Question: Let 1 denote true average tread life for a premium brand of P205/65R15 radial tire, and let 2 denote the true average tread

Let μ ₁ denote true average tread life for a premium brand of P205/65R15 radial tire, and let μ ₂ denote the true average tread life for an economy brand of the same size. Test H ₀: μ ₁ − μ ₂ = 5000 versus H _a: μ ₁ − μ ₂ > 5000 at level 0.01, using the following data: m = 50, x = 42,100, s ₁ = 2400, n = 50, y = 36,400, and s ₂ = 1800.

Calculate the test statistic and determine the P -value.

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