Another method of identifying an outlier is to investigate whether there is evidence that a value might have come from a population with a mean different from the mean of the population of the other values. Let X and Y represent random variables. X is distributed normally with mean μ, and standard deviation σ, and Y is distributed normally with mean H, and standard deviation σ. Consider 1 randomly selected value of Y and n-1 randomly selected values of X. (b) Consider the difference Y - X. (i) In terms of y and x, what is the mean of the difference Y-X? (ii) In terms of n and σ, what is the standard deviation of the difference Y-X?

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Another method of identifying an outlier is to investigate whether there is evidence that a value might have come
from a population with a mean different from the mean of the population of the other values.
Let X and Y represent random variables. X is distributed normally with mean μ, and standard deviation σ,
and Y is distributed normally with mean H, and standard deviation σ. Consider 1 randomly selected value of Y
and n-1 randomly selected values of X.
(b) Consider the difference Y - X.
(i) In terms of y and x, what is the mean of the difference Y-X?
(ii) In terms of n and σ, what is the standard deviation of the difference Y-X?
Transcribed Image Text:Another method of identifying an outlier is to investigate whether there is evidence that a value might have come from a population with a mean different from the mean of the population of the other values. Let X and Y represent random variables. X is distributed normally with mean μ, and standard deviation σ, and Y is distributed normally with mean H, and standard deviation σ. Consider 1 randomly selected value of Y and n-1 randomly selected values of X. (b) Consider the difference Y - X. (i) In terms of y and x, what is the mean of the difference Y-X? (ii) In terms of n and σ, what is the standard deviation of the difference Y-X?
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