Question

a company that makes an exercise machine asked some of its recent customers how long they have owned their machines, and how many hours per month they currently use their machines. which of the following is the best estimate of the average change in hours of exercise per month that was associated with a 1 month increase in ownership? choose 1 answer: a -5 hours b -3 hours c -\frac{3}{4} hours d 1 hour

Explanation:

Step1: Identify the concept

This is a problem about the slope in a linear - relationship context (average rate of change). If we consider the relationship between the number of months of ownership (independent variable $x$) and the number of hours of exercise per month (dependent variable $y$), the average change in $y$ for a 1 - unit increase in $x$ is the slope of the regression line (or the best - fit line). Without the data points, we assume a linear model $y=mx + b$, where $m$ is the slope we want to find.
Since we are not given data to calculate the slope exactly, we need to use the concept that the slope represents the change in $y$ divided by the change in $x$. Here, $\Delta x = 1$ month, and we want to find $\Delta y$.
Typically, as the number of months of ownership increases, the novelty wears off and the usage of the exercise machine decreases. So, the slope (average change in hours of exercise per month with a 1 - month increase in ownership) is negative.
We assume a general understanding of consumer behavior with products. A decrease of 5 hours per month seems too steep for a 1 - month increase in ownership. A decrease of 3 hours per month is also quite large. A decrease of $\frac{3}{4}$ hour per month is a more reasonable estimate of the decline in usage as ownership time increases.

Step2: Select the answer

Based on the above - mentioned reasoning, the best estimate is a decrease of $\frac{3}{4}$ hours per month.

Answer:

C. $-\frac{3}{4}$ hours