Although an exhaust fan is present in nearly every bathroom, they often are not used due to the high noise level. This is an unfortunate practice because regular use of the fan results in a reduction of indoor moisture. Excessive indoor moisture often results in the development of mold which may lead to adverse health consequences. Consumer Reports in its January 2004 issue reports on a wide variety of bathroom fans. The following table displays the price (P) in dollars of the fans and the quality of the fan measured in airflow (AF), cubic feet per minute (cfm).
| P |
95 |
115 |
110 |
15 |
20 |
20 |
75 |
150 |
60 |
60 |
| AF |
60 |
60 |
60 |
55 |
55 |
55 |
85 |
80 |
80 |
75 |
| P |
160 |
125 |
125 |
110 |
130 |
125 |
30 |
60 |
110 |
85 |
| AF |
90 |
90 |
100 |
110 |
90 |
90 |
90 |
110 |
110 |
60 |
a. Plot the data in a scatterplot and comment on the relationship between price and airflow.
b. Compute the correlation coefficient for this data set. Is there a strong or weak relationship between price and airflow of the fans?
c. Is your conclusion in part (b) consistent with your answer in part (a)?
d. Based on your answers in parts (a) and (b), would it be reasonable to conclude that higher priced fans generate greater airflow?