Question 1

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 non-dominant arm, we expect the bone in our dominant arm to be stronger than the bone in our non-dominant 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.

ID Non-dominant Dominant ID Non-dominant 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?

Question 2

Strong association but no correlation. Here is a data set that illustrates an important point about correlation:

X 25 35 45 55 65

Y 10 30 50 30 10

(a)Make a scatterplot of Y versus X.

(b)Describe the relationship between Y and X. Is it weak or strong? Is it linear?

(c)Find the correlation between Y and X

(d)What important point about correlation does this exercise illustrate?