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

question 66

Multiple Choice

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { \mathrm { m } }$ be a random sample from a population with mean $\mu _ { 1 } \text { and variance } \sigma _ { 1 } ^ { 2 } \text {, and let } Y _ { 1 } , Y _ { 2 } , \ldots \ldots , Y _ { n }$ be a random sample from a 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 not true?

• A) The natural estimator of \(\mu _ { 1 } - \mu _ { 2 } \text { is } \bar { X } - \bar { Y }\)
• B) The expected value of \(\bar { X } - \bar { Y } \text { is } \mu _ { 1 } - \mu _ { 2 }\)
• C) The expected value of \(\mu _ { 1 } - \mu _ { 2 } \text { is } \bar { X } - \bar { Y }\)
• 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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