The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is A)H₀: $\mu$ 40,000 C)H₀: $\mu$ 40,000 H_a: $\mu$ $\le$ 40,000 D)H₀: $\mu$ $\ge$ 40,000 H_a: $\mu$

Question

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is A)H₀: $\mu$ < 40,000 H_a: $\mu$ $\ge$ 40,000 B)H₀: $\mu$ $\le$ 40,000 H_a: $\mu$ > 40,000 C)H₀: $\mu$ > 40,000 H_a: $\mu$ $\le$ 40,000 D)H₀: $\mu$ $\ge$ 40,000 H_a: $\mu$ < 40,000

Quizplus · Accepted Answer

The null hypothesis (H0) is that the average life expectancy of the tires produced by the new process is the same as the previous average (40,000 miles). The alternative hypothesis (Ha) is that the new production process has increased the life expectancy of the tires. In order to test this, we need to use a one-tailed test, as we are only interested in whether the life expectancy has increased (not decreased). Therefore, the correct set of hypotheses is H₀: μ1 = μ0 vs. H_a: μ1 > μ0, where μ1 is the population mean life expectancy of the new tires and μ0 is the population mean life expectancy of the old tires. Choice B has the correct set of hypotheses.

The Average Life Expectancy of Tires Produced by the Whitney μ\muμ

The Average Life Expectancy of Tires Produced by the Whitney $\mu$