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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).

Weekly UsageAnnual(hours)Maintenance Expense1317.01022.02030.02837.03247.01730.52432.53139.04051.53840.0\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.

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Answered 7 months ago
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Tests for significance of relationship have hypotheses:

H0:β1=0vs.Ha:β10.H_0:\beta_1=0\qquad vs.\qquad H_a:\beta_1\neq 0.

Relationship between xx and yy is y=β0+β1x+ϵy=\beta_0+\beta_1x+\epsilon, with standard assumptions on ϵ\epsilon. These hypotheses can be tested with tt, FF and ρ\rho tests. This solution will use tt statistic.

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