2.E.070. A study collected arm bone strength information for two groups of young
ID: 3047444 • Letter: 2
Question
2.E.070. A study collected arm bone strength information for two groups of young men. The first group in the study was a control group of 15 men who are not baseball players. The table below gives the bone strengths of the dominant and the nondominant arms for those 15 men. ID Nondominant Dominant ID Nondominant Dominant 16.3 9 26.9 10 13.7 18.8 11 17.7 15.7 15.8 2 25.2 3 17.8 4 19.2 5 12.0 6 20.0 7 12.4 18.8 18.8 15.1 16.2 15.0 12.9 22.0 12 15.5 14.7 13 14.4 19.7 14 14.2 13.1 15 12.4 The least-squares regression line for these data is dominant 2.68+(0.939 x nondominant) The second group in the study comprised men who played baseball, we know that these baseball players use their dominant t nondominant arm were excluded), so they get more arm exercise than the controls. Here are the data for the baseball players arm in throwing (those who throw with their ID Nondominant Dominant ID Nondominant Dominant 16 17.0 17 16.9 18 17.8 19 21.3 20 21.0 21 14.6 22 31.6 19.4 20.5 19.2 24 19.0 25 13.4 25.1 26 13.6 15.1 40.4 28 17.3 20.8 29 14.6 36.9 30 22.5 26.5 30.4 17.4Explanation / Answer
(a) Difference = 22.9 - 17.7 = 5.2 cm4/1000 bone strength.
(b) If we consider the equation for a non-baseball player, the regression coefficient (coefficient of the nondominant variable) is 0.939 and in case of a baseball player, the regression coefficient (coefficient of the nondominant variable ) is 1.359. Also, the intercepts are 2.68 and 1.144 respectively. This tells us why we are getting different predicted values of dominant arm strengths for the same nondominant arm strength value.
For 1 cm4/1000 increase in non-dominant arm strength, the dominant arm strength of a baseball player will increase by 1.359 cm4/1000 and that of a non-baseball player by 0.939 cm4/1000.
(c) For non-dominant arm strength = 12, Dominant arm strength for baseball player = 17.5, Dominant arm strength for non-baseball player = 13.9, Difference = 3.6.
For non-dominant arm strength = 16, Difference = 5.2.
For non-dominant arm strength = 20, Dominant arm strength for baseball player = 28.3, Dominant arm strength for non-baseball player = 21.5, Difference = 6.8.
(d) For a non-dominant arm strength of 12 cm4/1000, it is observed that the predicted dominant arm strength of a baseball player will be 17.5 cm4/1000, whereas in case of a non-baseball player, it will be 13.9 cm4/1000. The difference in predicted dominant arm bone strengths will be 3.6 cm4/1000.
For a non-dominant arm strength of 16 cm4/1000, it is observed that the predicted dominant arm strength of a baseball player will be 22.9 cm4/1000, whereas in case of a non-baseball player, it will be 17.7 cm4/1000. The difference in predicted dominant arm bone strengths will be 5.2 cm4/1000.
For a non-dominant arm strength of 20 cm4/1000, it is observed that the predicted dominant arm strength of a baseball player will be 28.3 cm4/1000, whereas in case of a non-baseball player, it will be 21.5 cm4/1000. The difference in predicted dominant arm bone strengths will be 6.8 cm4/1000.
If we observe the values closely, the difference in predicted dominant arm bone strengths increases as we increase the non-dominant arm strengths of a baseball player and a non-baseball player. If we consider the equation for a non-baseball player, the regression coefficient (coefficient of the nondominant variable) is 0.939 and in case of a baseball player, the regression coefficient (coefficient of the nondominant variable ) is 1.359.
This tells us that in case of a non-baseball player, if the bone strength of the nondominant arm is changed by 1 cm4/1000 then the bone strength of their dominant arm will change by 0.939 cm4/1000.
In case of a baseball player, if the bone strength of the nondominant arm is changed by 1 cm4/1000 then the bone strength of their dominant arm will change by 1.359 cm4/1000.
This explains why the differences are not the same, since the regression coefficients are different in the two equations.
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