Answer to Question #278943 in Statistics and Probability for ali

Question

ABC Company, a manufacturer of automobile tires claims that the average life of the product is 45,600 miles. A random sample of 15 tires was chosen and resulted in a mean life of 43,500 miles with a standard deviation of 3,000 miles. Based on the above results, can you accept the manufacturer’s claim? Use α = 0.05

Answer 1

$n=15 \\ \bar{x} = 43500 \\ s = 3000 \\ H_0: \mu = 45600 \\ H_1: \mu < 45600 \\ α = 0.05$

Test-statistic

$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \\ t = \frac{43500 -45600}{3000 / \sqrt{15}} \\ t = -2.711 \\ d.f. = n-1 = 15-1 = 14 \\ t_{14, 0.05} = -1.761$

Since $t < t_{14, 0.05}$ we reject H₀ at 5 % level of significance and conclude that the company’s average product’s life is less than 45600 miles.