Solve the Problem Is There Sufficient Evidence to Support the Claim That the and D)used

question 30

Multiple Choice

Solve the problem.
-Four different leadership styles (A, B, C, and D) used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style groups (a total of 60 accountants) . Each accountant was asked to rate the degree to which their subordinates performed substandard field work on a 10-point scale -- called the "substandard work scale". The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of variance.

$$\begin{array}{l}\text { ONE-WAY ANOVA FOR SUBSTAND BY STYLE }\\\begin{array} { l | c | r | r | r | r } { \text { Source } } & \text { DF } & { \text { SS } } & { \text { MS } } & \text { F } & \text { P-value } \\\hline \text { Between Groups } & 3 & 3440.35 & 1146.784 & 6.050 & 0.0012 \\\text { Within Groups } & 56 & 10,614.86 & 189.551 & & \\\text { Total } & 59 & 14,055.21 & & &\end{array}\end{array}$$
Is there sufficient evidence to support the claim that the means of the four leadership style groups are not all the same?
Assume that a 0.05 significance level is used.

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Definitions:

Two-way Factor ANOVA

A statistical test used to determine the effect of two nominative variables on a continuous outcome.

Total Sum of Squares

A statistical measure that quantifies the total variance in the observed data points from the mean of the data.

Variation

The extent to which data points in a statistical distribution or dataset diverge from the average or mean.

Degrees of Freedom

The number of independent values or quantities that can freely vary in an analysis without violating any given constraints.