Have you ever wondered whether tall people have longer arms than short people? We'll explore this question by collecting data on two variables -- height and arm span (measured from left fingertip to right fingertip).

One way to ask this question is, "Is there a positive association between height and arm span?"

Through this question, we are seeking to establish an association between height and arm span. A positive association between two variables exists when an increase in one variable generally produces an increase in the other. For example, the association between a student's grades and the number of hours per week that student spends studying is generally a positive association. A negative association, in contrast, exists when an increase in one variable generally produces a decrease in the other. For example, the association between the number of doctors in a country and the percentage of the population that dies before adulthood is generally a negative one.

There are many other ways to ask this same question about height and arm span. Here are two, which we will concentrate on in Part A:

In Session 1, measurements (in centimeters) were given for the heights and arm spans of 24 people. Here are the collected data, sorted by increasing order of arm span:

Person # Arm Span Height 1 156 162 2 157 160 3 159 162 4 160 155 5 161 160 6 161 162 7 162 170 8 165 166 9 170 170 10 170 167 11 173 185 12 173 176

Person # Arm Span Height 13 177 173 14 177 176 15 178 178 16 184 180 17 188 188 18 188 187 19 188 182 20 188 181 21 188 192 22 194 193 23 196 184 24 200 186

This is bivariate data, since two measurements are given for each person.

Problem A1

The data given above are sorted by arm span. Are they also sorted by height? If not exactly, are they generally sorted by height, and, if so, in which direction? Does this suggest any type of association between height and arm span?

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