In a study of aerobic fitness, a sample of 31 men involved in a physical fitness course at a university was randomly selected. The measurements included : Oxygen: the oxygen intake rate (ml per kg body weight per minute), RunPulse: the heart rate while running. Our goal is to examine whether oxygen consumption is dependent upon the heart rate while running?

Our goal is to examine whether oxygen consumption is dependent upon the heart rate while running.

The following is part of the SAS output:

A.) Suppose that previous studies indicate that oxygen consumption decreases with an increasing heart rate while running. Does the study support this finding? Write down the hypotheses, calculate the test statistic and p-value, and state your conclusion in terms of the problem.

B.) Given that R2 = 0.1584, SSE = 716.5368, complete the following ANOVA table:

C.) What is the estimated standard deviation of the random errors in the model?

D.) What is the correlation coefficient between oxygen consumption and hear rate while running?

Parameter Est imates Parameter Estimate Standard Variable DF Error t Value Prt 82.4582!5 -0.20680 5.48 Intercept RunPulse 15.04386 0.08852 ?,0001 0.0266 -2.34

Explanation / Answer

a) Slope i.e. Runpluse = -0.20680 < 0 so there is negative correlation between oxygen consumption and heart rate while running
It means that As oxigen consumption decreases with an increasing heart rate while running

Testing:
H0: oxigen consumption not decreases with an increasing heart rate while running
H1: oxigen consumption decreases with an increasing heart rate while running
Test statistic t = -2.34
P-value = 0.0266 < alpha 0.05
so we reject H0
Thus we conclude that oxigen consumption decreases with an increasing heart rate while running

b)

c) Estimated Sd of the random error = sqrt(24.7082) = 4.97073
d) correlation coefficient between oxygen consumption and hear rate while running is sqrt(0.1584) = 0.397995

ANOVA Table Source Sum of Square df Mean Square F-ratio P-value Regression 134.8447 1 134.8447 5.4575 0.0266 Residuals 716.5368 29 24.7082 Total 851.3815 30 159.5529

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