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 \( \mu \mathrm{D} \)

---

Definitions:

Negative Exponential Distribution

A probability distribution used to model time between events in a Poisson process, often applied in reliability engineering and queuing theory.

Arrival Rates

The frequency at which entities arrive at a particular system or service point, commonly used in queueing theory and service process analysis.

Service Times

The duration required to complete a specific service task or process, critical in evaluating service efficiency and customer satisfaction.

Waiting-Line System

A mathematical model used to analyze lines or queues in order to minimize waiting times and improve service efficiency.