A Multiple-Comparison Procedure for Comparing Four Treatment Means Produced the Confidence

question 67

Short Answer

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there is no significant difference. $\begin{array}{l}\left(\mu_{\mathrm{A}}-\mu_{\mathrm{B}}\right):(18,34) \\\left(\mu_{\mathrm{A}}-\mu_{\mathrm{C}}\right):(7,23) \\\left(\mu_{\mathrm{A}}-\mu_{\mathrm{D}}\right):(6,18) \\\left(\mu_{\mathrm{B}}-\mu_{\mathrm{C}}\right):(-18,-4) \\\left(\mu_{\mathrm{B}}-\mu_{\mathrm{D}}\right):(-24,-4) \\\left(\mu_{\mathrm{C}}-\mu_{\mathrm{D}}\right):(-10,4)\end{array}$

A) $\mu_{\mathrm{A}}>\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}<\mu_{\mathrm{C}} ; \mu_{\mathrm{B}}<\mu_{\mathrm{D}} ;$ no significant difference between $\mu_{\mathrm{C}}$ and $\mu_{\mathrm{D}}$
B) $\mu_{\mathrm{A}}>\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}<\mu_{\mathrm{C}}: \mu_{\mathrm{B}}<\mu_{\mathrm{D}} ; \mu_{\mathrm{C}}<\mu_{\mathrm{D}}$
C) $\mu_{\mathrm{A}}<\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}>\mu_{\mathrm{C}} ; \mu_{\mathrm{B}}>\mu_{\mathrm{D}}$ ; no significant difference between $\mu_{\mathrm{C}}$ and $\mu_{\mathrm{D}}$
D) no significant difference between $\mu_{\mathrm{A}}$ and $\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}>\mu_{\mathrm{C}}$ ; $\mu_{\mathrm{B}}>\mu_{\mathrm{D}}$ ; no significant difference between $\mu_{\mathrm{C}}$ and $\mu \mathrm{D}$

• A) \( \mu_{\mathrm{A}}>\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}<\mu_{\mathrm{C}} ; \mu_{\mathrm{B}}<\mu_{\mathrm{D}} ; \) no significant difference between \( \mu_{\mathrm{C}} \) and \( \mu_{\mathrm{D}} \)
• B) \( \mu_{\mathrm{A}}>\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}>\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}<\mu_{\mathrm{C}}: \mu_{\mathrm{B}}<\mu_{\mathrm{D}} ; \mu_{\mathrm{C}}<\mu_{\mathrm{D}} \)
• C) \( \mu_{\mathrm{A}}<\mu_{\mathrm{B}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}>\mu_{\mathrm{C}} ; \mu_{\mathrm{B}}>\mu_{\mathrm{D}} \); no significant difference between \( \mu_{\mathrm{C}} \) and \( \mu_{\mathrm{D}} \)
• D) no significant difference between \( \mu_{\mathrm{A}} \) and \( \mu_{\mathrm{B}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{C}} ; \mu_{\mathrm{A}}<\mu_{\mathrm{D}} ; \mu_{\mathrm{B}}>\mu_{\mathrm{C}} \); \( \mu_{\mathrm{B}}>\mu_{\mathrm{D}} \); no significant difference between \( \mu_{\mathrm{C}} \) and \( \mu \mathrm{D} \)

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Definitions:

Scale 1:1

A drawing or model scale where one unit in the drawing or model is equal to one unit on the actual object, representing a real-life size.

Abbreviation R

Commonly represents "Radius" in technical drawings, indicating the measure of the distance from the center of a circle to its perimeter.

Concentric Circles

Circles that share the same center point but differ in radius.

Eccentric

Related to a mechanism or part of it that is off-center or not in the normal or expected position, often causing a deviation or irregular motion.