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.
-The appropriate test statistic to test the hypotheses is _____.
A)2.47
B)34.13
C)478.16
D)-34.13
E)-2.47

Question

Quizplus · Accepted Answer

The appropriate test statistic is calculated using the formula for a z-test, since the population standard deviation is known. The formula is $z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean (which would be hypothesized or known in some contexts, but is not explicitly given here, implying a test of the sample mean against a hypothesized or known value), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging the given values into the formula gives a z-value of approximately 2.47, indicating that choice A is correct.

In a Study of Distances Traveled by Buses Before the First