Question

5. (13pts) Let ui and u 2 denote true average tread lives for two competing brands of size P205/6 data: m -55, X 51,500, s1 1200 for sample of Brand A, and n 55, y 1300 for sample of Brand B. 5R15 radial tires (Brand A and B with ?, and ? 2, respectively). Using the following 48,400, and s2 a. (5pts) Compute a 95% CI for ?-? 2. b. ( 8pts) Does this data suggest that ?-A2-2500 at a significant level of 0.05? Show all hypotheses, test statistic value, rejection region, and conclusion in terms of problem context. (hint: two-sides test)

Answer 1

Brand A: x bar = 51500 s_1 = 1200 m = 55 Brand B: y bar = 48400 s_2 = 1300 n = 55 Degrees of Freedom: df = (s^2_1/m + s^2_2/n)^2/1/m - 1(s^2_1/m + 1/n - 1(s^2_2/n)^2 df = (1200^2/55 + 1300^2/55)^2/1/55 - 1(1200^2/55)^2 + 1/55 - 1(1300^2/55)^2 df = 107.3 Trimming the decimal part, df = 107 part - A: For 95% confidence interval, alpha = 1 - 0.95 = 0.05 \r\n alpha/2 = 0.05/2 = 0.025 From t - distribution table, the value of t having an area of (alpha/2 = 0.025) in its upper tail and for (df = 107) is given by = t_0.025 = 1.982 Margin of Error: MOE = t_0.025 times squareroot s^2_1/m + s^2_2/n MOE = 1.982 times squareroot 1200^2/55 + 1300^2/55 MOE = 472.91 95% confidence interval for mu_1 - mu_2: (x bar - y bar) plusminus MOE (51500 - 48400) plusminus 472.91 3100 plusminus 472.91