Draw a picture of the appropriate sampling distribution and

Question

In comparing means for two independent samples, suppose that μ₁ = μ₂ = 0, σ₁ = σ₂ = 3, and n₁ = n₂ = 30.

a. Draw a picture of the appropriate sampling distribution, and show where the value x^‾1 - x^‾2 = 2 falls on it.

b. Find the value of the standardized statistic corresponding to x^‾1 - x^‾2 = 2.

c. Draw a picture of the standard normal distribution with the standardized statistic you found in part (b) shown on it. Compare it to your picture in part (a).