Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { \mathrm { m } }$

question 45

Multiple Choice

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { \mathrm { m } }$ be a random sample from a normal population with mean $\mu _ { 1 } \text { and known variance } \sigma _ { 1 } ^ { 2 } \text {, }$ and let $Y _ { 1 } , Y _ { 2 } , \ldots \ldots , Y _ { n }$ be a random sample from a normal population with mean $\mu _ { 2 } \text { and variance } \sigma _ { 2 } ^ { 2 } \text {, }$ and that the X and Y samples are independent of one another. Which of the following statements are true?

• A) \(\bar { X }\)
• Is normally distributed with expected value \(\mu _ { 1 } \text { and variance }σ _ { 1 } ^ { 2 } / m\)
• B) \(\bar { Y }\)
• Is normally distributed with expected value \(\mu_{2} \text { and variance } σ_{2}^{2} / n\)
• C) \(\bar { X } - \bar { Y }\)
• Is normally distributed with expected value \(\mu _ { 1 } - \mu _ { 2 } \text { and variance } \left(σ _ { 1 } ^ { 2 } / m + \sigma _ { 2 } ^ { 2 } / n \right) \text {. }\)
• D) \(\bar { X } - \bar { Y }\)
• Is an unbiased estimator of \(\mu _ { 1 } - \mu _ { 2 }\)
• )
• E) All of the above statements are true.

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Definitions:

Service Quality Evaluation

The assessment process of determining the quality of services provided, often involving measures of customer satisfaction, service performance, and compliance with standards.

Performance Perceptions

How the quality, efficiency, or value of someone's work or a product is viewed or assessed by others.

Service Expectations

The anticipated level of service performance and quality that customers expect from a provider.

Prevention Costs

The expenses involved in avoiding defects in products or services, including costs related to quality planning and training.