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 1 15.6 16.4 9 15.8 20.1 2 25.2 26.8 10 13.8 18.7 3 17.8 18.7 11 17.6 18.7 4 19.1 22.0 12 15.4 15.2 5 12.0 14.8 13 14.3 16.2 6 20.0 19.9 14 14.2 15.0 7 12.3 13.2 15 12.3 12.8 8 14.3 17.4 The least-squares regression line for these data is dominant = 2.75 + (0.937 ✕ nondominant) The second group in the study comprised men who played baseball. We know that these baseball players use their dominant arm in throwing (those who throw with their nondominant arm were excluded), so they get more arm exercise than the controls. Here are the data for the baseball players. ID Nondominant Dominant ID Nondominant Dominant 16 17.0 19.2 24 15.2 19.4 17 16.8 19.0 25 13.4 20.4 18 17.7 25.2 26 13.7 17.1 19 21.3 37.7 27 20.4 26.5 20 21.0 40.3 28 17.2 30.3 21 14.7 20.7 29 14.7 17.3 22 31.5 36.8 30 22.6 35.0 23 14.8 21.1 Here is the equation of the least-squares line for the baseball players. dominant = 0.884 + (1.370 ✕ nondominant) Using these equations, we can predict two dominant-arm bone strengths, one for a baseball player and one for a person who is not a baseball player. The nondominant bone strengths are both 16.0 cm4/1000. The predicted dominant-arm bone strength for the baseball player is 22.8 cm4/1000, and the predicted dominant-arm bone strength for the person who is not a baseball player is 17.7 cm4/1000. (a) Compare the two predictions, baseball player minus control. (Round your answer to one decimal place.) Baseball players will have cm4/1000 more bone strength than a non-baseball player when they both have nondominant bone strength of 16.0 cm4/1000. (b) Explain how the difference in the two predictions is an estimate of the effect of baseball-throwing exercise on the strength of arm bones. (c) For nondominant-arm strengths of 12 and 20 cm4/1000, repeat your predictions and take the differences. Make a table of the results of all three calculations (for 12, 16, and 20 cm4/1000). (Round your answers to one decimal places.) Nondominant Dominant(for baseball players) Dominant(for non-baseball players) Difference 12 16 22.8 17.7 20 (d) Write a short summary of the results of your calculations for the three different nondominant-arm strengths. Be sure to include an explanation of why the differences are not the same for the three nondominant-arm strengths.

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 1 15.6 16.4 9 15.8 20.1 2 25.2 26.8 10 13.8 18.7 3 17.8 18.7 11 17.6 18.7 4 19.1 22.0 12 15.4 15.2 5 12.0 14.8 13 14.3 16.2 6 20.0 19.9 14 14.2 15.0 7 12.3 13.2 15 12.3 12.8 8 14.3 17.4 The least-squares regression line for these data is dominant = 2.75 + (0.937 ✕ nondominant) The second group in the study comprised men who played baseball. We know that these baseball players use their dominant arm in throwing (those who throw with their nondominant arm were excluded), so they get more arm exercise than the controls. Here are the data for the baseball players. ID Nondominant Dominant ID Nondominant Dominant 16 17.0 19.2 24 15.2 19.4 17 16.8 19.0 25 13.4 20.4 18 17.7 25.2 26 13.7 17.1 19 21.3 37.7 27 20.4 26.5 20 21.0 40.3 28 17.2 30.3 21 14.7 20.7 29 14.7 17.3 22 31.5 36.8 30 22.6 35.0 23 14.8 21.1 Here is the equation of the least-squares line for the baseball players. dominant = 0.884 + (1.370 ✕ nondominant) Using these equations, we can predict two dominant-arm bone strengths, one for a baseball player and one for a person who is not a baseball player. The nondominant bone strengths are both 16.0 cm4/1000. The predicted dominant-arm bone strength for the baseball player is 22.8 cm4/1000, and the predicted dominant-arm bone strength for the person who is not a baseball player is 17.7 cm4/1000. (a) Compare the two predictions, baseball player minus control. (Round your answer to one decimal place.) Baseball players will have cm4/1000 more bone strength than a non-baseball player when they both have nondominant bone strength of 16.0 cm4/1000. (b) Explain how the difference in the two predictions is an estimate of the effect of baseball-throwing exercise on the strength of arm bones. (c) For nondominant-arm strengths of 12 and 20 cm4/1000, repeat your predictions and take the differences. Make a table of the results of all three calculations (for 12, 16, and 20 cm4/1000). (Round your answers to one decimal places.) Nondominant Dominant(for baseball players) Dominant(for non-baseball players) Difference 12 16 22.8 17.7 20 (d) Write a short summary of the results of your calculations for the three different nondominant-arm strengths. Be sure to include an explanation of why the differences are not the same for the three nondominant-arm strengths.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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ID	Nondominant	Dominant	ID	Nondominant	Dominant
1	15.6	16.4	9	15.8	20.1
2	25.2	26.8	10	13.8	18.7
3	17.8	18.7	11	17.6	18.7
4	19.1	22.0	12	15.4	15.2
5	12.0	14.8	13	14.3	16.2
6	20.0	19.9	14	14.2	15.0
7	12.3	13.2	15	12.3	12.8
8	14.3	17.4

The least-squares regression line for these data is dominant = 2.75 + (0.937 ✕ nondominant)

The second group in the study comprised men who played baseball. We know that these baseball players use their dominant arm in throwing (those who throw with their nondominant arm were excluded), so they get more arm exercise than the controls. Here are the data for the baseball players.

ID	Nondominant	Dominant	ID	Nondominant	Dominant
16	17.0	19.2	24	15.2	19.4
17	16.8	19.0	25	13.4	20.4
18	17.7	25.2	26	13.7	17.1
19	21.3	37.7	27	20.4	26.5
20	21.0	40.3	28	17.2	30.3
21	14.7	20.7	29	14.7	17.3
22	31.5	36.8	30	22.6	35.0
23	14.8	21.1

Here is the equation of the least-squares line for the baseball players.

dominant = 0.884 + (1.370 ✕ nondominant)

Using these equations, we can predict two dominant-arm bone strengths, one for a baseball player and one for a person who is not a baseball player. The nondominant bone strengths are both 16.0 cm⁴/1000. The predicted dominant-arm bone strength for the baseball player is 22.8 cm⁴/1000, and the predicted dominant-arm bone strength for the person who is not a baseball player is 17.7 cm⁴/1000.

(a) Compare the two predictions, baseball player minus control. (Round your answer to one decimal place.)

Baseball players will have cm⁴/1000 more bone strength than a non-baseball player when they both have nondominant bone strength of 16.0 cm⁴/1000.

(b) Explain how the difference in the two predictions is an estimate of the effect of baseball-throwing exercise on the strength of arm bones.

(c) For nondominant-arm strengths of 12 and 20 cm⁴/1000, repeat your predictions and take the differences. Make a table of the results of all three calculations (for 12, 16, and 20 cm⁴/1000). (Round your answers to one decimal places.)

Nondominant	Dominant (for baseball players)	Dominant (for non-baseball players)
12
16	22.8	17.7
20

(d) Write a short summary of the results of your calculations for the three different nondominant-arm strengths. Be sure to include an explanation of why the differences are not the same for the three nondominant-arm strengths.

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