In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 km. The population standard deviation is known to be 37,500 km.
-How much evidence is there that the major engine failure will occur after 90,000 km?
A)No evidence
B)Some evidence
C)Strong evidence
D)Very strong evidence
E)Extremely strong evidence

Question

Quizplus · Accepted Answer

To determine the evidence that major engine failure will occur after 90,000 km, we can use a z-test for the mean. The z-score is calculated as $z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean (90,000 km in this case), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{96,700 - 90,000}{37,500/\sqrt{191}}$, we find that the z-score is significantly greater than 0, indicating that the mean distance before failure is significantly higher than 90,000 km. This provides very strong evidence against the null hypothesis that the mean distance before failure is 90,000 km or less.

In a Study of Distances Traveled by Buses Before the First