The Following ANOVA Table Shows the Results of an Experiment

question 21

Essay

The following ANOVA table shows the results of an experiment used to test how race car drivers and different tracks affect time.The experiment used 3 different drivers on 4 different tracks.Assuming no effect from the interaction between driver and track,test the claim that the three drivers have the same mean time. $$\begin{array}{l}\begin{array} { l r c c c c } &&\text { Sum of}&{ Mean }\\\text { Source } & \text { DF } & \text { Squares } & \text { Square } & \text { F-ratio } & \text { P-value } \\\text { Driver } & 2 & 2 & 1 & 0.33 & 0.729 \\\text { Tradk } & 3 & 98.25 & 32.75 & 10.92 & < 0.0001 \\\text { Error } & 6 & 18 & 3 & & \\\text { Total } & 11 & 118.25 & & &\end{array}\end{array}$$

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Definitions:

Contingency Theories

are theories that suggest the effectiveness of leadership depends on the context or environment, with no single best way to lead in all situations.

Leadership Style

The characteristic approach and manner in which a leader directs, motivates, and manages their team or organization.

LPC Score

A measure in the Fiedler contingency model that evaluates a leader's least preferred coworker to determine their leadership style as either task-oriented or relationship-oriented.

Task Structure

The way in which a job or task is organized, designed, and structured, including clarity, complexity, and the specified way to complete the task.