Question

Notation Twenty different statistics students are randomly selected. For each of them, their body temperature (°C) is measured and their head circumference (cm) is measured.

a. For this sample of paired data, what does r represent, and what does \(\rho \)represent?

b. Without doing any research or calculations, estimate the value of r.

c. Does r change if the body temperatures are converted to Fahrenheit degrees

Short answer

a. r represents the correlation coefficient for sample while\(\rho \)represents the correlation coefficient for the population.

b. The estimated value of r is 0 for the variables.

c. rwould not change when the temperatures are converted to Fahrenheit.

Step-by-step solution

Given information

Number of students selected are 20 (n).

The variables measured are body temperature in degree celcius and head circumference in cm.

Step 2:Identify the notations

a.

Each measure used in statistics have a different notation when computed for a sample or population.

In case the correlation coefficient is computed for a paired data set comprising of a sample from a certain population, it is represented by the statistic r.

In case the correlation coefficient is computed for a paired data set comprising of a population, it is represented by the parameter \(\rho \).

Estimate the value of correlation for sample

b.

The correlation measure can take any value between -1 and 1, both included, where the signs indicate direct and indirect relationship and the number reflects the strength of association.

In case of these variables, skull circumference and body temperatureofstudents are not expected to be associated. Thus, the correlation measure is expected to be 0.

Discuss the change in value of r with the change in temperatures

c.

Since the two measures are not associated withone another, the value of r would not change with the change in values of tempratures (change in magnitude due to change in unit)