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Population 1 is Normally distributed with a mean of 40 and a standard deviation of 4, and population 2 is Normally distributed with a mean of 25 and a standard deviation of 7. Suppose we select independent SRSs of n1 = 100 and n2 = 85 from population 1 and 2 respectively. Which of the following are the values of the mean and the standard deviation of the sampling distribution of x1-x2 ?

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Answer:

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Explanation:

The mean and the standard deviation of the sampling distribution of  x⁻₁ - x⁻₂ are respectively; 15, √[(4²/100)+ (7²/85)]

Sampling Distribution

We are given;

For Population 1;

  • Mean; x⁻₁ = 40
  • Standard deviation; σ₁ = 4
  • Sample size; n₁ = 100

For Population 2;

  • Mean; x⁻₂ = 25
  • Standard Deviation; σ₂ = 7
  • Sample size; n₂ = 85

Thus, the mean of the sampling distribution is;

x⁻₁ - x⁻₂ = 40 - 25

x⁻₁ - x⁻₂ = 15

Now, the formula for the standard deviation of the sampling distribution is; s = √[(σ₁²/n₁) + (σ₂²/n₂)]

Thus;

s = √[(4²/100)+ (7²/85)]

Read more about sampling distribution at; https://brainly.com/question/15205225

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