tutu In physiology, an objective measure of aerobic fitness is how efficiently the body can absorb and use oxygen (oxygen consumption). A physiologist, Dr. Castillejo, conducted a research wherein subjects participated in a predetermined exercise run of 1.5 miles. Measurements of oxygen consumption as well as several other variables such as age, gender, runtime, resting and maximum pulse rates, and weight were recorded from 50 randomly selected gym members. Dr. Castillejo is interested in determining whether any of these other variables can help predict oxygen consumption. She believes that a possible link between these factors will help her determine how to improve the health of her gym members. Help Dr. Castillejo in developing a proposal for the improvement of her gym members' health condition. The variables are described below. gender - either male or female runtime - time to run 1.5 miles (in min) age - age of the gym member in years weight - weight of the gym member (in kg) oxygen consumption - measure of the ability to use oxygen in the blood stream (in ml/min) rest pulse - resting pulse rate (in bpm) maximum pulse - maximum pulse rate during the run (in bpm) In a journal on clinical nutrition, one of the findings show that the type of workout or training has varying effect on the oxygen consumption. Dr. Castillejo wants to test if the average oxygen consumption differs among three training groups. To do this, gym members were randomly assigned to one of the three groups: strength training, aerobic training, and normal training. Those in the strength-training group performed progressive weight-resistance exercises for the upper and lower body while those in the aerobic group performed alternate leg and arm cycling. Use the R commander output below to test Dr. Castillejo's claim. Write a brief report about the analysis by identifying the set of hypotheses to be tested, the appropriate test to use, and implications and recommendations of/from the conclusions. R COMMANDER OUTPUT Shapiro-Wilk normality test data: training = Aerobic data: training = Normal data: training = Strength W = 0.86455, p-value = 0.02809 W = 0.85003, p-value = 0.008479 W = 0.86494, p-value = 0.01827 Levene's Test for Homogeneity of Variance (center = "mean") Df F value Pr (>F) group 2 0.9031 0.4122 47 R COMMANDER OUTPUT One-way Analysis of Variance (ANOVA) Df Sum Sq Mean Sq F value Pr (>F) training 2 69.59 34.79 111.8 <2e-16 *** Residuals 47 14.63 0.31 R COMMANDER OUTPUT Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Tukey Contrasts Fit: aov (formula = oxygen_consumption training, data = anova) Linear Hypotheses: Estimate Std. Error t value Pr (>|t|) -2.8761 Normal Aerobic == 0 Strength Aerobic == 0) -1.1563 1.7198 0.1951 -14.744 <0.00001 *** 0.1977 -5.850 <0.00001 *** 0.1887 9.114 <0.00001 *** Strength Normal == 0 R COMMANDER OUTPUT Kruskal-Wallis rank sum test data: oxygen_consumption by training Kruskal-Wallis chi-squared = 43.497, df = 2, p-value = 3.587e-10 R COMMANDER OUTPUT Comparison of x by group (Dunn's Test) (No adjustment) Col Mean-| Row Mean | Aerobic Normal Normal | 6.574507 I 0.0000* Strength | 3.098907 -3.550244 0.0010* 0.0002*

tutu In physiology, an objective measure of aerobic fitness is how efficiently the body can absorb and use oxygen (oxygen consumption). A physiologist, Dr. Castillejo, conducted a research wherein subjects participated in a predetermined exercise run of 1.5 miles. Measurements of oxygen consumption as well as several other variables such as age, gender, runtime, resting and maximum pulse rates, and weight were recorded from 50 randomly selected gym members. Dr. Castillejo is interested in determining whether any of these other variables can help predict oxygen consumption. She believes that a possible link between these factors will help her determine how to improve the health of her gym members. Help Dr. Castillejo in developing a proposal for the improvement of her gym members' health condition. The variables are described below. gender - either male or female runtime - time to run 1.5 miles (in min) age - age of the gym member in years weight - weight of the gym member (in kg) oxygen consumption - measure of the ability to use oxygen in the blood stream (in ml/min) rest pulse - resting pulse rate (in bpm) maximum pulse - maximum pulse rate during the run (in bpm) In a journal on clinical nutrition, one of the findings show that the type of workout or training has varying effect on the oxygen consumption. Dr. Castillejo wants to test if the average oxygen consumption differs among three training groups. To do this, gym members were randomly assigned to one of the three groups: strength training, aerobic training, and normal training. Those in the strength-training group performed progressive weight-resistance exercises for the upper and lower body while those in the aerobic group performed alternate leg and arm cycling. Use the R commander output below to test Dr. Castillejo's claim. Write a brief report about the analysis by identifying the set of hypotheses to be tested, the appropriate test to use, and implications and recommendations of/from the conclusions. R COMMANDER OUTPUT Shapiro-Wilk normality test data: training = Aerobic data: training = Normal data: training = Strength W = 0.86455, p-value = 0.02809 W = 0.85003, p-value = 0.008479 W = 0.86494, p-value = 0.01827 Levene's Test for Homogeneity of Variance (center = "mean") Df F value Pr (>F) group 2 0.9031 0.4122 47 R COMMANDER OUTPUT One-way Analysis of Variance (ANOVA) Df Sum Sq Mean Sq F value Pr (>F) training 2 69.59 34.79 111.8 <2e-16 * Residuals 47 14.63 0.31 R COMMANDER OUTPUT Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Tukey Contrasts Fit: aov (formula = oxygen_consumption training, data = anova) Linear Hypotheses: Estimate Std. Error t value Pr (>|t|) -2.8761 Normal Aerobic == 0 Strength Aerobic == 0) -1.1563 1.7198 0.1951 -14.744 <0.00001 * 0.1977 -5.850 <0.00001 * 0.1887 9.114 <0.00001 * Strength Normal == 0 R COMMANDER OUTPUT Kruskal-Wallis rank sum test data: oxygen_consumption by training Kruskal-Wallis chi-squared = 43.497, df = 2, p-value = 3.587e-10 R COMMANDER OUTPUT Comparison of x by group (Dunn's Test) (No adjustment) Col Mean-| Row Mean | Aerobic Normal Normal | 6.574507 I 0.0000* Strength | 3.098907 -3.550244 0.0010* 0.0002*

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 22EQ

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