Suppose ₁ and ₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level 0.01 to test H₁: ₁-₂=-10 versus H₂: ₁-₂ < -10 for the following data: m = 9, x = 113.5, s₁=5.06, n=9, y = 129.6, and s₂ = 5.36. Calculate the test statistic and determine the P-value. State the conclusion in the problem context. Step 1 To conduct a two-sample t test, first calculate the test statistic t. The formula for the test statistic is below, where we are given sample means x = 113.5 and y = 129.6, hypothesized difference 4₁ = -10, sample standard deviations s₁=5.06 and s₂ = 5.36, and sample sizes m = 9 and n = 9. Use these values to calculate t, rounded to one decimal place. x-Y-4 t = 113.5 129.6 = -2.5 11 5.062 -2.5 Step 2 The degrees of freedom for a two-sample t test is calculated with the formula below. Refer again to the given values s₁ = 5.06, s₂ = 5.36, m = 9, and n = 9. Calculate the degrees of freedom V, rounding the result down to the nearest integer. m-1 (2+2) (*.()* 129.6 - (-10) n-1 (5.00² + 5.362)² 5.062 9 5.362

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