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Two populations of measurements are normally distributed with μ₁ = 57 and µ₂ = 25. The two populations have the standard deviations of σ₁ = 12 and σ₂ = 6. Two independent samples of n₁ = n₂ = 36 are taken from these populations.
What is the expected value of the difference in sample means, X₁-X₂?

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varshaoman2020

Answer:

The expected value (\(E\)) of the difference in sample means (\(X_1 - X_2\)) is equal to the difference in population means (\(μ_1 - μ_2\)). Mathematically, it can be expressed as:

\[ E(X_1 - X_2) = μ_1 - μ_2 \]

Given that \(μ_1 = 57\) and \(μ_2 = 25\), the expected value of the difference in sample means is:

\[ E(X_1 - X_2) = 57 - 25 = 32 \]

So, the expected value of the difference in sample means (\(X_1 - X_2\)) is 32.

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