## Related questions with answers

Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).

$\begin{matrix} \text{Weekly Usage} & \text{Annual}\\ \text{(hours)} & \text{Maintenance Expense}\\ \hline \text{13} & \text{17.0}\\ \text{10} & \text{22.0}\\ \text{20} & \text{30.0}\\ \text{28} & \text{37.0}\\ \text{32} & \text{47.0}\\ \text{17} & \text{30.5}\\ \text{24} & \text{32.5}\\ \text{31} & \text{39.0}\\ \text{40} & \text{51.5}\\ \text{38} & \text{40.0}\\ \end{matrix}$

Test the significance of the relationship in part (a) at a .05 level of significance.

Solutions

VerifiedTests for significance of relationship have hypotheses:

$H_0:\beta_1=0\qquad vs.\qquad H_a:\beta_1\neq 0.$

Relationship between $x$ and $y$ is $y=\beta_0+\beta_1x+\epsilon$, with standard assumptions on $\epsilon$. These hypotheses can be tested with $t$, $F$ and $\rho$ tests. This solution will use $t$ statistic.

Given:

$\begin{align*} n&=\text{Sample size}=10 \\ \alpha&=\text{Significance level}=0.05 \end{align*}$

In this exercise, we determine the conclusion of an $F$-test of a significant linear relationship.

*How can the test statistic be derived?*

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