The average greyhound can reach a top speed of $18.8$ meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 50 of her dogs ran, on average, $19.2$ meters per second with a population standard deviation of $1.4$ meters per second. With $\alpha = 0.05$, is her claim correct?
A) Yes, because the test value 0.04 falls in the noncritical region.
B) No, because the test value 0.40 falls in the critical region.
C) No, because the test value 0.04 falls in the critical region.
D) Yes, because the test value 2.02 falls in the critical region.

Question

Quizplus · Accepted Answer

To determine if the breeder's dogs are significantly faster than the average greyhound, a one-sample z-test can be used. The test statistic is calculated using the formula $z = \frac{\bar{x} - \mu}{(\sigma / \sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{19.2 - 18.8}{(1.4 / \sqrt{50})} = 2.02$. A z-score of 2.02 falls in the critical region for a two-tailed test with $\alpha = 0.05$, indicating the breeder's claim is correct.

The Average Greyhound Can Reach a Top Speed Of 18.818.818.8 Meters Per Second

The Average Greyhound Can Reach a Top Speed Of $18.8$ Meters Per Second