Problem
Twenty different statistics students are randomly selected. For each of them, their body temperature $\left({ }^{\circ} \mathrm{C}\right)$ is measured and their head circumference ( $\mathrm{cm}$ ) is measured. a. For this sample of paired data, what does $r$ represent, and what does $p$ represent? b. Without doing any research or calculations, estimate the value of $r$. c. Does r change if body temperatures are converted to Fahrenheit degrees? a. Choose the correct answer below. A. $r$ is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statistics students, and $\rho$ is a statistic that represents the value of the linear correlation coefficient computed from the paired sample data. B. $r$ is a statistic that represents the value of the linear correlation coefficient computed from the paired sample data, and $p$ is a parameter that represents the proportion of the variation in head circumference that can be explained by variation in body temperature. C. $r$ is a statistic that represents the proportion of the variation in head circumference that can be explained by variation in body temperatcre, and $p$ is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statistics students. D. $r$ is a statistic that represents the value of the linear correlation coefficient computed from the paired sample data, and $p$ is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of al statistics students. b. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal rounded to one decimal place as needed.) A. The value of $r$ is estimated to be $\square$, because it is likely that body temperature and head circumference are strongly positively correlated. B. The value of $r$ is estimated to be $\square$, because it is likely that there is no correlation between body temperature and head circumference.
Solution
Step 1 ：a. The correct answer is B. $r$ is a statistic that represents the value of the linear correlation coefficient computed from the paired sample data, and $p$ is a parameter that represents the proportion of the variation in head circumference that can be explained by variation in body temperature.
Step 2 ：b. The correct choice is B. The value of $r$ is estimated to be close to 0, because it is likely that there is no correlation between body temperature and head circumference.
