A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be $\sigma = 5000 \text { miles }$ You sample 100 tires and will test the hypothesis $H _ { 0 } : \mu = 50,000$
versus $H _ { 1 } : \mu

Question

A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be $\sigma = 5000 \text { miles }$ You sample 100 tires and will test the hypothesis $H _ { 0 } : \mu = 50,000$
versus $H _ { 1 } : \mu < 50,000$ You sample 100 tires and at the $\alpha = 0.05$ level of significance.
Find the power of the test against the alternative $\mu _ { 1 } = 49,000$

Quizplus · Accepted Answer

The power of the test is calculated using the formula for the power of a one-sample z-test. The z-score for the critical value is -1.645 (for a one-tailed test at $\alpha = 0.05$). The z-score for the alternative mean is calculated using $(\mu_1 - \mu_0) / (\sigma/\sqrt{n})$. The power is the probability that the test statistic falls below the critical value when $\mu = 49,000$, which is approximately 0.6406.

A Tire Company Claims That the Lifetimes of Its Tires σ=5000 miles \sigma = 5000 \text { miles }σ=5000 miles

A Tire Company Claims That the Lifetimes of Its Tires $\sigma = 5000 \text { miles }$