Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { 40 }$

question 28

Multiple Choice

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { 40 }$ be a random sample from a normal population with mean $\mu _ { 1 }$ and variance $\sigma _ { 1 } ^ { 2 } = 2.56 \text {, and let } Y _ { 1 } , Y _ { 2 } , \ldots \ldots Y _ { 32 }$ be a random sample from a normal population with mean $\mu _ { 2 } \text { and variance } \sigma _ { 2 } ^ { 2 } = 1.96 \text {, }$ and that X and Y samples are independent of one another. Assume the sample mean values are $\bar { x } = 18 \text { and } \bar { y } = 17$ and we want to test $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0 \text { versus } H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } > 0 \text {. }$ Which of the following statements are correct?

• A) The value of the test statistic is z = 2.83
• B) The value of the test statistic is z = 1.88
• C) \(H _ { o }\)
• Is rejected at the .05 level if \(z \leq 1.96\)
• D) \(H _ { o }\)
• Is rejected at the .05 level if \(z \leq 1.65\)
• E) None of the above statements are correct.

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Definitions:

Poisson Distribution

A probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, assuming these events happen with a known constant rate and independently of the time since the last event.

Service Rate

The speed at which a service provider can complete work or deliver services, often measured in customers served per unit of time or tasks completed per day.

Arrival Rate

The frequency at which entities (such as customers, materials, or information) reach a system or service point, often measured in entities per time unit.

Queue Discipline

Describes the rule or set of rules used to prioritize and manage elements in a queue, determining the order in which they are serviced.