Samples Were Selected from Three Populations $$\begin{array}{l}\text { Sample } 1& \text { Sample } 2& \text { Sample } 3\\10 & 16 & 15 \\13 & 14 & 18 \\12 & 15 & \\13 & &\end{array}$$

question 40

Essay

Samples were selected from three populations. The data obtained are shown below.
$$\begin{array}{l}\text { Sample } 1& \text { Sample } 2& \text { Sample } 3\\10 & 16 & 15 \\13 & 14 & 18 \\12 & 15 & \\13 & &\end{array}$$ $\begin{array}{lcc}\text { Sample Mean } & 12 & 15 &16.5\\\text { Sample Variance } & 2.0 & 1.0&4.5\end{array}$
a. Compute the overall mean .
b. Set up an ANOVA table for this problem.
c. At 95% confidence, test to determine whether there is a significant difference in the means of the three populations. Use both the critical and p-value approaches.

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Definitions:

Aponeurosis

Aponeurosis refers to a type of flat and broad tendon that connects muscles to the parts they move, essentially serving as a fascial layer for muscle attachment.

Frontalis

The muscle of the forehead that elevates the eyebrows and wrinkles the skin of the forehead, part of the expression of surprise or concern.

Maxilla

The upper jawbone, forming the upper mouth section, the floors of the orbits, and sides of the nasal cavity.

Orbicularis Oculi

The orbicularis oculi is a circular muscle surrounding the eye that allows for blinking and squinting.