2.24 Bone strength. Osteoporosis is a condition where bones become weak. It affects more than 200 million people worldwide. Exercise is one way to produce strong bones and to prevent osteoporosis. Because we use our dominant arm (the right arm for most people) more than our nondominant arm, we expect the bone in our dominant arm to be stronger than the bone in our nondominant arm. By comparing the strengths, we can get an idea of the effect that exercise can have on bone strength. Here are some data on the strength of bones, measured in Newton meters divided by 1000 (Nm/1000), for the arms of 15 young men:11
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| ID | Nondominant | Dominant | ID | Nondominant | Dominant |
|---|---|---|---|---|---|
| 1 | 15.7 | 16.3 | 9 | 15.9 | 20.1 |
| 2 | 25.2 | 26.9 | 10 | 13.7 | 18.7 |
| 3 | 17.9 | 18.7 | 11 | 17.7 | 18.7 |
| 4 | 19.1 | 22.0 | 12 | 15.5 | 15.2 |
| 5 | 12.0 | 14.8 | 13 | 14.4 | 16.2 |
| 6 | 20.0 | 19.8 | 14 | 14.1 | 15.0 |
| 7 | 12.3 | 13.1 | 15 | 12.3 | 12.9 |
| 8 | 14.4 | 17.5 |
Before attempting to compare the arm strengths of the nondominant and dominant arms, let’s take a careful look at the data for these two variables.
(a) Make a scatterplot of the data with the nondominant arm strength on the x axis and the dominant arm strength on the y axis.
(b) Describe the overall pattern in the scatterplot and any striking deviations from the pattern.
(c) Describe the form, direction, and strength of the relationship.
(d) Identify any outliers.
(e) Is the relationship approximately linear?