Question

twenty different statistics students are randomly selected. for each of them, their body temperature (°c) is meas and their head circumference (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?

the linear correlation coefficient computed from the paired sample data.
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 □, because it is likely that body temperature and head circumference are strongly negatively correlated.
○ b. the value of r is estimated to be □, because it is likely that there is no correlation between body temperature and head circumference.
○ c. the value of r is estimated to be □, because it is likely that body temperature and head circumference are strongly positively correlated.

Explanation:

Step1: Analyze the relationship

Body temperature and head circumference are two variables that are not expected to have a linear relationship. There's no logical connection that would make them positively or negatively correlated in a strong way. So, we expect no correlation.

Step2: Determine the correlation coefficient

The linear correlation coefficient \( r \) for no correlation is around 0. So, we choose option B and estimate \( r \) as 0.

Answer:

B. The value of \( r \) is estimated to be \( 0 \), because it is likely that there is no correlation between body temperature and head circumference.